Experiment 3 · romaji r1 · fresh
SOURCE: outputs/replication/reconstructed-exp3/runs/fe6d03b4a13a4379860a44b365e1f1ab
Recorded prompts and outputs are reproduced below without shortening. CLI reasoning entries are emitted summaries. Raw records preserve metadata, notices and original failed resume attempts.

RECORDED INSTRUCTION FILE
Answer the user's request.


========================================================================
TURN t001
MESSAGE SENT TO CODEX
Below is a small character-level language model: a 4-layer transformer with 6 attention heads per layer, which reads up to 128 characters and outputs scores (logits) for the next character. This is exactly how it computes (numpy):

```python
import numpy as np
VOCAB = "\n " + "abcdefghijklmnopqrstuvwxyz"   # index 0 = newline, 1 = space, 2..27 = a..z
HEADS, LAYERS = 6, 4

def layer_norm(x, w, b):                     # over the last axis, eps 1e-5
    mu = x.mean(-1, keepdims=True)
    var = ((x - mu) ** 2).mean(-1, keepdims=True)
    return (x - mu) / np.sqrt(var + 1e-5) * w + b

def next_char_logits(text, p):
    """text: up to 128 characters (only the last 128 are used); p: dict of the weight arrays.
    Returns the 28 logits for the character that comes next."""
    ids = [VOCAB.index(c) for c in text[-128:]]
    n, d = len(ids), p["tok_emb"].shape[1]
    hd = d // HEADS
    x = p["tok_emb"][ids] + p["pos_emb"][:n]                  # (n, d); positions 0..n-1 from the start of the text
    for l in range(LAYERS):                                    # layer l uses the tensors named <name>.<l>
        h = layer_norm(x, p[f"ln1_w.{l}"], p[f"ln1_b.{l}"])
        q, k, v = h @ p[f"W_q.{l}"].T, h @ p[f"W_k.{l}"].T, h @ p[f"W_v.{l}"].T
        out = np.zeros((n, d))
        for j in range(HEADS):                                 # head j uses dimensions j*hd .. (j+1)*hd - 1
            s = slice(j * hd, (j + 1) * hd)
            att = q[:, s] @ k[:, s].T / np.sqrt(hd)            # (n, n)
            att = att + np.triu(np.full((n, n), -np.inf), 1)   # causal: position i sees positions 0..i
            att = np.exp(att - att.max(-1, keepdims=True))
            att = att / att.sum(-1, keepdims=True)
            out[:, s] = att @ v[:, s]
        x = x + out @ p[f"W_o.{l}"].T
        h = layer_norm(x, p[f"ln2_w.{l}"], p[f"ln2_b.{l}"])
        x = x + np.maximum(0.0, h @ p[f"W_fc.{l}"].T) @ p[f"W_proj.{l}"].T   # ReLU MLP, hidden 4 d
    h = layer_norm(x, p["lnf_w"], p["lnf_b"])
    return h[-1] @ p["W_out"].T + p["b_out"]                   # logits of the next character (28)
```

Training: from random initialization (every matrix entry drawn from a normal distribution with standard deviation 0.02, or 0.007071 for W_o and W_proj; LayerNorm weights 1 and biases 0; b_out 0), next-character prediction with AdamW (30,517 steps of 256 random 128-character windows, 1,000,000,000 characters in total; learning-rate warm-up then cosine decay; weight decay 0.01 on the matrices).

The training text was ONE of these three corpora:
- python: Python source code (about 36,600 files of Python libraries, docstrings and comments removed; 320 million characters)
- romaji: Japanese literature (the Aozora Bunko collection, about 17,000 works) written in romaji (Latin letters, Hepburn-style romanization; 564 million characters)
- english: English text (English Wikipedia articles; 500 million characters)
and it was used EITHER as is OR with the characters of every line randomly shuffled (each line keeps its letters and its length, the order of the characters inside the line is random, the order of the lines is kept).
Normalization (the same for all three corpora, before anything else): lowercased; in each line the leading spaces (indentation) were kept, every other character that is not a letter a-z became a space, runs of spaces were collapsed to one and trailing spaces removed. So the text contains only newlines, spaces and the letters a-z (the 28 characters of VOCAB).

WHAT YOU CAN USE. The weights inside the four transformer blocks, exactly as trained (float32): for layer l = 0, 1, 2 and 3, ln1_w.l, ln1_b.l, W_q.l, W_k.l, W_v.l, W_o.l (attention) and ln2_w.l, ln2_b.l, W_fc.l, W_proj.l (MLP). The input layer (tok_emb, the 28 x d character embeddings, and pos_emb, the 128 x d position embeddings) and the output layer (lnf_w, lnf_b, W_out, b_out) are NOT available. The d = 384 dimensions of the residual stream carry no labels. Head j of layer l uses rows 64j .. 64j+63 of W_q.l, W_k.l and W_v.l and columns 64j .. 64j+63 of W_o.l.

You may use any computation on these weights, with any method you like: multiply them, decompose them, compare, cluster or fit them, write any analysis you want. Two things are NOT allowed:
1. A forward pass: do not run the network or any of its layers (LayerNorm, attention with its softmax, the MLP with its ReLU) on any input, whether real, random or constructed, in code, in your head or on paper. Treating the weight matrices as linear-algebra objects (products, eigenvalues, singular vectors, applying one weight matrix to directions taken from other weights) is fine; simulating what the network does to an input is not.
2. Search: do not look anything up (there is no internet access in any case).

HOW YOU COMPUTE. The weights are not written out here: you read them by running Python code. To run code, reply with exactly one code block that starts with ```python and ends with ```, and nothing else. We run it and reply with its printed output. Available: numpy, scipy, scikit-learn, PyTorch (CPU), pandas, sympy, networkx. Before your code runs, numpy is imported as np and W is a dict of the weight arrays by name: W['W_q.0'] is 384 x 384, W['W_fc.0'] is 1536 x 384, W['W_proj.0'] is 384 x 1536, W['ln1_w.0'] has 384 entries, and so on; matrices are (out, in), as used in the code above. There is nothing else to read (no other files, no network). Each run is a fresh process (nothing is kept between runs), may take up to 600 seconds, and its output is cut at 20,000 characters. You may run code up to 100 times. When you are done, reply WITHOUT a code block, with your final answer in the order given in the question.

QUESTION. What was this network trained on, and how does it use the context? Answer in this order:
Observations: <what you see in the shown weights and what it suggests; quote the weights you rely on>
Heads: <one line per head, L0H0 .. L0H5, L1H0 .. L1H5, L2H0 .. L2H5, L3H0 .. L3H5: what it most likely does, as one of: 'previous' (attends to the previous character), 'local' (a few characters back), 'broad' (spread far back), 'copy' (induction: attends to the character right after an earlier occurrence of the current character or context, so the network can repeat earlier text), or 'unclear'; then your evidence>
Reasoning: <which training text fits these observations, and why>
corpus: <python | romaji | english>
order: <as is | shuffled>
probabilities: python=<p> romaji=<p> english=<p>; as is=<p> shuffled=<p>
Equal probabilities are not allowed. Even if the evidence is weak, give your best judgement.
CLI OUTPUT IN EVENT ORDER
ERROR
Failed to read global AGENTS.md instructions from `<local-home>/.codex/AGENTS.md`: Operation not permitted (os error 1)

ERROR
Code Mode is unavailable because code-mode host is disabled. Code mode will fail closed; enable `features.code_mode_host` and install `codex-code-mode-host`.

AGENT_MESSAGE
```python
import numpy as np
from scipy.linalg import svdvals
from threadpoolctl import threadpool_limits

def stats(a):
    a = np.asarray(a, dtype=np.float64)
    return "mean=%.4g sd=%.4g min=%.4g max=%.4g norm=%.4g" % (
        a.mean(), a.std(), a.min(), a.max(), np.linalg.norm(a))

def erank(s):
    p = s*s / np.sum(s*s)
    return np.exp(-np.sum(p*np.log(p+1e-300)))

with threadpool_limits(limits=2):
    print("Available:", sorted(W))
    for l in range(4):
        print("\nLAYER", l)
        for name in ["ln1_w", "ln1_b", "ln2_w", "ln2_b",
                     "W_q", "W_k", "W_v", "W_o", "W_fc", "W_proj"]:
            print(name, W[f"{name}.{l}"].shape, stats(W[f"{name}.{l}"]))
        g = np.asarray(W[f"ln1_w.{l}"], dtype=np.float64)
        b = np.asarray(W[f"ln1_b.{l}"], dtype=np.float64)
        for j in range(6):
            s = slice(64*j, 64*(j+1))
            q = np.asarray(W[f"W_q.{l}"][s], dtype=np.float64)
            k = np.asarray(W[f"W_k.{l}"][s], dtype=np.float64)
            v = np.asarray(W[f"W_v.{l}"][s], dtype=np.float64)
            o = np.asarray(W[f"W_o.{l}"][:,s], dtype=np.float64)
            qg, kg, vg = q*g, k*g, v*g
            qg -= qg.mean(axis=1, keepdims=True)
            kg -= kg.mean(axis=1, keepdims=True)
            vg -= vg.mean(axis=1, keepdims=True)
            A = qg.T @ kg / 8
            B = o @ vg
            sa, sb = svdvals(A)[:64], svdvals(B)[:64]
            na, nb = np.linalg.norm(A), np.linalg.norm(B)
            print(
                "L%dH%d QK: norm=%.3f top=%.3f erank=%.1f trace/norm=%.3f symmetry=%.3f;"
                " OV: norm=%.3f top=%.3f erank=%.1f trace/norm=%.3f;"
                " LN-bias key-vector=%.3f query-vector=%.3f"
                % (l,j,na,sa[0],erank(sa),np.trace(A)/na,
                   np.sum(A*A.T)/(na*na),
                   nb,sb[0],erank(sb),np.trace(B)/nb,
                   np.linalg.norm(kg.T@(q@b)/8),
                   np.linalg.norm(qg.T@(k@b)/8))
            )
```


PERMITTED EXPERIMENT HARNESS RECORD: python
{
  "run": 1,
  "turn": "t001",
  "code": "import numpy as np\nfrom scipy.linalg import svdvals\nfrom threadpoolctl import threadpool_limits\n\ndef stats(a):\n    a = np.asarray(a, dtype=np.float64)\n    return \"mean=%.4g sd=%.4g min=%.4g max=%.4g norm=%.4g\" % (\n        a.mean(), a.std(), a.min(), a.max(), np.linalg.norm(a))\n\ndef erank(s):\n    p = s*s / np.sum(s*s)\n    return np.exp(-np.sum(p*np.log(p+1e-300)))\n\nwith threadpool_limits(limits=2):\n    print(\"Available:\", sorted(W))\n    for l in range(4):\n        print(\"\\nLAYER\", l)\n        for name in [\"ln1_w\", \"ln1_b\", \"ln2_w\", \"ln2_b\",\n                     \"W_q\", \"W_k\", \"W_v\", \"W_o\", \"W_fc\", \"W_proj\"]:\n            print(name, W[f\"{name}.{l}\"].shape, stats(W[f\"{name}.{l}\"]))\n        g = np.asarray(W[f\"ln1_w.{l}\"], dtype=np.float64)\n        b = np.asarray(W[f\"ln1_b.{l}\"], dtype=np.float64)\n        for j in range(6):\n            s = slice(64*j, 64*(j+1))\n            q = np.asarray(W[f\"W_q.{l}\"][s], dtype=np.float64)\n            k = np.asarray(W[f\"W_k.{l}\"][s], dtype=np.float64)\n            v = np.asarray(W[f\"W_v.{l}\"][s], dtype=np.float64)\n            o = np.asarray(W[f\"W_o.{l}\"][:,s], dtype=np.float64)\n            qg, kg, vg = q*g, k*g, v*g\n            qg -= qg.mean(axis=1, keepdims=True)\n            kg -= kg.mean(axis=1, keepdims=True)\n            vg -= vg.mean(axis=1, keepdims=True)\n            A = qg.T @ kg / 8\n            B = o @ vg\n            sa, sb = svdvals(A)[:64], svdvals(B)[:64]\n            na, nb = np.linalg.norm(A), np.linalg.norm(B)\n            print(\n                \"L%dH%d QK: norm=%.3f top=%.3f erank=%.1f trace/norm=%.3f symmetry=%.3f;\"\n                \" OV: norm=%.3f top=%.3f erank=%.1f trace/norm=%.3f;\"\n                \" LN-bias key-vector=%.3f query-vector=%.3f\"\n                % (l,j,na,sa[0],erank(sa),np.trace(A)/na,\n                   np.sum(A*A.T)/(na*na),\n                   nb,sb[0],erank(sb),np.trace(B)/nb,\n                   np.linalg.norm(kg.T@(q@b)/8),\n                   np.linalg.norm(qg.T@(k@b)/8))\n            )",
  "out": "Available: ['W_fc.0', 'W_fc.1', 'W_fc.2', 'W_fc.3', 'W_k.0', 'W_k.1', 'W_k.2', 'W_k.3', 'W_o.0', 'W_o.1', 'W_o.2', 'W_o.3', 'W_proj.0', 'W_proj.1', 'W_proj.2', 'W_proj.3', 'W_q.0', 'W_q.1', 'W_q.2', 'W_q.3', 'W_v.0', 'W_v.1', 'W_v.2', 'W_v.3', 'ln1_b.0', 'ln1_b.1', 'ln1_b.2', 'ln1_b.3', 'ln1_w.0', 'ln1_w.1', 'ln1_w.2', 'ln1_w.3', 'ln2_b.0', 'ln2_b.1', 'ln2_b.2', 'ln2_b.3', 'ln2_w.0', 'ln2_w.1', 'ln2_w.2', 'ln2_w.3']\n\nLAYER 0\nln1_w (384,) mean=0.2965 sd=0.1884 min=0.03522 max=0.9785 norm=6.884\nln1_b (384,) mean=0.0003872 sd=0.03113 min=-0.09542 max=0.09061 norm=0.6101\nln2_w (384,) mean=0.8718 sd=0.3382 min=0.04203 max=1.775 norm=18.32\nln2_b (384,) mean=0.0134 sd=0.06913 min=-0.6236 max=0.4636 norm=1.38\nW_q (384, 384) mean=5.472e-05 sd=0.04601 min=-0.4639 max=0.4214 norm=17.67\nW_k (384, 384) mean=6.684e-06 sd=0.04822 min=-0.5163 max=0.5037 norm=18.52\nW_v (384, 384) mean=1.748e-05 sd=0.0389 min=-0.3922 max=0.3895 norm=14.94\nW_o (384, 384) mean=-0.0001201 sd=0.0431 min=-1.124 max=1.082 norm=16.55\nW_fc (1536, 384) mean=0.0007535 sd=0.0721 min=-0.8384 max=1.123 norm=55.38\nW_proj (384, 1536) mean=-9.916e-07 sd=0.06511 min=-0.6883 max=1.464 norm=50.01\nL0H0 QK: norm=0.293 top=0.248 erank=3.5 trace/norm=-0.357 symmetry=0.141; OV: norm=2.126 top=0.957 erank=12.4 trace/norm=-0.067; LN-bias key-vector=0.043 query-vector=0.106\nL0H1 QK: norm=0.159 top=0.150 erank=1.6 trace/norm=-0.619 symmetry=0.161; OV: norm=3.979 top=3.380 erank=2.0 trace/norm=0.231; LN-bias key-vector=0.013 query-vector=0.027\nL0H2 QK: norm=0.107 top=0.102 erank=1.7 trace/norm=-0.813 symmetry=0.289; OV: norm=3.033 top=2.643 erank=2.1 trace/norm=0.229; LN-bias key-vector=0.007 query-vector=0.033\nL0H3 QK: norm=0.698 top=0.244 erank=22.1 trace/norm=1.923 symmetry=-0.067; OV: norm=3.533 top=1.126 erank=24.8 trace/norm=-0.571; LN-bias key-vector=0.043 query-vector=0.052\nL0H4 QK: norm=0.088 top=0.080 erank=2.5 trace/norm=-0.519 symmetry=0.050; OV: norm=1.684 top=1.454 erank=2.5 trace/norm=0.103; LN-bias key-vector=0.017 query-vector=0.069\nL0H5 QK: norm=0.034 top=0.032 erank=1.9 trace/norm=-0.253 symmetry=0.024; OV: norm=18.812 top=16.278 erank=2.0 trace/norm=0.111; LN-bias key-vector=0.005 query-vector=0.015\n\nLAYER 1\nln1_w (384,) mean=0.5058 sd=0.08918 min=0.197 max=1.085 norm=10.07\nln1_b (384,) mean=0.01103 sd=0.1546 min=-1.568 max=1.365 norm=3.037\nln2_w (384,) mean=1.131 sd=0.1741 min=0.001865 max=1.52 norm=22.43\nln2_b (384,) mean=0.006468 sd=0.1435 min=-0.3892 max=0.417 norm=2.815\nW_q (384, 384) mean=-0.0002709 sd=0.1014 min=-0.441 max=0.4642 norm=38.93\nW_k (384, 384) mean=5.424e-05 sd=0.09087 min=-1.087 max=1.276 norm=34.89\nW_v (384, 384) mean=2.812e-05 sd=0.07486 min=-0.3539 max=0.3314 norm=28.74\nW_o (384, 384) mean=1.889e-05 sd=0.07416 min=-0.4175 max=0.455 norm=28.48\nW_fc (1536, 384) mean=0.001389 sd=0.1047 min=-0.6542 max=0.645 norm=80.38\nW_proj (384, 1536) mean=-8.241e-05 sd=0.1008 min=-0.5072 max=2.66 norm=77.38\nL1H0 QK: norm=1.978 top=1.185 erank=10.4 trace/norm=-0.884 symmetry=0.042; OV: norm=11.479 top=3.189 erank=29.8 trace/norm=-1.346; LN-bias key-vector=3.975 query-vector=2.959\nL1H1 QK: norm=1.843 top=1.154 erank=9.2 trace/norm=-0.845 symmetry=0.018; OV: norm=11.264 top=3.147 erank=26.6 trace/norm=-1.351; LN-bias key-vector=3.689 query-vector=2.802\nL1H2 QK: norm=1.781 top=1.176 erank=9.0 trace/norm=-1.060 symmetry=0.037; OV: norm=11.807 top=3.550 erank=25.4 trace/norm=-1.467; LN-bias key-vector=3.051 query-vector=2.509\nL1H3 QK: norm=1.787 top=1.187 erank=8.5 trace/norm=-0.846 symmetry=0.005; OV: norm=12.398 top=3.408 erank=26.7 trace/norm=-1.482; LN-bias key-vector=3.390 query-vector=2.624\nL1H4 QK: norm=1.629 top=1.059 erank=10.0 trace/norm=-1.234 symmetry=0.047; OV: norm=13.399 top=4.132 erank=26.4 trace/norm=-1.429; LN-bias key-vector=2.329 query-vector=2.031\nL1H5 QK: norm=1.863 top=1.146 erank=9.5 trace/norm=-0.875 symmetry=0.017; OV: norm=10.917 top=3.083 erank=26.4 trace/norm=-1.370; LN-bias key-vector=3.895 query-vector=2.825\n\nLAYER 2\nln1_w (384,) mean=0.6809 sd=0.06874 min=0.3175 max=1.093 norm=13.41\nln1_b (384,) mean=0.01305 sd=0.1565 min=-1.659 max=1.332 norm=3.077\nln2_w (384,) mean=1.31 sd=0.1148 min=0.01202 max=1.508 norm=25.78\nln2_b (384,) mean=0.01229 sd=0.1737 min=-0.517 max=0.4489 norm=3.413\nW_q (384, 384) mean=8.331e-05 sd=0.1013 min=-0.4865 max=0.4916 norm=38.9\nW_k (384, 384) mean=1.482e-05 sd=0.0957 min=-1.224 max=1.194 norm=36.75\nW_v (384, 384) mean=-3.459e-05 sd=0.08641 min=-0.4009 max=0.3919 norm=33.18\nW_o (384, 384) mean=-4.614e-06 sd=0.08446 min=-0.5312 max=0.5185 norm=32.43\nW_fc (1536, 384) mean=0.0003871 sd=0.1039 min=-0.5244 max=0.5953 norm=79.83\nW_proj (384, 1536) mean=-7.138e-05 sd=0.1016 min=-0.5107 max=0.8014 norm=78.05\nL2H0 QK: norm=1.631 top=0.689 erank=31.3 trace/norm=-0.953 symmetry=-0.040; OV: norm=16.379 top=5.289 erank=35.9 trace/norm=-1.028; LN-bias key-vector=2.020 query-vector=1.805\nL2H1 QK: norm=2.154 top=0.578 erank=40.5 trace/norm=-0.100 symmetry=-0.021; OV: norm=17.616 top=4.136 erank=44.6 trace/norm=-1.996; LN-bias key-vector=1.880 query-vector=1.629\nL2H2 QK: norm=1.720 top=0.518 erank=42.4 trace/norm=-0.754 symmetry=-0.004; OV: norm=18.662 top=5.045 erank=39.3 trace/norm=-1.604; LN-bias key-vector=1.608 query-vector=1.411\nL2H3 QK: norm=1.623 top=0.502 erank=42.2 trace/norm=-0.367 symmetry=-0.008; OV: norm=18.996 top=4.832 erank=41.7 trace/norm=-1.590; LN-bias key-vector=1.060 query-vector=0.840\nL2H4 QK: norm=2.215 top=0.813 erank=35.3 trace/norm=-0.442 symmetry=-0.032; OV: norm=14.875 top=3.533 erank=42.1 trace/norm=-2.103; LN-bias key-vector=2.305 query-vector=1.969\nL2H5 QK: norm=2.264 top=0.615 erank=39.4 trace/norm=-0.118 symmetry=-0.024; OV: norm=16.858 top=3.735 erank=45.4 trace/norm=-2.058; LN-bias key-vector=2.023 query-vector=1.738\n\nLAYER 3\nln1_w (384,) mean=0.7087 sd=0.04941 min=0.4078 max=0.8155 norm=13.92\nln1_b (384,) mean=0.02963 sd=0.09939 min=-0.7639 max=0.8241 norm=2.032\nln2_w (384,) mean=1.267 sd=0.08945 min=0.2328 max=1.453 norm=24.89\nln2_b (384,) mean=0.0128 sd=0.1413 min=-0.5402 max=0.3932 norm=2.78\nW_q (384, 384) mean=-8.166e-05 sd=0.08656 min=-0.3908 max=0.4595 norm=33.24\nW_k (384, 384) mean=-2.536e-05 sd=0.08454 min=-0.9139 max=0.9735 norm=32.46\nW_v (384, 384) mean=4.308e-05 sd=0.1027 min=-0.508 max=0.5939 norm=39.42\nW_o (384, 384) mean=9.028e-06 sd=0.1045 min=-1.517 max=1.527 norm=40.13\nW_fc (1536, 384) mean=0.0002521 sd=0.1019 min=-0.4902 max=0.55 norm=78.26\nW_proj (384, 1536) mean=0.0002828 sd=0.1108 min=-1.058 max=1.477 norm=85.12\nL3H0 QK: norm=2.029 top=0.435 erank=51.5 trace/norm=1.073 symmetry=0.006; OV: norm=20.711 top=5.784 erank=41.2 trace/norm=-2.223; LN-bias key-vector=0.500 query-vector=0.446\nL3H1 QK: norm=1.216 top=0.345 erank=45.8 trace/norm=0.355 symmetry=-0.002; OV: norm=26.504 top=8.230 erank=33.4 trace/norm=-1.586; LN-bias key-vector=0.280 query-vector=0.306\nL3H2 QK: norm=1.437 top=0.383 erank=50.0 trace/norm=0.243 symmetry=-0.010; OV: norm=23.504 top=7.460 erank=38.3 trace/norm=-1.593; LN-bias key-vector=0.495 query-vector=0.338\nL3H3 QK: norm=1.815 top=0.322 erank=57.8 trace/norm=3.212 symmetry=0.210; OV: norm=37.524 top=10.809 erank=30.0 trace/norm=-1.210; LN-bias key-vector=0.220 query-vector=0.179\nL3H4 QK: norm=0.622 top=0.236 erank=33.1 trace/norm=0.003 symmetry=0.001; OV: norm=49.234 top=21.266 erank=14.3 trace/norm=-0.794; LN-bias key-vector=0.144 query-vector=0.113\nL3H5 QK: norm=1.665 top=0.454 erank=51.3 trace/norm=0.863 symmetry=0.009; OV: norm=22.563 top=6.302 erank=40.0 trace/norm=-1.534; LN-bias key-vector=0.493 query-vector=0.422\n",
  "seconds": 0.898,
  "rc": 0,
  "timed_out": false,
  "truncated": false,
  "code_sha256": "fd52eeaf6e709635bb34b54539ed77675c810ce0162c1fb585f00a4361b3264a",
  "weights_sha256": "04ec0b300d207b26b92a1af6d49d56d452833e39b35826200bc1d821e5b7d930"
}

EXACT HARNESS FEEDBACK
Available: ['W_fc.0', 'W_fc.1', 'W_fc.2', 'W_fc.3', 'W_k.0', 'W_k.1', 'W_k.2', 'W_k.3', 'W_o.0', 'W_o.1', 'W_o.2', 'W_o.3', 'W_proj.0', 'W_proj.1', 'W_proj.2', 'W_proj.3', 'W_q.0', 'W_q.1', 'W_q.2', 'W_q.3', 'W_v.0', 'W_v.1', 'W_v.2', 'W_v.3', 'ln1_b.0', 'ln1_b.1', 'ln1_b.2', 'ln1_b.3', 'ln1_w.0', 'ln1_w.1', 'ln1_w.2', 'ln1_w.3', 'ln2_b.0', 'ln2_b.1', 'ln2_b.2', 'ln2_b.3', 'ln2_w.0', 'ln2_w.1', 'ln2_w.2', 'ln2_w.3']

LAYER 0
ln1_w (384,) mean=0.2965 sd=0.1884 min=0.03522 max=0.9785 norm=6.884
ln1_b (384,) mean=0.0003872 sd=0.03113 min=-0.09542 max=0.09061 norm=0.6101
ln2_w (384,) mean=0.8718 sd=0.3382 min=0.04203 max=1.775 norm=18.32
ln2_b (384,) mean=0.0134 sd=0.06913 min=-0.6236 max=0.4636 norm=1.38
W_q (384, 384) mean=5.472e-05 sd=0.04601 min=-0.4639 max=0.4214 norm=17.67
W_k (384, 384) mean=6.684e-06 sd=0.04822 min=-0.5163 max=0.5037 norm=18.52
W_v (384, 384) mean=1.748e-05 sd=0.0389 min=-0.3922 max=0.3895 norm=14.94
W_o (384, 384) mean=-0.0001201 sd=0.0431 min=-1.124 max=1.082 norm=16.55
W_fc (1536, 384) mean=0.0007535 sd=0.0721 min=-0.8384 max=1.123 norm=55.38
W_proj (384, 1536) mean=-9.916e-07 sd=0.06511 min=-0.6883 max=1.464 norm=50.01
L0H0 QK: norm=0.293 top=0.248 erank=3.5 trace/norm=-0.357 symmetry=0.141; OV: norm=2.126 top=0.957 erank=12.4 trace/norm=-0.067; LN-bias key-vector=0.043 query-vector=0.106
L0H1 QK: norm=0.159 top=0.150 erank=1.6 trace/norm=-0.619 symmetry=0.161; OV: norm=3.979 top=3.380 erank=2.0 trace/norm=0.231; LN-bias key-vector=0.013 query-vector=0.027
L0H2 QK: norm=0.107 top=0.102 erank=1.7 trace/norm=-0.813 symmetry=0.289; OV: norm=3.033 top=2.643 erank=2.1 trace/norm=0.229; LN-bias key-vector=0.007 query-vector=0.033
L0H3 QK: norm=0.698 top=0.244 erank=22.1 trace/norm=1.923 symmetry=-0.067; OV: norm=3.533 top=1.126 erank=24.8 trace/norm=-0.571; LN-bias key-vector=0.043 query-vector=0.052
L0H4 QK: norm=0.088 top=0.080 erank=2.5 trace/norm=-0.519 symmetry=0.050; OV: norm=1.684 top=1.454 erank=2.5 trace/norm=0.103; LN-bias key-vector=0.017 query-vector=0.069
L0H5 QK: norm=0.034 top=0.032 erank=1.9 trace/norm=-0.253 symmetry=0.024; OV: norm=18.812 top=16.278 erank=2.0 trace/norm=0.111; LN-bias key-vector=0.005 query-vector=0.015

LAYER 1
ln1_w (384,) mean=0.5058 sd=0.08918 min=0.197 max=1.085 norm=10.07
ln1_b (384,) mean=0.01103 sd=0.1546 min=-1.568 max=1.365 norm=3.037
ln2_w (384,) mean=1.131 sd=0.1741 min=0.001865 max=1.52 norm=22.43
ln2_b (384,) mean=0.006468 sd=0.1435 min=-0.3892 max=0.417 norm=2.815
W_q (384, 384) mean=-0.0002709 sd=0.1014 min=-0.441 max=0.4642 norm=38.93
W_k (384, 384) mean=5.424e-05 sd=0.09087 min=-1.087 max=1.276 norm=34.89
W_v (384, 384) mean=2.812e-05 sd=0.07486 min=-0.3539 max=0.3314 norm=28.74
W_o (384, 384) mean=1.889e-05 sd=0.07416 min=-0.4175 max=0.455 norm=28.48
W_fc (1536, 384) mean=0.001389 sd=0.1047 min=-0.6542 max=0.645 norm=80.38
W_proj (384, 1536) mean=-8.241e-05 sd=0.1008 min=-0.5072 max=2.66 norm=77.38
L1H0 QK: norm=1.978 top=1.185 erank=10.4 trace/norm=-0.884 symmetry=0.042; OV: norm=11.479 top=3.189 erank=29.8 trace/norm=-1.346; LN-bias key-vector=3.975 query-vector=2.959
L1H1 QK: norm=1.843 top=1.154 erank=9.2 trace/norm=-0.845 symmetry=0.018; OV: norm=11.264 top=3.147 erank=26.6 trace/norm=-1.351; LN-bias key-vector=3.689 query-vector=2.802
L1H2 QK: norm=1.781 top=1.176 erank=9.0 trace/norm=-1.060 symmetry=0.037; OV: norm=11.807 top=3.550 erank=25.4 trace/norm=-1.467; LN-bias key-vector=3.051 query-vector=2.509
L1H3 QK: norm=1.787 top=1.187 erank=8.5 trace/norm=-0.846 symmetry=0.005; OV: norm=12.398 top=3.408 erank=26.7 trace/norm=-1.482; LN-bias key-vector=3.390 query-vector=2.624
L1H4 QK: norm=1.629 top=1.059 erank=10.0 trace/norm=-1.234 symmetry=0.047; OV: norm=13.399 top=4.132 erank=26.4 trace/norm=-1.429; LN-bias key-vector=2.329 query-vector=2.031
L1H5 QK: norm=1.863 top=1.146 erank=9.5 trace/norm=-0.875 symmetry=0.017; OV: norm=10.917 top=3.083 erank=26.4 trace/norm=-1.370; LN-bias key-vector=3.895 query-vector=2.825

LAYER 2
ln1_w (384,) mean=0.6809 sd=0.06874 min=0.3175 max=1.093 norm=13.41
ln1_b (384,) mean=0.01305 sd=0.1565 min=-1.659 max=1.332 norm=3.077
ln2_w (384,) mean=1.31 sd=0.1148 min=0.01202 max=1.508 norm=25.78
ln2_b (384,) mean=0.01229 sd=0.1737 min=-0.517 max=0.4489 norm=3.413
W_q (384, 384) mean=8.331e-05 sd=0.1013 min=-0.4865 max=0.4916 norm=38.9
W_k (384, 384) mean=1.482e-05 sd=0.0957 min=-1.224 max=1.194 norm=36.75
W_v (384, 384) mean=-3.459e-05 sd=0.08641 min=-0.4009 max=0.3919 norm=33.18
W_o (384, 384) mean=-4.614e-06 sd=0.08446 min=-0.5312 max=0.5185 norm=32.43
W_fc (1536, 384) mean=0.0003871 sd=0.1039 min=-0.5244 max=0.5953 norm=79.83
W_proj (384, 1536) mean=-7.138e-05 sd=0.1016 min=-0.5107 max=0.8014 norm=78.05
L2H0 QK: norm=1.631 top=0.689 erank=31.3 trace/norm=-0.953 symmetry=-0.040; OV: norm=16.379 top=5.289 erank=35.9 trace/norm=-1.028; LN-bias key-vector=2.020 query-vector=1.805
L2H1 QK: norm=2.154 top=0.578 erank=40.5 trace/norm=-0.100 symmetry=-0.021; OV: norm=17.616 top=4.136 erank=44.6 trace/norm=-1.996; LN-bias key-vector=1.880 query-vector=1.629
L2H2 QK: norm=1.720 top=0.518 erank=42.4 trace/norm=-0.754 symmetry=-0.004; OV: norm=18.662 top=5.045 erank=39.3 trace/norm=-1.604; LN-bias key-vector=1.608 query-vector=1.411
L2H3 QK: norm=1.623 top=0.502 erank=42.2 trace/norm=-0.367 symmetry=-0.008; OV: norm=18.996 top=4.832 erank=41.7 trace/norm=-1.590; LN-bias key-vector=1.060 query-vector=0.840
L2H4 QK: norm=2.215 top=0.813 erank=35.3 trace/norm=-0.442 symmetry=-0.032; OV: norm=14.875 top=3.533 erank=42.1 trace/norm=-2.103; LN-bias key-vector=2.305 query-vector=1.969
L2H5 QK: norm=2.264 top=0.615 erank=39.4 trace/norm=-0.118 symmetry=-0.024; OV: norm=16.858 top=3.735 erank=45.4 trace/norm=-2.058; LN-bias key-vector=2.023 query-vector=1.738

LAYER 3
ln1_w (384,) mean=0.7087 sd=0.04941 min=0.4078 max=0.8155 norm=13.92
ln1_b (384,) mean=0.02963 sd=0.09939 min=-0.7639 max=0.8241 norm=2.032
ln2_w (384,) mean=1.267 sd=0.08945 min=0.2328 max=1.453 norm=24.89
ln2_b (384,) mean=0.0128 sd=0.1413 min=-0.5402 max=0.3932 norm=2.78
W_q (384, 384) mean=-8.166e-05 sd=0.08656 min=-0.3908 max=0.4595 norm=33.24
W_k (384, 384) mean=-2.536e-05 sd=0.08454 min=-0.9139 max=0.9735 norm=32.46
W_v (384, 384) mean=4.308e-05 sd=0.1027 min=-0.508 max=0.5939 norm=39.42
W_o (384, 384) mean=9.028e-06 sd=0.1045 min=-1.517 max=1.527 norm=40.13
W_fc (1536, 384) mean=0.0002521 sd=0.1019 min=-0.4902 max=0.55 norm=78.26
W_proj (384, 1536) mean=0.0002828 sd=0.1108 min=-1.058 max=1.477 norm=85.12
L3H0 QK: norm=2.029 top=0.435 erank=51.5 trace/norm=1.073 symmetry=0.006; OV: norm=20.711 top=5.784 erank=41.2 trace/norm=-2.223; LN-bias key-vector=0.500 query-vector=0.446
L3H1 QK: norm=1.216 top=0.345 erank=45.8 trace/norm=0.355 symmetry=-0.002; OV: norm=26.504 top=8.230 erank=33.4 trace/norm=-1.586; LN-bias key-vector=0.280 query-vector=0.306
L3H2 QK: norm=1.437 top=0.383 erank=50.0 trace/norm=0.243 symmetry=-0.010; OV: norm=23.504 top=7.460 erank=38.3 trace/norm=-1.593; LN-bias key-vector=0.495 query-vector=0.338
L3H3 QK: norm=1.815 top=0.322 erank=57.8 trace/norm=3.212 symmetry=0.210; OV: norm=37.524 top=10.809 erank=30.0 trace/norm=-1.210; LN-bias key-vector=0.220 query-vector=0.179
L3H4 QK: norm=0.622 top=0.236 erank=33.1 trace/norm=0.003 symmetry=0.001; OV: norm=49.234 top=21.266 erank=14.3 trace/norm=-0.794; LN-bias key-vector=0.144 query-vector=0.113
L3H5 QK: norm=1.665 top=0.454 erank=51.3 trace/norm=0.863 symmetry=0.009; OV: norm=22.563 top=6.302 erank=40.0 trace/norm=-1.534; LN-bias key-vector=0.493 query-vector=0.422


========================================================================
TURN t002
MESSAGE SENT TO CODEX
OUTPUT of run 1 of at most 100:
```
Available: ['W_fc.0', 'W_fc.1', 'W_fc.2', 'W_fc.3', 'W_k.0', 'W_k.1', 'W_k.2', 'W_k.3', 'W_o.0', 'W_o.1', 'W_o.2', 'W_o.3', 'W_proj.0', 'W_proj.1', 'W_proj.2', 'W_proj.3', 'W_q.0', 'W_q.1', 'W_q.2', 'W_q.3', 'W_v.0', 'W_v.1', 'W_v.2', 'W_v.3', 'ln1_b.0', 'ln1_b.1', 'ln1_b.2', 'ln1_b.3', 'ln1_w.0', 'ln1_w.1', 'ln1_w.2', 'ln1_w.3', 'ln2_b.0', 'ln2_b.1', 'ln2_b.2', 'ln2_b.3', 'ln2_w.0', 'ln2_w.1', 'ln2_w.2', 'ln2_w.3']

LAYER 0
ln1_w (384,) mean=0.2965 sd=0.1884 min=0.03522 max=0.9785 norm=6.884
ln1_b (384,) mean=0.0003872 sd=0.03113 min=-0.09542 max=0.09061 norm=0.6101
ln2_w (384,) mean=0.8718 sd=0.3382 min=0.04203 max=1.775 norm=18.32
ln2_b (384,) mean=0.0134 sd=0.06913 min=-0.6236 max=0.4636 norm=1.38
W_q (384, 384) mean=5.472e-05 sd=0.04601 min=-0.4639 max=0.4214 norm=17.67
W_k (384, 384) mean=6.684e-06 sd=0.04822 min=-0.5163 max=0.5037 norm=18.52
W_v (384, 384) mean=1.748e-05 sd=0.0389 min=-0.3922 max=0.3895 norm=14.94
W_o (384, 384) mean=-0.0001201 sd=0.0431 min=-1.124 max=1.082 norm=16.55
W_fc (1536, 384) mean=0.0007535 sd=0.0721 min=-0.8384 max=1.123 norm=55.38
W_proj (384, 1536) mean=-9.916e-07 sd=0.06511 min=-0.6883 max=1.464 norm=50.01
L0H0 QK: norm=0.293 top=0.248 erank=3.5 trace/norm=-0.357 symmetry=0.141; OV: norm=2.126 top=0.957 erank=12.4 trace/norm=-0.067; LN-bias key-vector=0.043 query-vector=0.106
L0H1 QK: norm=0.159 top=0.150 erank=1.6 trace/norm=-0.619 symmetry=0.161; OV: norm=3.979 top=3.380 erank=2.0 trace/norm=0.231; LN-bias key-vector=0.013 query-vector=0.027
L0H2 QK: norm=0.107 top=0.102 erank=1.7 trace/norm=-0.813 symmetry=0.289; OV: norm=3.033 top=2.643 erank=2.1 trace/norm=0.229; LN-bias key-vector=0.007 query-vector=0.033
L0H3 QK: norm=0.698 top=0.244 erank=22.1 trace/norm=1.923 symmetry=-0.067; OV: norm=3.533 top=1.126 erank=24.8 trace/norm=-0.571; LN-bias key-vector=0.043 query-vector=0.052
L0H4 QK: norm=0.088 top=0.080 erank=2.5 trace/norm=-0.519 symmetry=0.050; OV: norm=1.684 top=1.454 erank=2.5 trace/norm=0.103; LN-bias key-vector=0.017 query-vector=0.069
L0H5 QK: norm=0.034 top=0.032 erank=1.9 trace/norm=-0.253 symmetry=0.024; OV: norm=18.812 top=16.278 erank=2.0 trace/norm=0.111; LN-bias key-vector=0.005 query-vector=0.015

LAYER 1
ln1_w (384,) mean=0.5058 sd=0.08918 min=0.197 max=1.085 norm=10.07
ln1_b (384,) mean=0.01103 sd=0.1546 min=-1.568 max=1.365 norm=3.037
ln2_w (384,) mean=1.131 sd=0.1741 min=0.001865 max=1.52 norm=22.43
ln2_b (384,) mean=0.006468 sd=0.1435 min=-0.3892 max=0.417 norm=2.815
W_q (384, 384) mean=-0.0002709 sd=0.1014 min=-0.441 max=0.4642 norm=38.93
W_k (384, 384) mean=5.424e-05 sd=0.09087 min=-1.087 max=1.276 norm=34.89
W_v (384, 384) mean=2.812e-05 sd=0.07486 min=-0.3539 max=0.3314 norm=28.74
W_o (384, 384) mean=1.889e-05 sd=0.07416 min=-0.4175 max=0.455 norm=28.48
W_fc (1536, 384) mean=0.001389 sd=0.1047 min=-0.6542 max=0.645 norm=80.38
W_proj (384, 1536) mean=-8.241e-05 sd=0.1008 min=-0.5072 max=2.66 norm=77.38
L1H0 QK: norm=1.978 top=1.185 erank=10.4 trace/norm=-0.884 symmetry=0.042; OV: norm=11.479 top=3.189 erank=29.8 trace/norm=-1.346; LN-bias key-vector=3.975 query-vector=2.959
L1H1 QK: norm=1.843 top=1.154 erank=9.2 trace/norm=-0.845 symmetry=0.018; OV: norm=11.264 top=3.147 erank=26.6 trace/norm=-1.351; LN-bias key-vector=3.689 query-vector=2.802
L1H2 QK: norm=1.781 top=1.176 erank=9.0 trace/norm=-1.060 symmetry=0.037; OV: norm=11.807 top=3.550 erank=25.4 trace/norm=-1.467; LN-bias key-vector=3.051 query-vector=2.509
L1H3 QK: norm=1.787 top=1.187 erank=8.5 trace/norm=-0.846 symmetry=0.005; OV: norm=12.398 top=3.408 erank=26.7 trace/norm=-1.482; LN-bias key-vector=3.390 query-vector=2.624
L1H4 QK: norm=1.629 top=1.059 erank=10.0 trace/norm=-1.234 symmetry=0.047; OV: norm=13.399 top=4.132 erank=26.4 trace/norm=-1.429; LN-bias key-vector=2.329 query-vector=2.031
L1H5 QK: norm=1.863 top=1.146 erank=9.5 trace/norm=-0.875 symmetry=0.017; OV: norm=10.917 top=3.083 erank=26.4 trace/norm=-1.370; LN-bias key-vector=3.895 query-vector=2.825

LAYER 2
ln1_w (384,) mean=0.6809 sd=0.06874 min=0.3175 max=1.093 norm=13.41
ln1_b (384,) mean=0.01305 sd=0.1565 min=-1.659 max=1.332 norm=3.077
ln2_w (384,) mean=1.31 sd=0.1148 min=0.01202 max=1.508 norm=25.78
ln2_b (384,) mean=0.01229 sd=0.1737 min=-0.517 max=0.4489 norm=3.413
W_q (384, 384) mean=8.331e-05 sd=0.1013 min=-0.4865 max=0.4916 norm=38.9
W_k (384, 384) mean=1.482e-05 sd=0.0957 min=-1.224 max=1.194 norm=36.75
W_v (384, 384) mean=-3.459e-05 sd=0.08641 min=-0.4009 max=0.3919 norm=33.18
W_o (384, 384) mean=-4.614e-06 sd=0.08446 min=-0.5312 max=0.5185 norm=32.43
W_fc (1536, 384) mean=0.0003871 sd=0.1039 min=-0.5244 max=0.5953 norm=79.83
W_proj (384, 1536) mean=-7.138e-05 sd=0.1016 min=-0.5107 max=0.8014 norm=78.05
L2H0 QK: norm=1.631 top=0.689 erank=31.3 trace/norm=-0.953 symmetry=-0.040; OV: norm=16.379 top=5.289 erank=35.9 trace/norm=-1.028; LN-bias key-vector=2.020 query-vector=1.805
L2H1 QK: norm=2.154 top=0.578 erank=40.5 trace/norm=-0.100 symmetry=-0.021; OV: norm=17.616 top=4.136 erank=44.6 trace/norm=-1.996; LN-bias key-vector=1.880 query-vector=1.629
L2H2 QK: norm=1.720 top=0.518 erank=42.4 trace/norm=-0.754 symmetry=-0.004; OV: norm=18.662 top=5.045 erank=39.3 trace/norm=-1.604; LN-bias key-vector=1.608 query-vector=1.411
L2H3 QK: norm=1.623 top=0.502 erank=42.2 trace/norm=-0.367 symmetry=-0.008; OV: norm=18.996 top=4.832 erank=41.7 trace/norm=-1.590; LN-bias key-vector=1.060 query-vector=0.840
L2H4 QK: norm=2.215 top=0.813 erank=35.3 trace/norm=-0.442 symmetry=-0.032; OV: norm=14.875 top=3.533 erank=42.1 trace/norm=-2.103; LN-bias key-vector=2.305 query-vector=1.969
L2H5 QK: norm=2.264 top=0.615 erank=39.4 trace/norm=-0.118 symmetry=-0.024; OV: norm=16.858 top=3.735 erank=45.4 trace/norm=-2.058; LN-bias key-vector=2.023 query-vector=1.738

LAYER 3
ln1_w (384,) mean=0.7087 sd=0.04941 min=0.4078 max=0.8155 norm=13.92
ln1_b (384,) mean=0.02963 sd=0.09939 min=-0.7639 max=0.8241 norm=2.032
ln2_w (384,) mean=1.267 sd=0.08945 min=0.2328 max=1.453 norm=24.89
ln2_b (384,) mean=0.0128 sd=0.1413 min=-0.5402 max=0.3932 norm=2.78
W_q (384, 384) mean=-8.166e-05 sd=0.08656 min=-0.3908 max=0.4595 norm=33.24
W_k (384, 384) mean=-2.536e-05 sd=0.08454 min=-0.9139 max=0.9735 norm=32.46
W_v (384, 384) mean=4.308e-05 sd=0.1027 min=-0.508 max=0.5939 norm=39.42
W_o (384, 384) mean=9.028e-06 sd=0.1045 min=-1.517 max=1.527 norm=40.13
W_fc (1536, 384) mean=0.0002521 sd=0.1019 min=-0.4902 max=0.55 norm=78.26
W_proj (384, 1536) mean=0.0002828 sd=0.1108 min=-1.058 max=1.477 norm=85.12
L3H0 QK: norm=2.029 top=0.435 erank=51.5 trace/norm=1.073 symmetry=0.006; OV: norm=20.711 top=5.784 erank=41.2 trace/norm=-2.223; LN-bias key-vector=0.500 query-vector=0.446
L3H1 QK: norm=1.216 top=0.345 erank=45.8 trace/norm=0.355 symmetry=-0.002; OV: norm=26.504 top=8.230 erank=33.4 trace/norm=-1.586; LN-bias key-vector=0.280 query-vector=0.306
L3H2 QK: norm=1.437 top=0.383 erank=50.0 trace/norm=0.243 symmetry=-0.010; OV: norm=23.504 top=7.460 erank=38.3 trace/norm=-1.593; LN-bias key-vector=0.495 query-vector=0.338
L3H3 QK: norm=1.815 top=0.322 erank=57.8 trace/norm=3.212 symmetry=0.210; OV: norm=37.524 top=10.809 erank=30.0 trace/norm=-1.210; LN-bias key-vector=0.220 query-vector=0.179
L3H4 QK: norm=0.622 top=0.236 erank=33.1 trace/norm=0.003 symmetry=0.001; OV: norm=49.234 top=21.266 erank=14.3 trace/norm=-0.794; LN-bias key-vector=0.144 query-vector=0.113
L3H5 QK: norm=1.665 top=0.454 erank=51.3 trace/norm=0.863 symmetry=0.009; OV: norm=22.563 top=6.302 erank=40.0 trace/norm=-1.534; LN-bias key-vector=0.493 query-vector=0.422

```
CLI OUTPUT IN EVENT ORDER
ERROR
Failed to read global AGENTS.md instructions from `<local-home>/.codex/AGENTS.md`: Operation not permitted (os error 1)

ERROR
Code Mode is unavailable because code-mode host is disabled. Code mode will fail closed; enable `features.code_mode_host` and install `codex-code-mode-host`.

AGENT_MESSAGE
```python
import numpy as np
from scipy.linalg import svd, svdvals
from threadpoolctl import threadpool_limits

def cos(a,b):
    return np.sum(a*b)/(np.linalg.norm(a)*np.linalg.norm(b)+1e-30)

with threadpool_limits(limits=2):
    As, Bs, keybias, names = [], [], [], []
    for l in range(4):
        g = W[f"ln1_w.{l}"].astype(float)
        b = W[f"ln1_b.{l}"].astype(float)
        for j in range(6):
            sl = slice(64*j,64*j+64)
            q = W[f"W_q.{l}"][sl].astype(float)
            k = W[f"W_k.{l}"][sl].astype(float)
            v = W[f"W_v.{l}"][sl].astype(float)
            o = W[f"W_o.{l}"][:,sl].astype(float)
            qg,kg,vg = q*g,k*g,v*g
            qg -= qg.mean(1,keepdims=True)
            kg -= kg.mean(1,keepdims=True)
            vg -= vg.mean(1,keepdims=True)
            As.append(qg.T@kg/8)
            Bs.append(o@vg)
            keybias.append(kg.T@(q@b)/8)
            names.append(f"L{l}H{j}")
    for l in range(4):
        ix = range(6*l,6*l+6)
        print("\nLAYER",l,"QK cosine matrix")
        print(np.round([[cos(As[i],As[j]) for j in ix] for i in ix],3))
        print("OV cosine matrix")
        print(np.round([[cos(Bs[i],Bs[j]) for j in ix] for i in ix],3))
        print("key-bias cosine matrix")
        print(np.round([[cos(keybias[i],keybias[j]) for j in ix] for i in ix],3))
    print("\nSPECTRA: first 12 singular values")
    for i in list(range(6))+list(range(18,24)):
        sa=svdvals(As[i]); sb=svdvals(Bs[i])
        print(names[i],"QK",np.round(sa[:12],3),"OV",np.round(sb[:12],3))
    print("\nCROSS-HEAD QK similarities: strongest other-layer matches")
    for i in range(24):
        cs=[(cos(As[i],As[j]),names[j]) for j in range(24) if j//6!=i//6]
        print(names[i],sorted(cs,reverse=True)[:3])
    print("\nMLP LINEAR-ALGEBRA STATISTICS (no nonlinearities applied)")
    for l in range(4):
        f=W[f"W_fc.{l}"].astype(float)*W[f"ln2_w.{l}"]
        f-=f.mean(1,keepdims=True)
        p=W[f"W_proj.{l}"].astype(float)
        sf=svdvals(f); sp=svdvals(p)
        M=p@f
        sm=svdvals(M)
        rowcos=np.sum(f*p.T,axis=1)/(np.linalg.norm(f,axis=1)*np.linalg.norm(p,axis=0))
        print("L",l,"FC spectrum",np.round(sf[:20],2))
        print("PROJ spectrum",np.round(sp[:20],2))
        print("PROJ@FC spectrum",np.round(sm[:20],2),
              "trace/norm",round(np.trace(M)/np.linalg.norm(M),3),
              "neuron input/output cos quantiles",np.round(np.quantile(rowcos,[0,.1,.5,.9,1]),3))
    print("\nMost anisotropic coordinates")
    for l in range(4):
        g=W[f"ln1_w.{l}"]
        b=W[f"ln1_b.{l}"]
        ids=np.argsort(np.abs(b))[-8:][::-1]
        print("L",l,"largest ln1 biases",[(int(i),round(float(b[i]),3),round(float(g[i]),3)) for i in ids])
    ids=np.argsort(W["ln1_w.0"])[-20:][::-1]
    print("Largest L0 ln1 scales",[(int(i),round(float(W["ln1_w.0"][i]),3)) for i in ids])
```


PERMITTED EXPERIMENT HARNESS RECORD: python
{
  "run": 2,
  "turn": "t002",
  "code": "import numpy as np\nfrom scipy.linalg import svd, svdvals\nfrom threadpoolctl import threadpool_limits\n\ndef cos(a,b):\n    return np.sum(a*b)/(np.linalg.norm(a)*np.linalg.norm(b)+1e-30)\n\nwith threadpool_limits(limits=2):\n    As, Bs, keybias, names = [], [], [], []\n    for l in range(4):\n        g = W[f\"ln1_w.{l}\"].astype(float)\n        b = W[f\"ln1_b.{l}\"].astype(float)\n        for j in range(6):\n            sl = slice(64*j,64*j+64)\n            q = W[f\"W_q.{l}\"][sl].astype(float)\n            k = W[f\"W_k.{l}\"][sl].astype(float)\n            v = W[f\"W_v.{l}\"][sl].astype(float)\n            o = W[f\"W_o.{l}\"][:,sl].astype(float)\n            qg,kg,vg = q*g,k*g,v*g\n            qg -= qg.mean(1,keepdims=True)\n            kg -= kg.mean(1,keepdims=True)\n            vg -= vg.mean(1,keepdims=True)\n            As.append(qg.T@kg/8)\n            Bs.append(o@vg)\n            keybias.append(kg.T@(q@b)/8)\n            names.append(f\"L{l}H{j}\")\n    for l in range(4):\n        ix = range(6*l,6*l+6)\n        print(\"\\nLAYER\",l,\"QK cosine matrix\")\n        print(np.round([[cos(As[i],As[j]) for j in ix] for i in ix],3))\n        print(\"OV cosine matrix\")\n        print(np.round([[cos(Bs[i],Bs[j]) for j in ix] for i in ix],3))\n        print(\"key-bias cosine matrix\")\n        print(np.round([[cos(keybias[i],keybias[j]) for j in ix] for i in ix],3))\n    print(\"\\nSPECTRA: first 12 singular values\")\n    for i in list(range(6))+list(range(18,24)):\n        sa=svdvals(As[i]); sb=svdvals(Bs[i])\n        print(names[i],\"QK\",np.round(sa[:12],3),\"OV\",np.round(sb[:12],3))\n    print(\"\\nCROSS-HEAD QK similarities: strongest other-layer matches\")\n    for i in range(24):\n        cs=[(cos(As[i],As[j]),names[j]) for j in range(24) if j//6!=i//6]\n        print(names[i],sorted(cs,reverse=True)[:3])\n    print(\"\\nMLP LINEAR-ALGEBRA STATISTICS (no nonlinearities applied)\")\n    for l in range(4):\n        f=W[f\"W_fc.{l}\"].astype(float)*W[f\"ln2_w.{l}\"]\n        f-=f.mean(1,keepdims=True)\n        p=W[f\"W_proj.{l}\"].astype(float)\n        sf=svdvals(f); sp=svdvals(p)\n        M=p@f\n        sm=svdvals(M)\n        rowcos=np.sum(f*p.T,axis=1)/(np.linalg.norm(f,axis=1)*np.linalg.norm(p,axis=0))\n        print(\"L\",l,\"FC spectrum\",np.round(sf[:20],2))\n        print(\"PROJ spectrum\",np.round(sp[:20],2))\n        print(\"PROJ@FC spectrum\",np.round(sm[:20],2),\n              \"trace/norm\",round(np.trace(M)/np.linalg.norm(M),3),\n              \"neuron input/output cos quantiles\",np.round(np.quantile(rowcos,[0,.1,.5,.9,1]),3))\n    print(\"\\nMost anisotropic coordinates\")\n    for l in range(4):\n        g=W[f\"ln1_w.{l}\"]\n        b=W[f\"ln1_b.{l}\"]\n        ids=np.argsort(np.abs(b))[-8:][::-1]\n        print(\"L\",l,\"largest ln1 biases\",[(int(i),round(float(b[i]),3),round(float(g[i]),3)) for i in ids])\n    ids=np.argsort(W[\"ln1_w.0\"])[-20:][::-1]\n    print(\"Largest L0 ln1 scales\",[(int(i),round(float(W[\"ln1_w.0\"][i]),3)) for i in ids])",
  "out": "\nLAYER 0 QK cosine matrix\n[[ 1.     0.012  0.008  0.137  0.013  0.044]\n [ 0.012  1.     0.691 -0.026  0.57   0.026]\n [ 0.008  0.691  1.    -0.063  0.493 -0.075]\n [ 0.137 -0.026 -0.063  1.    -0.044  0.01 ]\n [ 0.013  0.57   0.493 -0.044  1.     0.033]\n [ 0.044  0.026 -0.075  0.01   0.033  1.   ]]\nOV cosine matrix\n[[ 1.     0.018  0.017 -0.036  0.026  0.017]\n [ 0.018  1.     0.925  0.006  0.869  0.644]\n [ 0.017  0.925  1.     0.009  0.811  0.692]\n [-0.036  0.006  0.009  1.     0.011 -0.001]\n [ 0.026  0.869  0.811  0.011  1.     0.592]\n [ 0.017  0.644  0.692 -0.001  0.592  1.   ]]\nkey-bias cosine matrix\n[[ 1.    -0.054 -0.104 -0.041  0.29  -0.095]\n [-0.054  1.     0.347 -0.093  0.41  -0.226]\n [-0.104  0.347  1.    -0.057  0.567  0.524]\n [-0.041 -0.093 -0.057  1.     0.022  0.074]\n [ 0.29   0.41   0.567  0.022  1.     0.373]\n [-0.095 -0.226  0.524  0.074  0.373  1.   ]]\n\nLAYER 1 QK cosine matrix\n[[1.    0.357 0.372 0.345 0.334 0.376]\n [0.357 1.    0.371 0.361 0.302 0.398]\n [0.372 0.371 1.    0.368 0.375 0.351]\n [0.345 0.361 0.368 1.    0.32  0.394]\n [0.334 0.302 0.375 0.32  1.    0.288]\n [0.376 0.398 0.351 0.394 0.288 1.   ]]\nOV cosine matrix\n[[ 1.    -0.02   0.03  -0.012  0.001  0.029]\n [-0.02   1.    -0.009 -0.028 -0.018  0.016]\n [ 0.03  -0.009  1.     0.001  0.014 -0.017]\n [-0.012 -0.028  0.001  1.    -0.001 -0.015]\n [ 0.001 -0.018  0.014 -0.001  1.    -0.014]\n [ 0.029  0.016 -0.017 -0.015 -0.014  1.   ]]\nkey-bias cosine matrix\n[[1.    0.829 0.853 0.823 0.825 0.86 ]\n [0.829 1.    0.851 0.864 0.821 0.861]\n [0.853 0.851 1.    0.83  0.834 0.833]\n [0.823 0.864 0.83  1.    0.834 0.873]\n [0.825 0.821 0.834 0.834 1.    0.828]\n [0.86  0.861 0.833 0.873 0.828 1.   ]]\n\nLAYER 2 QK cosine matrix\n[[1.    0.128 0.161 0.117 0.179 0.134]\n [0.128 1.    0.116 0.086 0.121 0.116]\n [0.161 0.116 1.    0.101 0.144 0.123]\n [0.117 0.086 0.101 1.    0.092 0.093]\n [0.179 0.121 0.144 0.092 1.    0.134]\n [0.134 0.116 0.123 0.093 0.134 1.   ]]\nOV cosine matrix\n[[ 1.    -0.023 -0.039 -0.022 -0.005  0.001]\n [-0.023  1.    -0.001  0.002 -0.012 -0.008]\n [-0.039 -0.001  1.     0.013  0.004  0.022]\n [-0.022  0.002  0.013  1.     0.001  0.   ]\n [-0.005 -0.012  0.004  0.001  1.     0.004]\n [ 0.001 -0.008  0.022  0.     0.004  1.   ]]\nkey-bias cosine matrix\n[[1.    0.807 0.766 0.703 0.82  0.835]\n [0.807 1.    0.811 0.719 0.824 0.837]\n [0.766 0.811 1.    0.699 0.832 0.827]\n [0.703 0.719 0.699 1.    0.715 0.73 ]\n [0.82  0.824 0.832 0.715 1.    0.845]\n [0.835 0.837 0.827 0.73  0.845 1.   ]]\n\nLAYER 3 QK cosine matrix\n[[1.    0.058 0.082 0.06  0.007 0.108]\n [0.058 1.    0.069 0.034 0.041 0.075]\n [0.082 0.069 1.    0.031 0.036 0.094]\n [0.06  0.034 0.031 1.    0.036 0.058]\n [0.007 0.041 0.036 0.036 1.    0.027]\n [0.108 0.075 0.094 0.058 0.027 1.   ]]\nOV cosine matrix\n[[ 1.    -0.012  0.024  0.011 -0.002  0.034]\n [-0.012  1.    -0.021  0.024  0.059  0.001]\n [ 0.024 -0.021  1.     0.003  0.078  0.026]\n [ 0.011  0.024  0.003  1.     0.042 -0.001]\n [-0.002  0.059  0.078  0.042  1.     0.057]\n [ 0.034  0.001  0.026 -0.001  0.057  1.   ]]\nkey-bias cosine matrix\n[[ 1.     0.6    0.747  0.013  0.159  0.776]\n [ 0.6    1.     0.553  0.015  0.289  0.669]\n [ 0.747  0.553  1.     0.011  0.208  0.736]\n [ 0.013  0.015  0.011  1.     0.026 -0.046]\n [ 0.159  0.289  0.208  0.026  1.     0.254]\n [ 0.776  0.669  0.736 -0.046  0.254  1.   ]]\n\nSPECTRA: first 12 singular values\nL0H0 QK [0.248 0.102 0.047 0.043 0.037 0.036 0.034 0.031 0.026 0.023 0.022 0.022] OV [0.957 0.898 0.818 0.641 0.554 0.474 0.439 0.406 0.372 0.348 0.329 0.308]\nL0H1 QK [0.15  0.042 0.021 0.012 0.01  0.007 0.007 0.004 0.004 0.004 0.003 0.003] OV [3.38  2.023 0.344 0.179 0.147 0.132 0.123 0.118 0.108 0.098 0.09  0.087]\nL0H2 QK [0.102 0.018 0.016 0.012 0.008 0.007 0.005 0.004 0.004 0.004 0.003 0.003] OV [2.643 1.363 0.399 0.175 0.159 0.142 0.126 0.105 0.096 0.094 0.085 0.085]\nL0H3 QK [0.244 0.222 0.201 0.182 0.179 0.157 0.155 0.149 0.14  0.136 0.131 0.128] OV [1.126 0.955 0.95  0.889 0.863 0.854 0.842 0.78  0.759 0.723 0.708 0.673]\nL0H4 QK [0.08  0.022 0.019 0.013 0.011 0.008 0.007 0.006 0.005 0.005 0.004 0.004] OV [1.454 0.723 0.213 0.141 0.138 0.115 0.109 0.097 0.094 0.084 0.079 0.075]\nL0H5 QK [0.032 0.004 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002] OV [16.278  8.778  2.833  1.117  1.039  0.631  0.533  0.448  0.413  0.326\n  0.266  0.221]\nL3H0 QK [0.435 0.414 0.39  0.38  0.373 0.36  0.357 0.347 0.337 0.333 0.331 0.328] OV [5.784 5.655 5.063 4.642 4.213 3.824 3.807 3.649 3.604 3.567 3.389 3.298]\nL3H1 QK [0.345 0.308 0.285 0.253 0.244 0.227 0.211 0.207 0.2   0.193 0.19  0.186] OV [8.23  7.821 6.561 6.475 6.066 5.764 5.569 5.125 5.038 4.788 4.661 4.484]\nL3H2 QK [0.383 0.304 0.294 0.277 0.266 0.258 0.254 0.243 0.239 0.231 0.229 0.223] OV [7.46  6.108 5.569 5.335 5.047 4.689 4.586 4.379 4.357 4.143 3.993 3.795]\nL3H3 QK [0.322 0.311 0.307 0.304 0.297 0.294 0.288 0.286 0.284 0.282 0.277 0.273] OV [10.809  9.984  9.82   9.426  9.144  9.057  8.451  7.949  7.672  7.388\n  7.361  6.959]\nL3H4 QK [0.236 0.202 0.17  0.149 0.132 0.124 0.111 0.105 0.102 0.096 0.092 0.09 ] OV [21.266 17.675 16.977 15.046 14.398 13.303 12.126 11.541  8.688  8.574\n  7.486  6.519]\nL3H5 QK [0.454 0.321 0.315 0.299 0.289 0.288 0.284 0.28  0.276 0.271 0.265 0.261] OV [6.302 5.976 5.474 5.086 4.976 4.706 4.351 4.061 3.987 3.899 3.807 3.631]\n\nCROSS-HEAD QK similarities: strongest other-layer matches\nL0H0 [(np.float64(0.00979153483382163), 'L1H5'), (np.float64(0.008427259356622762), 'L2H0'), (np.float64(0.008223779217835316), 'L1H3')]\nL0H1 [(np.float64(0.0010880394971872875), 'L2H0'), (np.float64(0.0008593703704631152), 'L2H2'), (np.float64(-0.0001032708915409376), 'L2H1')]\nL0H2 [(np.float64(0.0050234992549716305), 'L2H0'), (np.float64(0.004594332635559284), 'L1H2'), (np.float64(0.004580946146990521), 'L1H4')]\nL0H3 [(np.float64(0.016643867610997714), 'L1H5'), (np.float64(0.016533999939375973), 'L3H3'), (np.float64(0.016121030549748686), 'L1H0')]\nL0H4 [(np.float64(0.005772833757418792), 'L2H2'), (np.float64(0.0036898938096945545), 'L1H4'), (np.float64(0.0027571174250421446), 'L1H2')]\nL0H5 [(np.float64(0.010936402216938758), 'L3H4'), (np.float64(-0.001411510777306644), 'L3H3'), (np.float64(-0.002164029793589887), 'L2H0')]\nL1H0 [(np.float64(0.18506694011229038), 'L2H0'), (np.float64(0.1488677247000508), 'L2H4'), (np.float64(0.12564662600924476), 'L2H2')]\nL1H1 [(np.float64(0.17022256856726697), 'L2H0'), (np.float64(0.1573422419093759), 'L2H4'), (np.float64(0.13271517165724014), 'L2H1')]\nL1H2 [(np.float64(0.18100756505856744), 'L2H0'), (np.float64(0.1668710304689896), 'L2H4'), (np.float64(0.12374133848220824), 'L2H5')]\nL1H3 [(np.float64(0.19214667678145736), 'L2H0'), (np.float64(0.16266425883219318), 'L2H4'), (np.float64(0.13267644666785067), 'L2H5')]\nL1H4 [(np.float64(0.1772663620980154), 'L2H0'), (np.float64(0.12116380081634327), 'L2H4'), (np.float64(0.09611140079226985), 'L2H2')]\nL1H5 [(np.float64(0.17310967356438595), 'L2H0'), (np.float64(0.14688132938479792), 'L2H4'), (np.float64(0.12588727047420217), 'L2H5')]\nL2H0 [(np.float64(0.19214667678145736), 'L1H3'), (np.float64(0.18506694011229038), 'L1H0'), (np.float64(0.18100756505856744), 'L1H2')]\nL2H1 [(np.float64(0.13271517165724014), 'L1H1'), (np.float64(0.12621364897594486), 'L1H3'), (np.float64(0.12278561406882613), 'L1H2')]\nL2H2 [(np.float64(0.12742023396713717), 'L1H3'), (np.float64(0.12564662600924476), 'L1H0'), (np.float64(0.12162773073563991), 'L1H1')]\nL2H3 [(np.float64(0.09685903841896927), 'L1H3'), (np.float64(0.0910249506652174), 'L1H1'), (np.float64(0.08406845805609671), 'L1H5')]\nL2H4 [(np.float64(0.1668710304689896), 'L1H2'), (np.float64(0.16266425883219318), 'L1H3'), (np.float64(0.1573422419093759), 'L1H1')]\nL2H5 [(np.float64(0.13267644666785067), 'L1H3'), (np.float64(0.12880880741147002), 'L1H1'), (np.float64(0.12588727047420217), 'L1H5')]\nL3H0 [(np.float64(0.06303436921510018), 'L2H4'), (np.float64(0.061698054643142985), 'L2H1'), (np.float64(0.0586590497588326), 'L2H5')]\nL3H1 [(np.float64(0.0507185844159886), 'L2H4'), (np.float64(0.050181191045734784), 'L2H0'), (np.float64(0.047482565641790125), 'L1H3')]\nL3H2 [(np.float64(0.06161449958325272), 'L2H2'), (np.float64(0.061561032715421016), 'L2H0'), (np.float64(0.059263577539727344), 'L1H3')]\nL3H3 [(np.float64(0.021274040539388073), 'L2H5'), (np.float64(0.016533999939375973), 'L0H3'), (np.float64(0.01648908421968714), 'L2H1')]\nL3H4 [(np.float64(0.017223015933478858), 'L1H3'), (np.float64(0.01672416710494667), 'L2H0'), (np.float64(0.015104739991435589), 'L2H3')]\nL3H5 [(np.float64(0.05636998232246223), 'L1H3'), (np.float64(0.05594018357599625), 'L2H1'), (np.float64(0.053872260032412106), 'L2H0')]\n\nMLP LINEAR-ALGEBRA STATISTICS (no nonlinearities applied)\nL 0 FC spectrum [17.58 13.47 11.76 10.19  9.61  9.54  9.34  9.14  8.75  8.68  8.58  8.39\n  8.    7.93  7.84  7.73  7.52  7.39  7.16  7.08]\nPROJ spectrum [10.9   7.7   7.17  6.64  6.54  6.29  6.2   6.13  5.94  5.92  5.76  5.64\n  5.55  5.48  5.39  5.36  5.26  5.21  5.17  5.15]\nPROJ@FC spectrum [125.96  60.95  37.56  32.55  31.    29.68  28.22  27.4   26.51  25.84\n  25.26  24.58  23.93  23.43  22.22  21.62  21.43  21.02  20.57  20.24] trace/norm 0.068 neuron input/output cos quantiles [-0.619 -0.118 -0.022  0.087  0.599]\nL 1 FC spectrum [22.95 13.34 13.21 13.05 12.74 12.71 12.3  12.24 11.92 11.81 11.75 11.47\n 11.43 11.31 11.18 11.05 10.96 10.58 10.53 10.28]\nPROJ spectrum [9.04 8.46 8.1  7.33 7.32 7.09 6.77 6.67 6.57 6.43 6.37 6.28 6.25 6.23\n 6.13 6.05 6.01 5.96 5.91 5.9 ]\nPROJ@FC spectrum [74.44 32.73 28.44 27.61 26.93 26.2  25.44 25.24 24.83 24.1  23.77 23.48\n 22.89 22.71 22.09 21.9  21.63 21.44 21.03 20.84] trace/norm -2.058 neuron input/output cos quantiles [-0.535 -0.143 -0.06   0.028  0.446]\nL 2 FC spectrum [20.71 12.17 11.48 11.41 11.12 10.28 10.09  9.9   9.84  9.75  9.66  9.6\n  9.56  9.51  9.34  9.25  9.15  9.07  9.01  8.96]\nPROJ spectrum [10.2   9.03  8.88  8.41  8.22  8.09  7.99  7.83  7.68  7.49  7.37  7.26\n  7.17  7.07  7.03  6.8   6.74  6.66  6.46  6.43]\nPROJ@FC spectrum [78.87 33.38 30.76 30.37 29.11 28.15 28.07 26.66 25.88 25.73 25.46 25.05\n 24.7  24.16 23.66 23.24 23.04 22.55 22.08 21.91] trace/norm -3.224 neuron input/output cos quantiles [-0.439 -0.175 -0.093  0.     0.445]\nL 3 FC spectrum [19.3  11.   10.8  10.27  9.8   9.56  9.5   9.38  9.02  8.85  8.78  8.63\n  8.41  8.36  8.22  8.06  8.03  7.96  7.85  7.79]\nPROJ spectrum [28.46 22.21 21.34 20.71 19.94 19.66 18.99 18.74 18.29 17.46 17.13 16.56\n 15.33 14.87 14.33 13.44 12.67 12.45 12.32 11.53]\nPROJ@FC spectrum [187.97  87.29  73.96  51.12  47.59  45.79  43.3   42.18  40.74  39.28\n  38.62  35.97  33.01  31.93  31.52  30.51  28.8   28.34  27.74  26.58] trace/norm -2.422 neuron input/output cos quantiles [-0.389 -0.209 -0.096  0.04   0.262]\n\nMost anisotropic coordinates\nL 0 largest ln1 biases [(312, -0.095, 0.214), (146, 0.091, 0.18), (12, 0.086, 0.12), (104, -0.084, 0.211), (289, 0.083, 0.376), (156, -0.078, 0.095), (303, -0.078, 0.404), (328, 0.076, 0.173)]\nL 1 largest ln1 biases [(39, -1.568, 0.299), (58, 1.365, 0.375), (99, -1.336, 0.716), (184, -0.562, 0.249), (383, -0.462, 0.338), (21, -0.43, 1.085), (153, 0.297, 0.42), (266, 0.277, 0.47)]\nL 2 largest ln1 biases [(99, -1.659, 0.943), (58, 1.332, 0.477), (39, -1.199, 0.422), (383, -0.507, 0.317), (184, -0.505, 0.337), (21, -0.453, 1.093), (63, -0.325, 0.481), (266, 0.299, 0.491)]\nL 3 largest ln1 biases [(58, 0.824, 0.466), (99, -0.764, 0.751), (5, 0.436, 0.541), (383, -0.397, 0.408), (266, 0.343, 0.524), (21, -0.315, 0.802), (184, -0.289, 0.562), (45, 0.289, 0.511)]\nLargest L0 ln1 scales [(180, 0.978), (184, 0.974), (162, 0.97), (99, 0.917), (211, 0.896), (256, 0.892), (300, 0.804), (317, 0.804), (223, 0.802), (39, 0.799), (173, 0.793), (4, 0.786), (228, 0.786), (69, 0.772), (89, 0.767), (100, 0.766), (56, 0.753), (65, 0.749), (354, 0.746), (246, 0.726)]\n",
  "seconds": 1.093,
  "rc": 0,
  "timed_out": false,
  "truncated": false,
  "code_sha256": "291748aed39367b4bacbc52b0fdc7a0d030d721934db94a271960a61fd0d514b",
  "weights_sha256": "04ec0b300d207b26b92a1af6d49d56d452833e39b35826200bc1d821e5b7d930"
}

EXACT HARNESS FEEDBACK

LAYER 0 QK cosine matrix
[[ 1.     0.012  0.008  0.137  0.013  0.044]
 [ 0.012  1.     0.691 -0.026  0.57   0.026]
 [ 0.008  0.691  1.    -0.063  0.493 -0.075]
 [ 0.137 -0.026 -0.063  1.    -0.044  0.01 ]
 [ 0.013  0.57   0.493 -0.044  1.     0.033]
 [ 0.044  0.026 -0.075  0.01   0.033  1.   ]]
OV cosine matrix
[[ 1.     0.018  0.017 -0.036  0.026  0.017]
 [ 0.018  1.     0.925  0.006  0.869  0.644]
 [ 0.017  0.925  1.     0.009  0.811  0.692]
 [-0.036  0.006  0.009  1.     0.011 -0.001]
 [ 0.026  0.869  0.811  0.011  1.     0.592]
 [ 0.017  0.644  0.692 -0.001  0.592  1.   ]]
key-bias cosine matrix
[[ 1.    -0.054 -0.104 -0.041  0.29  -0.095]
 [-0.054  1.     0.347 -0.093  0.41  -0.226]
 [-0.104  0.347  1.    -0.057  0.567  0.524]
 [-0.041 -0.093 -0.057  1.     0.022  0.074]
 [ 0.29   0.41   0.567  0.022  1.     0.373]
 [-0.095 -0.226  0.524  0.074  0.373  1.   ]]

LAYER 1 QK cosine matrix
[[1.    0.357 0.372 0.345 0.334 0.376]
 [0.357 1.    0.371 0.361 0.302 0.398]
 [0.372 0.371 1.    0.368 0.375 0.351]
 [0.345 0.361 0.368 1.    0.32  0.394]
 [0.334 0.302 0.375 0.32  1.    0.288]
 [0.376 0.398 0.351 0.394 0.288 1.   ]]
OV cosine matrix
[[ 1.    -0.02   0.03  -0.012  0.001  0.029]
 [-0.02   1.    -0.009 -0.028 -0.018  0.016]
 [ 0.03  -0.009  1.     0.001  0.014 -0.017]
 [-0.012 -0.028  0.001  1.    -0.001 -0.015]
 [ 0.001 -0.018  0.014 -0.001  1.    -0.014]
 [ 0.029  0.016 -0.017 -0.015 -0.014  1.   ]]
key-bias cosine matrix
[[1.    0.829 0.853 0.823 0.825 0.86 ]
 [0.829 1.    0.851 0.864 0.821 0.861]
 [0.853 0.851 1.    0.83  0.834 0.833]
 [0.823 0.864 0.83  1.    0.834 0.873]
 [0.825 0.821 0.834 0.834 1.    0.828]
 [0.86  0.861 0.833 0.873 0.828 1.   ]]

LAYER 2 QK cosine matrix
[[1.    0.128 0.161 0.117 0.179 0.134]
 [0.128 1.    0.116 0.086 0.121 0.116]
 [0.161 0.116 1.    0.101 0.144 0.123]
 [0.117 0.086 0.101 1.    0.092 0.093]
 [0.179 0.121 0.144 0.092 1.    0.134]
 [0.134 0.116 0.123 0.093 0.134 1.   ]]
OV cosine matrix
[[ 1.    -0.023 -0.039 -0.022 -0.005  0.001]
 [-0.023  1.    -0.001  0.002 -0.012 -0.008]
 [-0.039 -0.001  1.     0.013  0.004  0.022]
 [-0.022  0.002  0.013  1.     0.001  0.   ]
 [-0.005 -0.012  0.004  0.001  1.     0.004]
 [ 0.001 -0.008  0.022  0.     0.004  1.   ]]
key-bias cosine matrix
[[1.    0.807 0.766 0.703 0.82  0.835]
 [0.807 1.    0.811 0.719 0.824 0.837]
 [0.766 0.811 1.    0.699 0.832 0.827]
 [0.703 0.719 0.699 1.    0.715 0.73 ]
 [0.82  0.824 0.832 0.715 1.    0.845]
 [0.835 0.837 0.827 0.73  0.845 1.   ]]

LAYER 3 QK cosine matrix
[[1.    0.058 0.082 0.06  0.007 0.108]
 [0.058 1.    0.069 0.034 0.041 0.075]
 [0.082 0.069 1.    0.031 0.036 0.094]
 [0.06  0.034 0.031 1.    0.036 0.058]
 [0.007 0.041 0.036 0.036 1.    0.027]
 [0.108 0.075 0.094 0.058 0.027 1.   ]]
OV cosine matrix
[[ 1.    -0.012  0.024  0.011 -0.002  0.034]
 [-0.012  1.    -0.021  0.024  0.059  0.001]
 [ 0.024 -0.021  1.     0.003  0.078  0.026]
 [ 0.011  0.024  0.003  1.     0.042 -0.001]
 [-0.002  0.059  0.078  0.042  1.     0.057]
 [ 0.034  0.001  0.026 -0.001  0.057  1.   ]]
key-bias cosine matrix
[[ 1.     0.6    0.747  0.013  0.159  0.776]
 [ 0.6    1.     0.553  0.015  0.289  0.669]
 [ 0.747  0.553  1.     0.011  0.208  0.736]
 [ 0.013  0.015  0.011  1.     0.026 -0.046]
 [ 0.159  0.289  0.208  0.026  1.     0.254]
 [ 0.776  0.669  0.736 -0.046  0.254  1.   ]]

SPECTRA: first 12 singular values
L0H0 QK [0.248 0.102 0.047 0.043 0.037 0.036 0.034 0.031 0.026 0.023 0.022 0.022] OV [0.957 0.898 0.818 0.641 0.554 0.474 0.439 0.406 0.372 0.348 0.329 0.308]
L0H1 QK [0.15  0.042 0.021 0.012 0.01  0.007 0.007 0.004 0.004 0.004 0.003 0.003] OV [3.38  2.023 0.344 0.179 0.147 0.132 0.123 0.118 0.108 0.098 0.09  0.087]
L0H2 QK [0.102 0.018 0.016 0.012 0.008 0.007 0.005 0.004 0.004 0.004 0.003 0.003] OV [2.643 1.363 0.399 0.175 0.159 0.142 0.126 0.105 0.096 0.094 0.085 0.085]
L0H3 QK [0.244 0.222 0.201 0.182 0.179 0.157 0.155 0.149 0.14  0.136 0.131 0.128] OV [1.126 0.955 0.95  0.889 0.863 0.854 0.842 0.78  0.759 0.723 0.708 0.673]
L0H4 QK [0.08  0.022 0.019 0.013 0.011 0.008 0.007 0.006 0.005 0.005 0.004 0.004] OV [1.454 0.723 0.213 0.141 0.138 0.115 0.109 0.097 0.094 0.084 0.079 0.075]
L0H5 QK [0.032 0.004 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002] OV [16.278  8.778  2.833  1.117  1.039  0.631  0.533  0.448  0.413  0.326
  0.266  0.221]
L3H0 QK [0.435 0.414 0.39  0.38  0.373 0.36  0.357 0.347 0.337 0.333 0.331 0.328] OV [5.784 5.655 5.063 4.642 4.213 3.824 3.807 3.649 3.604 3.567 3.389 3.298]
L3H1 QK [0.345 0.308 0.285 0.253 0.244 0.227 0.211 0.207 0.2   0.193 0.19  0.186] OV [8.23  7.821 6.561 6.475 6.066 5.764 5.569 5.125 5.038 4.788 4.661 4.484]
L3H2 QK [0.383 0.304 0.294 0.277 0.266 0.258 0.254 0.243 0.239 0.231 0.229 0.223] OV [7.46  6.108 5.569 5.335 5.047 4.689 4.586 4.379 4.357 4.143 3.993 3.795]
L3H3 QK [0.322 0.311 0.307 0.304 0.297 0.294 0.288 0.286 0.284 0.282 0.277 0.273] OV [10.809  9.984  9.82   9.426  9.144  9.057  8.451  7.949  7.672  7.388
  7.361  6.959]
L3H4 QK [0.236 0.202 0.17  0.149 0.132 0.124 0.111 0.105 0.102 0.096 0.092 0.09 ] OV [21.266 17.675 16.977 15.046 14.398 13.303 12.126 11.541  8.688  8.574
  7.486  6.519]
L3H5 QK [0.454 0.321 0.315 0.299 0.289 0.288 0.284 0.28  0.276 0.271 0.265 0.261] OV [6.302 5.976 5.474 5.086 4.976 4.706 4.351 4.061 3.987 3.899 3.807 3.631]

CROSS-HEAD QK similarities: strongest other-layer matches
L0H0 [(np.float64(0.00979153483382163), 'L1H5'), (np.float64(0.008427259356622762), 'L2H0'), (np.float64(0.008223779217835316), 'L1H3')]
L0H1 [(np.float64(0.0010880394971872875), 'L2H0'), (np.float64(0.0008593703704631152), 'L2H2'), (np.float64(-0.0001032708915409376), 'L2H1')]
L0H2 [(np.float64(0.0050234992549716305), 'L2H0'), (np.float64(0.004594332635559284), 'L1H2'), (np.float64(0.004580946146990521), 'L1H4')]
L0H3 [(np.float64(0.016643867610997714), 'L1H5'), (np.float64(0.016533999939375973), 'L3H3'), (np.float64(0.016121030549748686), 'L1H0')]
L0H4 [(np.float64(0.005772833757418792), 'L2H2'), (np.float64(0.0036898938096945545), 'L1H4'), (np.float64(0.0027571174250421446), 'L1H2')]
L0H5 [(np.float64(0.010936402216938758), 'L3H4'), (np.float64(-0.001411510777306644), 'L3H3'), (np.float64(-0.002164029793589887), 'L2H0')]
L1H0 [(np.float64(0.18506694011229038), 'L2H0'), (np.float64(0.1488677247000508), 'L2H4'), (np.float64(0.12564662600924476), 'L2H2')]
L1H1 [(np.float64(0.17022256856726697), 'L2H0'), (np.float64(0.1573422419093759), 'L2H4'), (np.float64(0.13271517165724014), 'L2H1')]
L1H2 [(np.float64(0.18100756505856744), 'L2H0'), (np.float64(0.1668710304689896), 'L2H4'), (np.float64(0.12374133848220824), 'L2H5')]
L1H3 [(np.float64(0.19214667678145736), 'L2H0'), (np.float64(0.16266425883219318), 'L2H4'), (np.float64(0.13267644666785067), 'L2H5')]
L1H4 [(np.float64(0.1772663620980154), 'L2H0'), (np.float64(0.12116380081634327), 'L2H4'), (np.float64(0.09611140079226985), 'L2H2')]
L1H5 [(np.float64(0.17310967356438595), 'L2H0'), (np.float64(0.14688132938479792), 'L2H4'), (np.float64(0.12588727047420217), 'L2H5')]
L2H0 [(np.float64(0.19214667678145736), 'L1H3'), (np.float64(0.18506694011229038), 'L1H0'), (np.float64(0.18100756505856744), 'L1H2')]
L2H1 [(np.float64(0.13271517165724014), 'L1H1'), (np.float64(0.12621364897594486), 'L1H3'), (np.float64(0.12278561406882613), 'L1H2')]
L2H2 [(np.float64(0.12742023396713717), 'L1H3'), (np.float64(0.12564662600924476), 'L1H0'), (np.float64(0.12162773073563991), 'L1H1')]
L2H3 [(np.float64(0.09685903841896927), 'L1H3'), (np.float64(0.0910249506652174), 'L1H1'), (np.float64(0.08406845805609671), 'L1H5')]
L2H4 [(np.float64(0.1668710304689896), 'L1H2'), (np.float64(0.16266425883219318), 'L1H3'), (np.float64(0.1573422419093759), 'L1H1')]
L2H5 [(np.float64(0.13267644666785067), 'L1H3'), (np.float64(0.12880880741147002), 'L1H1'), (np.float64(0.12588727047420217), 'L1H5')]
L3H0 [(np.float64(0.06303436921510018), 'L2H4'), (np.float64(0.061698054643142985), 'L2H1'), (np.float64(0.0586590497588326), 'L2H5')]
L3H1 [(np.float64(0.0507185844159886), 'L2H4'), (np.float64(0.050181191045734784), 'L2H0'), (np.float64(0.047482565641790125), 'L1H3')]
L3H2 [(np.float64(0.06161449958325272), 'L2H2'), (np.float64(0.061561032715421016), 'L2H0'), (np.float64(0.059263577539727344), 'L1H3')]
L3H3 [(np.float64(0.021274040539388073), 'L2H5'), (np.float64(0.016533999939375973), 'L0H3'), (np.float64(0.01648908421968714), 'L2H1')]
L3H4 [(np.float64(0.017223015933478858), 'L1H3'), (np.float64(0.01672416710494667), 'L2H0'), (np.float64(0.015104739991435589), 'L2H3')]
L3H5 [(np.float64(0.05636998232246223), 'L1H3'), (np.float64(0.05594018357599625), 'L2H1'), (np.float64(0.053872260032412106), 'L2H0')]

MLP LINEAR-ALGEBRA STATISTICS (no nonlinearities applied)
L 0 FC spectrum [17.58 13.47 11.76 10.19  9.61  9.54  9.34  9.14  8.75  8.68  8.58  8.39
  8.    7.93  7.84  7.73  7.52  7.39  7.16  7.08]
PROJ spectrum [10.9   7.7   7.17  6.64  6.54  6.29  6.2   6.13  5.94  5.92  5.76  5.64
  5.55  5.48  5.39  5.36  5.26  5.21  5.17  5.15]
PROJ@FC spectrum [125.96  60.95  37.56  32.55  31.    29.68  28.22  27.4   26.51  25.84
  25.26  24.58  23.93  23.43  22.22  21.62  21.43  21.02  20.57  20.24] trace/norm 0.068 neuron input/output cos quantiles [-0.619 -0.118 -0.022  0.087  0.599]
L 1 FC spectrum [22.95 13.34 13.21 13.05 12.74 12.71 12.3  12.24 11.92 11.81 11.75 11.47
 11.43 11.31 11.18 11.05 10.96 10.58 10.53 10.28]
PROJ spectrum [9.04 8.46 8.1  7.33 7.32 7.09 6.77 6.67 6.57 6.43 6.37 6.28 6.25 6.23
 6.13 6.05 6.01 5.96 5.91 5.9 ]
PROJ@FC spectrum [74.44 32.73 28.44 27.61 26.93 26.2  25.44 25.24 24.83 24.1  23.77 23.48
 22.89 22.71 22.09 21.9  21.63 21.44 21.03 20.84] trace/norm -2.058 neuron input/output cos quantiles [-0.535 -0.143 -0.06   0.028  0.446]
L 2 FC spectrum [20.71 12.17 11.48 11.41 11.12 10.28 10.09  9.9   9.84  9.75  9.66  9.6
  9.56  9.51  9.34  9.25  9.15  9.07  9.01  8.96]
PROJ spectrum [10.2   9.03  8.88  8.41  8.22  8.09  7.99  7.83  7.68  7.49  7.37  7.26
  7.17  7.07  7.03  6.8   6.74  6.66  6.46  6.43]
PROJ@FC spectrum [78.87 33.38 30.76 30.37 29.11 28.15 28.07 26.66 25.88 25.73 25.46 25.05
 24.7  24.16 23.66 23.24 23.04 22.55 22.08 21.91] trace/norm -3.224 neuron input/output cos quantiles [-0.439 -0.175 -0.093  0.     0.445]
L 3 FC spectrum [19.3  11.   10.8  10.27  9.8   9.56  9.5   9.38  9.02  8.85  8.78  8.63
  8.41  8.36  8.22  8.06  8.03  7.96  7.85  7.79]
PROJ spectrum [28.46 22.21 21.34 20.71 19.94 19.66 18.99 18.74 18.29 17.46 17.13 16.56
 15.33 14.87 14.33 13.44 12.67 12.45 12.32 11.53]
PROJ@FC spectrum [187.97  87.29  73.96  51.12  47.59  45.79  43.3   42.18  40.74  39.28
  38.62  35.97  33.01  31.93  31.52  30.51  28.8   28.34  27.74  26.58] trace/norm -2.422 neuron input/output cos quantiles [-0.389 -0.209 -0.096  0.04   0.262]

Most anisotropic coordinates
L 0 largest ln1 biases [(312, -0.095, 0.214), (146, 0.091, 0.18), (12, 0.086, 0.12), (104, -0.084, 0.211), (289, 0.083, 0.376), (156, -0.078, 0.095), (303, -0.078, 0.404), (328, 0.076, 0.173)]
L 1 largest ln1 biases [(39, -1.568, 0.299), (58, 1.365, 0.375), (99, -1.336, 0.716), (184, -0.562, 0.249), (383, -0.462, 0.338), (21, -0.43, 1.085), (153, 0.297, 0.42), (266, 0.277, 0.47)]
L 2 largest ln1 biases [(99, -1.659, 0.943), (58, 1.332, 0.477), (39, -1.199, 0.422), (383, -0.507, 0.317), (184, -0.505, 0.337), (21, -0.453, 1.093), (63, -0.325, 0.481), (266, 0.299, 0.491)]
L 3 largest ln1 biases [(58, 0.824, 0.466), (99, -0.764, 0.751), (5, 0.436, 0.541), (383, -0.397, 0.408), (266, 0.343, 0.524), (21, -0.315, 0.802), (184, -0.289, 0.562), (45, 0.289, 0.511)]
Largest L0 ln1 scales [(180, 0.978), (184, 0.974), (162, 0.97), (99, 0.917), (211, 0.896), (256, 0.892), (300, 0.804), (317, 0.804), (223, 0.802), (39, 0.799), (173, 0.793), (4, 0.786), (228, 0.786), (69, 0.772), (89, 0.767), (100, 0.766), (56, 0.753), (65, 0.749), (354, 0.746), (246, 0.726)]


========================================================================
TURN t003
MESSAGE SENT TO CODEX
OUTPUT of run 2 of at most 100:
```

LAYER 0 QK cosine matrix
[[ 1.     0.012  0.008  0.137  0.013  0.044]
 [ 0.012  1.     0.691 -0.026  0.57   0.026]
 [ 0.008  0.691  1.    -0.063  0.493 -0.075]
 [ 0.137 -0.026 -0.063  1.    -0.044  0.01 ]
 [ 0.013  0.57   0.493 -0.044  1.     0.033]
 [ 0.044  0.026 -0.075  0.01   0.033  1.   ]]
OV cosine matrix
[[ 1.     0.018  0.017 -0.036  0.026  0.017]
 [ 0.018  1.     0.925  0.006  0.869  0.644]
 [ 0.017  0.925  1.     0.009  0.811  0.692]
 [-0.036  0.006  0.009  1.     0.011 -0.001]
 [ 0.026  0.869  0.811  0.011  1.     0.592]
 [ 0.017  0.644  0.692 -0.001  0.592  1.   ]]
key-bias cosine matrix
[[ 1.    -0.054 -0.104 -0.041  0.29  -0.095]
 [-0.054  1.     0.347 -0.093  0.41  -0.226]
 [-0.104  0.347  1.    -0.057  0.567  0.524]
 [-0.041 -0.093 -0.057  1.     0.022  0.074]
 [ 0.29   0.41   0.567  0.022  1.     0.373]
 [-0.095 -0.226  0.524  0.074  0.373  1.   ]]

LAYER 1 QK cosine matrix
[[1.    0.357 0.372 0.345 0.334 0.376]
 [0.357 1.    0.371 0.361 0.302 0.398]
 [0.372 0.371 1.    0.368 0.375 0.351]
 [0.345 0.361 0.368 1.    0.32  0.394]
 [0.334 0.302 0.375 0.32  1.    0.288]
 [0.376 0.398 0.351 0.394 0.288 1.   ]]
OV cosine matrix
[[ 1.    -0.02   0.03  -0.012  0.001  0.029]
 [-0.02   1.    -0.009 -0.028 -0.018  0.016]
 [ 0.03  -0.009  1.     0.001  0.014 -0.017]
 [-0.012 -0.028  0.001  1.    -0.001 -0.015]
 [ 0.001 -0.018  0.014 -0.001  1.    -0.014]
 [ 0.029  0.016 -0.017 -0.015 -0.014  1.   ]]
key-bias cosine matrix
[[1.    0.829 0.853 0.823 0.825 0.86 ]
 [0.829 1.    0.851 0.864 0.821 0.861]
 [0.853 0.851 1.    0.83  0.834 0.833]
 [0.823 0.864 0.83  1.    0.834 0.873]
 [0.825 0.821 0.834 0.834 1.    0.828]
 [0.86  0.861 0.833 0.873 0.828 1.   ]]

LAYER 2 QK cosine matrix
[[1.    0.128 0.161 0.117 0.179 0.134]
 [0.128 1.    0.116 0.086 0.121 0.116]
 [0.161 0.116 1.    0.101 0.144 0.123]
 [0.117 0.086 0.101 1.    0.092 0.093]
 [0.179 0.121 0.144 0.092 1.    0.134]
 [0.134 0.116 0.123 0.093 0.134 1.   ]]
OV cosine matrix
[[ 1.    -0.023 -0.039 -0.022 -0.005  0.001]
 [-0.023  1.    -0.001  0.002 -0.012 -0.008]
 [-0.039 -0.001  1.     0.013  0.004  0.022]
 [-0.022  0.002  0.013  1.     0.001  0.   ]
 [-0.005 -0.012  0.004  0.001  1.     0.004]
 [ 0.001 -0.008  0.022  0.     0.004  1.   ]]
key-bias cosine matrix
[[1.    0.807 0.766 0.703 0.82  0.835]
 [0.807 1.    0.811 0.719 0.824 0.837]
 [0.766 0.811 1.    0.699 0.832 0.827]
 [0.703 0.719 0.699 1.    0.715 0.73 ]
 [0.82  0.824 0.832 0.715 1.    0.845]
 [0.835 0.837 0.827 0.73  0.845 1.   ]]

LAYER 3 QK cosine matrix
[[1.    0.058 0.082 0.06  0.007 0.108]
 [0.058 1.    0.069 0.034 0.041 0.075]
 [0.082 0.069 1.    0.031 0.036 0.094]
 [0.06  0.034 0.031 1.    0.036 0.058]
 [0.007 0.041 0.036 0.036 1.    0.027]
 [0.108 0.075 0.094 0.058 0.027 1.   ]]
OV cosine matrix
[[ 1.    -0.012  0.024  0.011 -0.002  0.034]
 [-0.012  1.    -0.021  0.024  0.059  0.001]
 [ 0.024 -0.021  1.     0.003  0.078  0.026]
 [ 0.011  0.024  0.003  1.     0.042 -0.001]
 [-0.002  0.059  0.078  0.042  1.     0.057]
 [ 0.034  0.001  0.026 -0.001  0.057  1.   ]]
key-bias cosine matrix
[[ 1.     0.6    0.747  0.013  0.159  0.776]
 [ 0.6    1.     0.553  0.015  0.289  0.669]
 [ 0.747  0.553  1.     0.011  0.208  0.736]
 [ 0.013  0.015  0.011  1.     0.026 -0.046]
 [ 0.159  0.289  0.208  0.026  1.     0.254]
 [ 0.776  0.669  0.736 -0.046  0.254  1.   ]]

SPECTRA: first 12 singular values
L0H0 QK [0.248 0.102 0.047 0.043 0.037 0.036 0.034 0.031 0.026 0.023 0.022 0.022] OV [0.957 0.898 0.818 0.641 0.554 0.474 0.439 0.406 0.372 0.348 0.329 0.308]
L0H1 QK [0.15  0.042 0.021 0.012 0.01  0.007 0.007 0.004 0.004 0.004 0.003 0.003] OV [3.38  2.023 0.344 0.179 0.147 0.132 0.123 0.118 0.108 0.098 0.09  0.087]
L0H2 QK [0.102 0.018 0.016 0.012 0.008 0.007 0.005 0.004 0.004 0.004 0.003 0.003] OV [2.643 1.363 0.399 0.175 0.159 0.142 0.126 0.105 0.096 0.094 0.085 0.085]
L0H3 QK [0.244 0.222 0.201 0.182 0.179 0.157 0.155 0.149 0.14  0.136 0.131 0.128] OV [1.126 0.955 0.95  0.889 0.863 0.854 0.842 0.78  0.759 0.723 0.708 0.673]
L0H4 QK [0.08  0.022 0.019 0.013 0.011 0.008 0.007 0.006 0.005 0.005 0.004 0.004] OV [1.454 0.723 0.213 0.141 0.138 0.115 0.109 0.097 0.094 0.084 0.079 0.075]
L0H5 QK [0.032 0.004 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002] OV [16.278  8.778  2.833  1.117  1.039  0.631  0.533  0.448  0.413  0.326
  0.266  0.221]
L3H0 QK [0.435 0.414 0.39  0.38  0.373 0.36  0.357 0.347 0.337 0.333 0.331 0.328] OV [5.784 5.655 5.063 4.642 4.213 3.824 3.807 3.649 3.604 3.567 3.389 3.298]
L3H1 QK [0.345 0.308 0.285 0.253 0.244 0.227 0.211 0.207 0.2   0.193 0.19  0.186] OV [8.23  7.821 6.561 6.475 6.066 5.764 5.569 5.125 5.038 4.788 4.661 4.484]
L3H2 QK [0.383 0.304 0.294 0.277 0.266 0.258 0.254 0.243 0.239 0.231 0.229 0.223] OV [7.46  6.108 5.569 5.335 5.047 4.689 4.586 4.379 4.357 4.143 3.993 3.795]
L3H3 QK [0.322 0.311 0.307 0.304 0.297 0.294 0.288 0.286 0.284 0.282 0.277 0.273] OV [10.809  9.984  9.82   9.426  9.144  9.057  8.451  7.949  7.672  7.388
  7.361  6.959]
L3H4 QK [0.236 0.202 0.17  0.149 0.132 0.124 0.111 0.105 0.102 0.096 0.092 0.09 ] OV [21.266 17.675 16.977 15.046 14.398 13.303 12.126 11.541  8.688  8.574
  7.486  6.519]
L3H5 QK [0.454 0.321 0.315 0.299 0.289 0.288 0.284 0.28  0.276 0.271 0.265 0.261] OV [6.302 5.976 5.474 5.086 4.976 4.706 4.351 4.061 3.987 3.899 3.807 3.631]

CROSS-HEAD QK similarities: strongest other-layer matches
L0H0 [(np.float64(0.00979153483382163), 'L1H5'), (np.float64(0.008427259356622762), 'L2H0'), (np.float64(0.008223779217835316), 'L1H3')]
L0H1 [(np.float64(0.0010880394971872875), 'L2H0'), (np.float64(0.0008593703704631152), 'L2H2'), (np.float64(-0.0001032708915409376), 'L2H1')]
L0H2 [(np.float64(0.0050234992549716305), 'L2H0'), (np.float64(0.004594332635559284), 'L1H2'), (np.float64(0.004580946146990521), 'L1H4')]
L0H3 [(np.float64(0.016643867610997714), 'L1H5'), (np.float64(0.016533999939375973), 'L3H3'), (np.float64(0.016121030549748686), 'L1H0')]
L0H4 [(np.float64(0.005772833757418792), 'L2H2'), (np.float64(0.0036898938096945545), 'L1H4'), (np.float64(0.0027571174250421446), 'L1H2')]
L0H5 [(np.float64(0.010936402216938758), 'L3H4'), (np.float64(-0.001411510777306644), 'L3H3'), (np.float64(-0.002164029793589887), 'L2H0')]
L1H0 [(np.float64(0.18506694011229038), 'L2H0'), (np.float64(0.1488677247000508), 'L2H4'), (np.float64(0.12564662600924476), 'L2H2')]
L1H1 [(np.float64(0.17022256856726697), 'L2H0'), (np.float64(0.1573422419093759), 'L2H4'), (np.float64(0.13271517165724014), 'L2H1')]
L1H2 [(np.float64(0.18100756505856744), 'L2H0'), (np.float64(0.1668710304689896), 'L2H4'), (np.float64(0.12374133848220824), 'L2H5')]
L1H3 [(np.float64(0.19214667678145736), 'L2H0'), (np.float64(0.16266425883219318), 'L2H4'), (np.float64(0.13267644666785067), 'L2H5')]
L1H4 [(np.float64(0.1772663620980154), 'L2H0'), (np.float64(0.12116380081634327), 'L2H4'), (np.float64(0.09611140079226985), 'L2H2')]
L1H5 [(np.float64(0.17310967356438595), 'L2H0'), (np.float64(0.14688132938479792), 'L2H4'), (np.float64(0.12588727047420217), 'L2H5')]
L2H0 [(np.float64(0.19214667678145736), 'L1H3'), (np.float64(0.18506694011229038), 'L1H0'), (np.float64(0.18100756505856744), 'L1H2')]
L2H1 [(np.float64(0.13271517165724014), 'L1H1'), (np.float64(0.12621364897594486), 'L1H3'), (np.float64(0.12278561406882613), 'L1H2')]
L2H2 [(np.float64(0.12742023396713717), 'L1H3'), (np.float64(0.12564662600924476), 'L1H0'), (np.float64(0.12162773073563991), 'L1H1')]
L2H3 [(np.float64(0.09685903841896927), 'L1H3'), (np.float64(0.0910249506652174), 'L1H1'), (np.float64(0.08406845805609671), 'L1H5')]
L2H4 [(np.float64(0.1668710304689896), 'L1H2'), (np.float64(0.16266425883219318), 'L1H3'), (np.float64(0.1573422419093759), 'L1H1')]
L2H5 [(np.float64(0.13267644666785067), 'L1H3'), (np.float64(0.12880880741147002), 'L1H1'), (np.float64(0.12588727047420217), 'L1H5')]
L3H0 [(np.float64(0.06303436921510018), 'L2H4'), (np.float64(0.061698054643142985), 'L2H1'), (np.float64(0.0586590497588326), 'L2H5')]
L3H1 [(np.float64(0.0507185844159886), 'L2H4'), (np.float64(0.050181191045734784), 'L2H0'), (np.float64(0.047482565641790125), 'L1H3')]
L3H2 [(np.float64(0.06161449958325272), 'L2H2'), (np.float64(0.061561032715421016), 'L2H0'), (np.float64(0.059263577539727344), 'L1H3')]
L3H3 [(np.float64(0.021274040539388073), 'L2H5'), (np.float64(0.016533999939375973), 'L0H3'), (np.float64(0.01648908421968714), 'L2H1')]
L3H4 [(np.float64(0.017223015933478858), 'L1H3'), (np.float64(0.01672416710494667), 'L2H0'), (np.float64(0.015104739991435589), 'L2H3')]
L3H5 [(np.float64(0.05636998232246223), 'L1H3'), (np.float64(0.05594018357599625), 'L2H1'), (np.float64(0.053872260032412106), 'L2H0')]

MLP LINEAR-ALGEBRA STATISTICS (no nonlinearities applied)
L 0 FC spectrum [17.58 13.47 11.76 10.19  9.61  9.54  9.34  9.14  8.75  8.68  8.58  8.39
  8.    7.93  7.84  7.73  7.52  7.39  7.16  7.08]
PROJ spectrum [10.9   7.7   7.17  6.64  6.54  6.29  6.2   6.13  5.94  5.92  5.76  5.64
  5.55  5.48  5.39  5.36  5.26  5.21  5.17  5.15]
PROJ@FC spectrum [125.96  60.95  37.56  32.55  31.    29.68  28.22  27.4   26.51  25.84
  25.26  24.58  23.93  23.43  22.22  21.62  21.43  21.02  20.57  20.24] trace/norm 0.068 neuron input/output cos quantiles [-0.619 -0.118 -0.022  0.087  0.599]
L 1 FC spectrum [22.95 13.34 13.21 13.05 12.74 12.71 12.3  12.24 11.92 11.81 11.75 11.47
 11.43 11.31 11.18 11.05 10.96 10.58 10.53 10.28]
PROJ spectrum [9.04 8.46 8.1  7.33 7.32 7.09 6.77 6.67 6.57 6.43 6.37 6.28 6.25 6.23
 6.13 6.05 6.01 5.96 5.91 5.9 ]
PROJ@FC spectrum [74.44 32.73 28.44 27.61 26.93 26.2  25.44 25.24 24.83 24.1  23.77 23.48
 22.89 22.71 22.09 21.9  21.63 21.44 21.03 20.84] trace/norm -2.058 neuron input/output cos quantiles [-0.535 -0.143 -0.06   0.028  0.446]
L 2 FC spectrum [20.71 12.17 11.48 11.41 11.12 10.28 10.09  9.9   9.84  9.75  9.66  9.6
  9.56  9.51  9.34  9.25  9.15  9.07  9.01  8.96]
PROJ spectrum [10.2   9.03  8.88  8.41  8.22  8.09  7.99  7.83  7.68  7.49  7.37  7.26
  7.17  7.07  7.03  6.8   6.74  6.66  6.46  6.43]
PROJ@FC spectrum [78.87 33.38 30.76 30.37 29.11 28.15 28.07 26.66 25.88 25.73 25.46 25.05
 24.7  24.16 23.66 23.24 23.04 22.55 22.08 21.91] trace/norm -3.224 neuron input/output cos quantiles [-0.439 -0.175 -0.093  0.     0.445]
L 3 FC spectrum [19.3  11.   10.8  10.27  9.8   9.56  9.5   9.38  9.02  8.85  8.78  8.63
  8.41  8.36  8.22  8.06  8.03  7.96  7.85  7.79]
PROJ spectrum [28.46 22.21 21.34 20.71 19.94 19.66 18.99 18.74 18.29 17.46 17.13 16.56
 15.33 14.87 14.33 13.44 12.67 12.45 12.32 11.53]
PROJ@FC spectrum [187.97  87.29  73.96  51.12  47.59  45.79  43.3   42.18  40.74  39.28
  38.62  35.97  33.01  31.93  31.52  30.51  28.8   28.34  27.74  26.58] trace/norm -2.422 neuron input/output cos quantiles [-0.389 -0.209 -0.096  0.04   0.262]

Most anisotropic coordinates
L 0 largest ln1 biases [(312, -0.095, 0.214), (146, 0.091, 0.18), (12, 0.086, 0.12), (104, -0.084, 0.211), (289, 0.083, 0.376), (156, -0.078, 0.095), (303, -0.078, 0.404), (328, 0.076, 0.173)]
L 1 largest ln1 biases [(39, -1.568, 0.299), (58, 1.365, 0.375), (99, -1.336, 0.716), (184, -0.562, 0.249), (383, -0.462, 0.338), (21, -0.43, 1.085), (153, 0.297, 0.42), (266, 0.277, 0.47)]
L 2 largest ln1 biases [(99, -1.659, 0.943), (58, 1.332, 0.477), (39, -1.199, 0.422), (383, -0.507, 0.317), (184, -0.505, 0.337), (21, -0.453, 1.093), (63, -0.325, 0.481), (266, 0.299, 0.491)]
L 3 largest ln1 biases [(58, 0.824, 0.466), (99, -0.764, 0.751), (5, 0.436, 0.541), (383, -0.397, 0.408), (266, 0.343, 0.524), (21, -0.315, 0.802), (184, -0.289, 0.562), (45, 0.289, 0.511)]
Largest L0 ln1 scales [(180, 0.978), (184, 0.974), (162, 0.97), (99, 0.917), (211, 0.896), (256, 0.892), (300, 0.804), (317, 0.804), (223, 0.802), (39, 0.799), (173, 0.793), (4, 0.786), (228, 0.786), (69, 0.772), (89, 0.767), (100, 0.766), (56, 0.753), (65, 0.749), (354, 0.746), (246, 0.726)]

```
CLI OUTPUT IN EVENT ORDER
ERROR
Failed to read global AGENTS.md instructions from `<local-home>/.codex/AGENTS.md`: Operation not permitted (os error 1)

ERROR
Code Mode is unavailable because code-mode host is disabled. Code mode will fail closed; enable `features.code_mode_host` and install `codex-code-mode-host`.

AGENT_MESSAGE
```python
import numpy as np
from scipy.linalg import svd, eigvals
from threadpoolctl import threadpool_limits

with threadpool_limits(limits=2):
    A=[]; B=[]; Q=[]; K=[]; V=[]; O=[]
    for l in range(4):
        g=W[f"ln1_w.{l}"].astype(float)
        for j in range(6):
            s=slice(64*j,64*j+64)
            mats=[W[f"{n}.{l}"][s].astype(float)*g for n in ["W_q","W_k","W_v"]]
            for m in mats:
                m-=m.mean(1,keepdims=True)
            q,k,v=mats
            o=W[f"W_o.{l}"][:,s].astype(float)
            Q.append(q); K.append(k); V.append(v); O.append(o)
            A.append(q.T@k/8); B.append(o@v)
    print("L0 QK eigenvalues, dominant invariant-space overlaps")
    for j in range(6):
        u,s,vt=svd(A[j],full_matrices=False)
        ev=eigvals(K[j]@Q[j].T/8)
        ev=ev[np.argsort(np.abs(ev))[::-1]]
        r=max(1,int(np.searchsorted(np.cumsum(s*s)/sum(s*s),.95))+1)
        left=u[:,:r]; right=vt[:r].T
        vv=svd(V[j],full_matrices=False)[2][:min(28,r+5)].T
        print("H",j,"rank95",r,"L/R overlap",round(np.linalg.norm(left.T@right)**2/r,3),
              "V energy in QK-left/right",np.round([
                  np.linalg.norm(V[j]@left)**2/np.linalg.norm(V[j])**2,
                  np.linalg.norm(V[j]@right)**2/np.linalg.norm(V[j])**2],3))
        print("eigenvalues",np.round(ev[:16],3))
    print("\nQK-OV composition: trace(A_lh @ B_earlier)/(|A_lh| |B_earlier|)")
    for i in range(6,24):
        vals=[np.trace(A[i]@B[j])/(np.linalg.norm(A[i])*np.linalg.norm(B[j]))
              for j in range((i//6)*6)]
        print("L%dH%d"%(i//6,i%6),np.round(vals,3))
    print("\nStrongest composition positivity, with nonrandom comparison")
    for i in range(6,24):
        cand=[]
        for j in range((i//6)*6):
            C=A[i]@B[j]
            n=np.linalg.norm(C)
            t=np.trace(C)/n
            sym=np.sum(C*C.T)/(n*n)
            gain=n/(np.linalg.norm(A[i])*np.linalg.norm(B[j]))
            cand.append((t,sym,gain,j))
        cand.sort(reverse=True)
        print("L%dH%d"%(i//6,i%6),[
            ("L%dH%d"%(j//6,j%6),round(t,3),round(sym,3),round(gain,3))
            for t,sym,gain,j in cand[:4]])
    print("\nL0 value-subspace sharing and query/key orthogonality")
    vv=np.concatenate(V[:6])
    _,ss,vt=svd(vv,full_matrices=False)
    print("Combined value singular values",np.round(ss[:45],3))
    for r in [2,10,20,28,40]:
        basis=vt[:r].T
        print("value basis rank",r)
        for j in range(6):
            print("H",j,"Q/K/V energy",np.round([
                np.linalg.norm(M@basis)**2/np.linalg.norm(M)**2
                for M in [Q[j],K[j],V[j]]],3))
```


PERMITTED EXPERIMENT HARNESS RECORD: python
{
  "run": 3,
  "turn": "t003",
  "code": "import numpy as np\nfrom scipy.linalg import svd, eigvals\nfrom threadpoolctl import threadpool_limits\n\nwith threadpool_limits(limits=2):\n    A=[]; B=[]; Q=[]; K=[]; V=[]; O=[]\n    for l in range(4):\n        g=W[f\"ln1_w.{l}\"].astype(float)\n        for j in range(6):\n            s=slice(64*j,64*j+64)\n            mats=[W[f\"{n}.{l}\"][s].astype(float)*g for n in [\"W_q\",\"W_k\",\"W_v\"]]\n            for m in mats:\n                m-=m.mean(1,keepdims=True)\n            q,k,v=mats\n            o=W[f\"W_o.{l}\"][:,s].astype(float)\n            Q.append(q); K.append(k); V.append(v); O.append(o)\n            A.append(q.T@k/8); B.append(o@v)\n    print(\"L0 QK eigenvalues, dominant invariant-space overlaps\")\n    for j in range(6):\n        u,s,vt=svd(A[j],full_matrices=False)\n        ev=eigvals(K[j]@Q[j].T/8)\n        ev=ev[np.argsort(np.abs(ev))[::-1]]\n        r=max(1,int(np.searchsorted(np.cumsum(s*s)/sum(s*s),.95))+1)\n        left=u[:,:r]; right=vt[:r].T\n        vv=svd(V[j],full_matrices=False)[2][:min(28,r+5)].T\n        print(\"H\",j,\"rank95\",r,\"L/R overlap\",round(np.linalg.norm(left.T@right)**2/r,3),\n              \"V energy in QK-left/right\",np.round([\n                  np.linalg.norm(V[j]@left)**2/np.linalg.norm(V[j])**2,\n                  np.linalg.norm(V[j]@right)**2/np.linalg.norm(V[j])**2],3))\n        print(\"eigenvalues\",np.round(ev[:16],3))\n    print(\"\\nQK-OV composition: trace(A_lh @ B_earlier)/(|A_lh| |B_earlier|)\")\n    for i in range(6,24):\n        vals=[np.trace(A[i]@B[j])/(np.linalg.norm(A[i])*np.linalg.norm(B[j]))\n              for j in range((i//6)*6)]\n        print(\"L%dH%d\"%(i//6,i%6),np.round(vals,3))\n    print(\"\\nStrongest composition positivity, with nonrandom comparison\")\n    for i in range(6,24):\n        cand=[]\n        for j in range((i//6)*6):\n            C=A[i]@B[j]\n            n=np.linalg.norm(C)\n            t=np.trace(C)/n\n            sym=np.sum(C*C.T)/(n*n)\n            gain=n/(np.linalg.norm(A[i])*np.linalg.norm(B[j]))\n            cand.append((t,sym,gain,j))\n        cand.sort(reverse=True)\n        print(\"L%dH%d\"%(i//6,i%6),[\n            (\"L%dH%d\"%(j//6,j%6),round(t,3),round(sym,3),round(gain,3))\n            for t,sym,gain,j in cand[:4]])\n    print(\"\\nL0 value-subspace sharing and query/key orthogonality\")\n    vv=np.concatenate(V[:6])\n    _,ss,vt=svd(vv,full_matrices=False)\n    print(\"Combined value singular values\",np.round(ss[:45],3))\n    for r in [2,10,20,28,40]:\n        basis=vt[:r].T\n        print(\"value basis rank\",r)\n        for j in range(6):\n            print(\"H\",j,\"Q/K/V energy\",np.round([\n                np.linalg.norm(M@basis)**2/np.linalg.norm(M)**2\n                for M in [Q[j],K[j],V[j]]],3))",
  "out": "L0 QK eigenvalues, dominant invariant-space overlaps\nH 0 rank95 10 L/R overlap 0.445 V energy in QK-left/right [0.057 0.082]\neigenvalues [ 0.08 +0.j     0.048+0.j    -0.024+0.006j -0.024-0.006j -0.023+0.j\n  0.018+0.013j  0.018-0.013j -0.02 +0.j    -0.014+0.012j -0.014-0.012j\n -0.014+0.003j -0.014-0.003j -0.014+0.j    -0.011+0.004j -0.011-0.004j\n -0.011+0.002j]\nH 1 rank95 2 L/R overlap 0.106 V energy in QK-left/right [0.199 0.043]\neigenvalues [-0.062+0.j    -0.01 +0.j    -0.009+0.j     0.004+0.j    -0.004+0.j\n -0.003+0.002j -0.003-0.002j -0.002+0.j    -0.002-0.j    -0.002+0.001j\n -0.002-0.001j -0.001-0.j    -0.001+0.j    -0.001-0.001j -0.001+0.001j\n  0.001+0.j   ]\nH 2 rank95 3 L/R overlap 0.268 V energy in QK-left/right [0.212 0.111]\neigenvalues [-0.057+0.j    -0.007+0.003j -0.007-0.003j -0.003+0.001j -0.003-0.001j\n -0.002+0.j    -0.001+0.j    -0.001-0.j    -0.001+0.001j -0.001-0.001j\n  0.001+0.001j  0.001-0.001j -0.   +0.001j -0.   -0.001j -0.001+0.j\n  0.   +0.001j]\nH 3 rank95 23 L/R overlap 0.799 V energy in QK-left/right [0.143 0.165]\neigenvalues [0.137+0.133j 0.137-0.133j 0.11 +0.089j 0.11 -0.089j 0.095+0.098j\n 0.095-0.098j 0.084+0.104j 0.084-0.104j 0.064+0.114j 0.064-0.114j\n 0.096+0.069j 0.096-0.069j 0.011+0.117j 0.011-0.117j 0.112+0.j\n 0.056-0.07j ]\nH 4 rank95 5 L/R overlap 0.137 V energy in QK-left/right [0.175 0.055]\neigenvalues [-0.015+0.j    -0.01 +0.j    -0.008+0.j    -0.003+0.j    -0.003-0.j\n -0.002+0.001j -0.002-0.001j -0.   +0.002j -0.   -0.002j -0.001+0.001j\n -0.001-0.001j -0.002+0.j    -0.001-0.001j -0.001+0.001j  0.001-0.001j\n  0.001+0.001j]\nH 5 rank95 10 L/R overlap 0.105 V energy in QK-left/right [0.347 0.038]\neigenvalues [-0.005+0.j     0.001+0.j    -0.001+0.j    -0.   +0.001j -0.   -0.001j\n -0.001+0.j    -0.001+0.j    -0.001-0.j     0.   +0.001j  0.   -0.001j\n -0.   +0.001j -0.   -0.001j -0.   +0.001j -0.   -0.001j  0.   +0.001j\n  0.   -0.001j]\n\nQK-OV composition: trace(A_lh @ B_earlier)/(|A_lh| |B_earlier|)\nL1H0 [0.002 0.034 0.05  0.006 0.029 0.048]\nL1H1 [0.    0.006 0.025 0.014 0.004 0.021]\nL1H2 [-0.002  0.03   0.042  0.012  0.031  0.047]\nL1H3 [0.001 0.028 0.045 0.005 0.024 0.043]\nL1H4 [0.001 0.017 0.03  0.001 0.023 0.037]\nL1H5 [-0.001  0.019  0.04   0.011  0.019  0.031]\nL2H0 [-0.     0.038  0.058  0.004  0.023  0.067  0.001  0.007  0.004  0.009\n -0.007  0.002]\nL2H1 [ 0.001  0.021  0.033  0.001  0.013  0.042 -0.004 -0.009 -0.014 -0.009\n -0.015 -0.01 ]\nL2H2 [ 0.003  0.026  0.039  0.005  0.014  0.046 -0.001  0.003 -0.001 -0.002\n -0.007  0.001]\nL2H3 [ 0.003  0.016  0.023  0.005  0.012  0.025  0.002  0.002 -0.002 -0.\n -0.007 -0.004]\nL2H4 [-0.001  0.03   0.045  0.009  0.022  0.051 -0.     0.002 -0.012 -0.015\n -0.003  0.002]\nL2H5 [ 0.001  0.021  0.036  0.001  0.014  0.047 -0.009 -0.    -0.008 -0.007\n -0.007 -0.009]\nL3H0 [-0.002  0.008  0.013 -0.01   0.005  0.013 -0.01  -0.008 -0.018 -0.013\n -0.012 -0.014 -0.008 -0.014 -0.019 -0.016 -0.036 -0.02 ]\nL3H1 [ 0.002  0.01   0.013 -0.002  0.004  0.014 -0.006  0.002  0.003 -0.001\n -0.003  0.002 -0.009 -0.    -0.004  0.003 -0.002 -0.002]\nL3H2 [-0.     0.007  0.012  0.002  0.001  0.004 -0.007 -0.001  0.    -0.\n -0.002 -0.001 -0.003 -0.001 -0.011 -0.008 -0.01  -0.005]\nL3H3 [-0.008  0.002  0.002  0.063  0.002 -0.002  0.031  0.021  0.001 -0.003\n -0.019  0.027  0.028  0.033  0.009  0.013  0.022  0.048]\nL3H4 [ 0.005  0.009  0.009  0.006  0.01   0.009  0.     0.002  0.002 -0.001\n  0.005  0.002  0.008  0.009  0.014  0.009  0.012  0.009]\nL3H5 [-0.     0.002  0.007 -0.003  0.     0.009 -0.012 -0.007 -0.005 -0.009\n -0.007 -0.007 -0.015 -0.016 -0.013 -0.013 -0.012 -0.01 ]\n\nStrongest composition positivity, with nonrandom comparison\nL1H0 [('L0H2', np.float64(0.134), np.float64(0.009), np.float64(0.376)), ('L0H5', np.float64(0.103), np.float64(0.002), np.float64(0.467)), ('L0H3', np.float64(0.102), np.float64(0.013), np.float64(0.057)), ('L0H4', np.float64(0.096), np.float64(0.013), np.float64(0.304))]\nL1H1 [('L0H3', np.float64(0.218), np.float64(0.016), np.float64(0.065)), ('L0H2', np.float64(0.065), np.float64(0.005), np.float64(0.387)), ('L0H5', np.float64(0.043), np.float64(0.004), np.float64(0.489)), ('L0H1', np.float64(0.017), np.float64(0.005), np.float64(0.371))]\nL1H2 [('L0H3', np.float64(0.168), np.float64(0.017), np.float64(0.072)), ('L0H2', np.float64(0.106), np.float64(0.006), np.float64(0.396)), ('L0H4', np.float64(0.1), np.float64(0.011), np.float64(0.313)), ('L0H5', np.float64(0.092), np.float64(0.002), np.float64(0.509))]\nL1H3 [('L0H2', np.float64(0.113), np.float64(0.008), np.float64(0.4)), ('L0H5', np.float64(0.085), np.float64(0.002), np.float64(0.508)), ('L0H3', np.float64(0.076), np.float64(0.014), np.float64(0.068)), ('L0H4', np.float64(0.075), np.float64(0.014), np.float64(0.321))]\nL1H4 [('L0H2', np.float64(0.079), np.float64(-0.0), np.float64(0.375)), ('L0H4', np.float64(0.078), np.float64(0.004), np.float64(0.297)), ('L0H5', np.float64(0.075), np.float64(-0.001), np.float64(0.494)), ('L0H1', np.float64(0.046), np.float64(-0.002), np.float64(0.36))]\nL1H5 [('L0H3', np.float64(0.2), np.float64(0.029), np.float64(0.056)), ('L0H2', np.float64(0.102), np.float64(0.007), np.float64(0.387)), ('L0H5', np.float64(0.064), np.float64(0.003), np.float64(0.478)), ('L0H4', np.float64(0.062), np.float64(0.021), np.float64(0.314))]\nL2H0 [('L1H3', np.float64(0.206), np.float64(-0.001), np.float64(0.045)), ('L0H2', np.float64(0.196), np.float64(0.027), np.float64(0.298)), ('L0H5', np.float64(0.193), np.float64(0.016), np.float64(0.345)), ('L1H1', np.float64(0.163), np.float64(0.003), np.float64(0.043))]\nL2H1 [('L0H5', np.float64(0.199), np.float64(0.014), np.float64(0.214)), ('L0H2', np.float64(0.179), np.float64(0.023), np.float64(0.186)), ('L0H1', np.float64(0.117), np.float64(0.022), np.float64(0.18)), ('L0H4', np.float64(0.08), np.float64(0.023), np.float64(0.161))]\nL2H2 [('L0H5', np.float64(0.186), np.float64(0.017), np.float64(0.248)), ('L0H2', np.float64(0.182), np.float64(0.027), np.float64(0.214)), ('L0H1', np.float64(0.124), np.float64(0.024), np.float64(0.208)), ('L0H3', np.float64(0.1), np.float64(0.0), np.float64(0.053))]\nL2H3 [('L0H2', np.float64(0.129), np.float64(0.012), np.float64(0.174)), ('L0H5', np.float64(0.112), np.float64(0.007), np.float64(0.22)), ('L0H1', np.float64(0.097), np.float64(0.008), np.float64(0.168)), ('L0H4', np.float64(0.086), np.float64(0.007), np.float64(0.141))]\nL2H4 [('L0H2', np.float64(0.186), np.float64(0.025), np.float64(0.243)), ('L0H5', np.float64(0.182), np.float64(0.015), np.float64(0.281)), ('L0H3', np.float64(0.16), np.float64(0.009), np.float64(0.055)), ('L0H1', np.float64(0.128), np.float64(0.021), np.float64(0.233))]\nL2H5 [('L0H5', np.float64(0.212), np.float64(0.018), np.float64(0.224)), ('L0H2', np.float64(0.188), np.float64(0.021), np.float64(0.193)), ('L0H1', np.float64(0.113), np.float64(0.021), np.float64(0.187)), ('L0H4', np.float64(0.081), np.float64(0.025), np.float64(0.167))]\nL3H0 [('L0H2', np.float64(0.107), np.float64(0.015), np.float64(0.119)), ('L0H5', np.float64(0.087), np.float64(0.004), np.float64(0.15)), ('L0H1', np.float64(0.069), np.float64(0.01), np.float64(0.117)), ('L0H4', np.float64(0.048), np.float64(0.014), np.float64(0.103))]\nL3H1 [('L0H2', np.float64(0.093), np.float64(0.013), np.float64(0.144)), ('L0H5', np.float64(0.077), np.float64(0.005), np.float64(0.182)), ('L1H2', np.float64(0.073), np.float64(0.0), np.float64(0.046)), ('L0H1', np.float64(0.07), np.float64(0.014), np.float64(0.14))]\nL3H2 [('L0H2', np.float64(0.081), np.float64(0.015), np.float64(0.147)), ('L0H1', np.float64(0.048), np.float64(0.014), np.float64(0.145)), ('L0H3', np.float64(0.034), np.float64(0.006), np.float64(0.051)), ('L0H5', np.float64(0.019), np.float64(0.005), np.float64(0.188))]\nL3H3 [('L0H3', np.float64(0.924), np.float64(0.067), np.float64(0.068)), ('L2H5', np.float64(0.809), np.float64(0.013), np.float64(0.06)), ('L2H1', np.float64(0.563), np.float64(0.002), np.float64(0.058)), ('L1H0', np.float64(0.515), np.float64(0.001), np.float64(0.059))]\nL3H4 [('L2H2', np.float64(0.281), np.float64(0.002), np.float64(0.051)), ('L2H4', np.float64(0.273), np.float64(0.006), np.float64(0.045)), ('L2H5', np.float64(0.203), np.float64(0.001), np.float64(0.046)), ('L0H4', np.float64(0.196), np.float64(0.022), np.float64(0.053))]\nL3H5 [('L0H2', np.float64(0.05), np.float64(0.004), np.float64(0.146)), ('L0H5', np.float64(0.048), np.float64(0.001), np.float64(0.185)), ('L0H1', np.float64(0.017), np.float64(0.004), np.float64(0.142)), ('L0H4', np.float64(0.0), np.float64(0.01), np.float64(0.12))]\n\nL0 value-subspace sharing and query/key orthogonality\nCombined value singular values [3.339 2.305 1.516 0.814 0.773 0.711 0.682 0.672 0.651 0.633 0.618 0.597\n 0.574 0.561 0.558 0.537 0.525 0.508 0.498 0.487 0.476 0.469 0.461 0.45\n 0.432 0.427 0.417 0.41  0.408 0.395 0.388 0.382 0.38  0.376 0.363 0.359\n 0.356 0.348 0.342 0.334 0.333 0.326 0.317 0.308 0.307]\nvalue basis rank 2\nH 0 Q/K/V energy [0.234 0.308 0.003]\nH 1 Q/K/V energy [0.249 0.056 0.524]\nH 2 Q/K/V energy [0.31 0.08 0.52]\nH 3 Q/K/V energy [0.044 0.198 0.003]\nH 4 Q/K/V energy [0.14  0.045 0.339]\nH 5 Q/K/V energy [0.449 0.007 0.721]\nvalue basis rank 10\nH 0 Q/K/V energy [0.409 0.381 0.268]\nH 1 Q/K/V energy [0.54  0.18  0.678]\nH 2 Q/K/V energy [0.473 0.176 0.631]\nH 3 Q/K/V energy [0.091 0.243 0.214]\nH 4 Q/K/V energy [0.38  0.135 0.467]\nH 5 Q/K/V energy [0.527 0.096 0.891]\nvalue basis rank 20\nH 0 Q/K/V energy [0.459 0.44  0.514]\nH 1 Q/K/V energy [0.575 0.28  0.712]\nH 2 Q/K/V energy [0.503 0.256 0.667]\nH 3 Q/K/V energy [0.125 0.275 0.51 ]\nH 4 Q/K/V energy [0.414 0.197 0.504]\nH 5 Q/K/V energy [0.548 0.15  0.924]\nvalue basis rank 28\nH 0 Q/K/V energy [0.499 0.489 0.617]\nH 1 Q/K/V energy [0.595 0.356 0.737]\nH 2 Q/K/V energy [0.527 0.318 0.697]\nH 3 Q/K/V energy [0.175 0.324 0.651]\nH 4 Q/K/V energy [0.44  0.247 0.549]\nH 5 Q/K/V energy [0.573 0.198 0.943]\nvalue basis rank 40\nH 0 Q/K/V energy [0.569 0.576 0.711]\nH 1 Q/K/V energy [0.641 0.419 0.789]\nH 2 Q/K/V energy [0.573 0.383 0.754]\nH 3 Q/K/V energy [0.31  0.467 0.774]\nH 4 Q/K/V energy [0.509 0.317 0.628]\nH 5 Q/K/V energy [0.61  0.275 0.958]\n",
  "seconds": 1.114,
  "rc": 0,
  "timed_out": false,
  "truncated": false,
  "code_sha256": "cbdb2c519218c533235a4b711fe9324d8541ec4be41eabc8bf147dee056f95b4",
  "weights_sha256": "04ec0b300d207b26b92a1af6d49d56d452833e39b35826200bc1d821e5b7d930"
}

EXACT HARNESS FEEDBACK
L0 QK eigenvalues, dominant invariant-space overlaps
H 0 rank95 10 L/R overlap 0.445 V energy in QK-left/right [0.057 0.082]
eigenvalues [ 0.08 +0.j     0.048+0.j    -0.024+0.006j -0.024-0.006j -0.023+0.j
  0.018+0.013j  0.018-0.013j -0.02 +0.j    -0.014+0.012j -0.014-0.012j
 -0.014+0.003j -0.014-0.003j -0.014+0.j    -0.011+0.004j -0.011-0.004j
 -0.011+0.002j]
H 1 rank95 2 L/R overlap 0.106 V energy in QK-left/right [0.199 0.043]
eigenvalues [-0.062+0.j    -0.01 +0.j    -0.009+0.j     0.004+0.j    -0.004+0.j
 -0.003+0.002j -0.003-0.002j -0.002+0.j    -0.002-0.j    -0.002+0.001j
 -0.002-0.001j -0.001-0.j    -0.001+0.j    -0.001-0.001j -0.001+0.001j
  0.001+0.j   ]
H 2 rank95 3 L/R overlap 0.268 V energy in QK-left/right [0.212 0.111]
eigenvalues [-0.057+0.j    -0.007+0.003j -0.007-0.003j -0.003+0.001j -0.003-0.001j
 -0.002+0.j    -0.001+0.j    -0.001-0.j    -0.001+0.001j -0.001-0.001j
  0.001+0.001j  0.001-0.001j -0.   +0.001j -0.   -0.001j -0.001+0.j
  0.   +0.001j]
H 3 rank95 23 L/R overlap 0.799 V energy in QK-left/right [0.143 0.165]
eigenvalues [0.137+0.133j 0.137-0.133j 0.11 +0.089j 0.11 -0.089j 0.095+0.098j
 0.095-0.098j 0.084+0.104j 0.084-0.104j 0.064+0.114j 0.064-0.114j
 0.096+0.069j 0.096-0.069j 0.011+0.117j 0.011-0.117j 0.112+0.j
 0.056-0.07j ]
H 4 rank95 5 L/R overlap 0.137 V energy in QK-left/right [0.175 0.055]
eigenvalues [-0.015+0.j    -0.01 +0.j    -0.008+0.j    -0.003+0.j    -0.003-0.j
 -0.002+0.001j -0.002-0.001j -0.   +0.002j -0.   -0.002j -0.001+0.001j
 -0.001-0.001j -0.002+0.j    -0.001-0.001j -0.001+0.001j  0.001-0.001j
  0.001+0.001j]
H 5 rank95 10 L/R overlap 0.105 V energy in QK-left/right [0.347 0.038]
eigenvalues [-0.005+0.j     0.001+0.j    -0.001+0.j    -0.   +0.001j -0.   -0.001j
 -0.001+0.j    -0.001+0.j    -0.001-0.j     0.   +0.001j  0.   -0.001j
 -0.   +0.001j -0.   -0.001j -0.   +0.001j -0.   -0.001j  0.   +0.001j
  0.   -0.001j]

QK-OV composition: trace(A_lh @ B_earlier)/(|A_lh| |B_earlier|)
L1H0 [0.002 0.034 0.05  0.006 0.029 0.048]
L1H1 [0.    0.006 0.025 0.014 0.004 0.021]
L1H2 [-0.002  0.03   0.042  0.012  0.031  0.047]
L1H3 [0.001 0.028 0.045 0.005 0.024 0.043]
L1H4 [0.001 0.017 0.03  0.001 0.023 0.037]
L1H5 [-0.001  0.019  0.04   0.011  0.019  0.031]
L2H0 [-0.     0.038  0.058  0.004  0.023  0.067  0.001  0.007  0.004  0.009
 -0.007  0.002]
L2H1 [ 0.001  0.021  0.033  0.001  0.013  0.042 -0.004 -0.009 -0.014 -0.009
 -0.015 -0.01 ]
L2H2 [ 0.003  0.026  0.039  0.005  0.014  0.046 -0.001  0.003 -0.001 -0.002
 -0.007  0.001]
L2H3 [ 0.003  0.016  0.023  0.005  0.012  0.025  0.002  0.002 -0.002 -0.
 -0.007 -0.004]
L2H4 [-0.001  0.03   0.045  0.009  0.022  0.051 -0.     0.002 -0.012 -0.015
 -0.003  0.002]
L2H5 [ 0.001  0.021  0.036  0.001  0.014  0.047 -0.009 -0.    -0.008 -0.007
 -0.007 -0.009]
L3H0 [-0.002  0.008  0.013 -0.01   0.005  0.013 -0.01  -0.008 -0.018 -0.013
 -0.012 -0.014 -0.008 -0.014 -0.019 -0.016 -0.036 -0.02 ]
L3H1 [ 0.002  0.01   0.013 -0.002  0.004  0.014 -0.006  0.002  0.003 -0.001
 -0.003  0.002 -0.009 -0.    -0.004  0.003 -0.002 -0.002]
L3H2 [-0.     0.007  0.012  0.002  0.001  0.004 -0.007 -0.001  0.    -0.
 -0.002 -0.001 -0.003 -0.001 -0.011 -0.008 -0.01  -0.005]
L3H3 [-0.008  0.002  0.002  0.063  0.002 -0.002  0.031  0.021  0.001 -0.003
 -0.019  0.027  0.028  0.033  0.009  0.013  0.022  0.048]
L3H4 [ 0.005  0.009  0.009  0.006  0.01   0.009  0.     0.002  0.002 -0.001
  0.005  0.002  0.008  0.009  0.014  0.009  0.012  0.009]
L3H5 [-0.     0.002  0.007 -0.003  0.     0.009 -0.012 -0.007 -0.005 -0.009
 -0.007 -0.007 -0.015 -0.016 -0.013 -0.013 -0.012 -0.01 ]

Strongest composition positivity, with nonrandom comparison
L1H0 [('L0H2', np.float64(0.134), np.float64(0.009), np.float64(0.376)), ('L0H5', np.float64(0.103), np.float64(0.002), np.float64(0.467)), ('L0H3', np.float64(0.102), np.float64(0.013), np.float64(0.057)), ('L0H4', np.float64(0.096), np.float64(0.013), np.float64(0.304))]
L1H1 [('L0H3', np.float64(0.218), np.float64(0.016), np.float64(0.065)), ('L0H2', np.float64(0.065), np.float64(0.005), np.float64(0.387)), ('L0H5', np.float64(0.043), np.float64(0.004), np.float64(0.489)), ('L0H1', np.float64(0.017), np.float64(0.005), np.float64(0.371))]
L1H2 [('L0H3', np.float64(0.168), np.float64(0.017), np.float64(0.072)), ('L0H2', np.float64(0.106), np.float64(0.006), np.float64(0.396)), ('L0H4', np.float64(0.1), np.float64(0.011), np.float64(0.313)), ('L0H5', np.float64(0.092), np.float64(0.002), np.float64(0.509))]
L1H3 [('L0H2', np.float64(0.113), np.float64(0.008), np.float64(0.4)), ('L0H5', np.float64(0.085), np.float64(0.002), np.float64(0.508)), ('L0H3', np.float64(0.076), np.float64(0.014), np.float64(0.068)), ('L0H4', np.float64(0.075), np.float64(0.014), np.float64(0.321))]
L1H4 [('L0H2', np.float64(0.079), np.float64(-0.0), np.float64(0.375)), ('L0H4', np.float64(0.078), np.float64(0.004), np.float64(0.297)), ('L0H5', np.float64(0.075), np.float64(-0.001), np.float64(0.494)), ('L0H1', np.float64(0.046), np.float64(-0.002), np.float64(0.36))]
L1H5 [('L0H3', np.float64(0.2), np.float64(0.029), np.float64(0.056)), ('L0H2', np.float64(0.102), np.float64(0.007), np.float64(0.387)), ('L0H5', np.float64(0.064), np.float64(0.003), np.float64(0.478)), ('L0H4', np.float64(0.062), np.float64(0.021), np.float64(0.314))]
L2H0 [('L1H3', np.float64(0.206), np.float64(-0.001), np.float64(0.045)), ('L0H2', np.float64(0.196), np.float64(0.027), np.float64(0.298)), ('L0H5', np.float64(0.193), np.float64(0.016), np.float64(0.345)), ('L1H1', np.float64(0.163), np.float64(0.003), np.float64(0.043))]
L2H1 [('L0H5', np.float64(0.199), np.float64(0.014), np.float64(0.214)), ('L0H2', np.float64(0.179), np.float64(0.023), np.float64(0.186)), ('L0H1', np.float64(0.117), np.float64(0.022), np.float64(0.18)), ('L0H4', np.float64(0.08), np.float64(0.023), np.float64(0.161))]
L2H2 [('L0H5', np.float64(0.186), np.float64(0.017), np.float64(0.248)), ('L0H2', np.float64(0.182), np.float64(0.027), np.float64(0.214)), ('L0H1', np.float64(0.124), np.float64(0.024), np.float64(0.208)), ('L0H3', np.float64(0.1), np.float64(0.0), np.float64(0.053))]
L2H3 [('L0H2', np.float64(0.129), np.float64(0.012), np.float64(0.174)), ('L0H5', np.float64(0.112), np.float64(0.007), np.float64(0.22)), ('L0H1', np.float64(0.097), np.float64(0.008), np.float64(0.168)), ('L0H4', np.float64(0.086), np.float64(0.007), np.float64(0.141))]
L2H4 [('L0H2', np.float64(0.186), np.float64(0.025), np.float64(0.243)), ('L0H5', np.float64(0.182), np.float64(0.015), np.float64(0.281)), ('L0H3', np.float64(0.16), np.float64(0.009), np.float64(0.055)), ('L0H1', np.float64(0.128), np.float64(0.021), np.float64(0.233))]
L2H5 [('L0H5', np.float64(0.212), np.float64(0.018), np.float64(0.224)), ('L0H2', np.float64(0.188), np.float64(0.021), np.float64(0.193)), ('L0H1', np.float64(0.113), np.float64(0.021), np.float64(0.187)), ('L0H4', np.float64(0.081), np.float64(0.025), np.float64(0.167))]
L3H0 [('L0H2', np.float64(0.107), np.float64(0.015), np.float64(0.119)), ('L0H5', np.float64(0.087), np.float64(0.004), np.float64(0.15)), ('L0H1', np.float64(0.069), np.float64(0.01), np.float64(0.117)), ('L0H4', np.float64(0.048), np.float64(0.014), np.float64(0.103))]
L3H1 [('L0H2', np.float64(0.093), np.float64(0.013), np.float64(0.144)), ('L0H5', np.float64(0.077), np.float64(0.005), np.float64(0.182)), ('L1H2', np.float64(0.073), np.float64(0.0), np.float64(0.046)), ('L0H1', np.float64(0.07), np.float64(0.014), np.float64(0.14))]
L3H2 [('L0H2', np.float64(0.081), np.float64(0.015), np.float64(0.147)), ('L0H1', np.float64(0.048), np.float64(0.014), np.float64(0.145)), ('L0H3', np.float64(0.034), np.float64(0.006), np.float64(0.051)), ('L0H5', np.float64(0.019), np.float64(0.005), np.float64(0.188))]
L3H3 [('L0H3', np.float64(0.924), np.float64(0.067), np.float64(0.068)), ('L2H5', np.float64(0.809), np.float64(0.013), np.float64(0.06)), ('L2H1', np.float64(0.563), np.float64(0.002), np.float64(0.058)), ('L1H0', np.float64(0.515), np.float64(0.001), np.float64(0.059))]
L3H4 [('L2H2', np.float64(0.281), np.float64(0.002), np.float64(0.051)), ('L2H4', np.float64(0.273), np.float64(0.006), np.float64(0.045)), ('L2H5', np.float64(0.203), np.float64(0.001), np.float64(0.046)), ('L0H4', np.float64(0.196), np.float64(0.022), np.float64(0.053))]
L3H5 [('L0H2', np.float64(0.05), np.float64(0.004), np.float64(0.146)), ('L0H5', np.float64(0.048), np.float64(0.001), np.float64(0.185)), ('L0H1', np.float64(0.017), np.float64(0.004), np.float64(0.142)), ('L0H4', np.float64(0.0), np.float64(0.01), np.float64(0.12))]

L0 value-subspace sharing and query/key orthogonality
Combined value singular values [3.339 2.305 1.516 0.814 0.773 0.711 0.682 0.672 0.651 0.633 0.618 0.597
 0.574 0.561 0.558 0.537 0.525 0.508 0.498 0.487 0.476 0.469 0.461 0.45
 0.432 0.427 0.417 0.41  0.408 0.395 0.388 0.382 0.38  0.376 0.363 0.359
 0.356 0.348 0.342 0.334 0.333 0.326 0.317 0.308 0.307]
value basis rank 2
H 0 Q/K/V energy [0.234 0.308 0.003]
H 1 Q/K/V energy [0.249 0.056 0.524]
H 2 Q/K/V energy [0.31 0.08 0.52]
H 3 Q/K/V energy [0.044 0.198 0.003]
H 4 Q/K/V energy [0.14  0.045 0.339]
H 5 Q/K/V energy [0.449 0.007 0.721]
value basis rank 10
H 0 Q/K/V energy [0.409 0.381 0.268]
H 1 Q/K/V energy [0.54  0.18  0.678]
H 2 Q/K/V energy [0.473 0.176 0.631]
H 3 Q/K/V energy [0.091 0.243 0.214]
H 4 Q/K/V energy [0.38  0.135 0.467]
H 5 Q/K/V energy [0.527 0.096 0.891]
value basis rank 20
H 0 Q/K/V energy [0.459 0.44  0.514]
H 1 Q/K/V energy [0.575 0.28  0.712]
H 2 Q/K/V energy [0.503 0.256 0.667]
H 3 Q/K/V energy [0.125 0.275 0.51 ]
H 4 Q/K/V energy [0.414 0.197 0.504]
H 5 Q/K/V energy [0.548 0.15  0.924]
value basis rank 28
H 0 Q/K/V energy [0.499 0.489 0.617]
H 1 Q/K/V energy [0.595 0.356 0.737]
H 2 Q/K/V energy [0.527 0.318 0.697]
H 3 Q/K/V energy [0.175 0.324 0.651]
H 4 Q/K/V energy [0.44  0.247 0.549]
H 5 Q/K/V energy [0.573 0.198 0.943]
value basis rank 40
H 0 Q/K/V energy [0.569 0.576 0.711]
H 1 Q/K/V energy [0.641 0.419 0.789]
H 2 Q/K/V energy [0.573 0.383 0.754]
H 3 Q/K/V energy [0.31  0.467 0.774]
H 4 Q/K/V energy [0.509 0.317 0.628]
H 5 Q/K/V energy [0.61  0.275 0.958]


========================================================================
TURN t004
MESSAGE SENT TO CODEX
OUTPUT of run 3 of at most 100:
```
L0 QK eigenvalues, dominant invariant-space overlaps
H 0 rank95 10 L/R overlap 0.445 V energy in QK-left/right [0.057 0.082]
eigenvalues [ 0.08 +0.j     0.048+0.j    -0.024+0.006j -0.024-0.006j -0.023+0.j
  0.018+0.013j  0.018-0.013j -0.02 +0.j    -0.014+0.012j -0.014-0.012j
 -0.014+0.003j -0.014-0.003j -0.014+0.j    -0.011+0.004j -0.011-0.004j
 -0.011+0.002j]
H 1 rank95 2 L/R overlap 0.106 V energy in QK-left/right [0.199 0.043]
eigenvalues [-0.062+0.j    -0.01 +0.j    -0.009+0.j     0.004+0.j    -0.004+0.j
 -0.003+0.002j -0.003-0.002j -0.002+0.j    -0.002-0.j    -0.002+0.001j
 -0.002-0.001j -0.001-0.j    -0.001+0.j    -0.001-0.001j -0.001+0.001j
  0.001+0.j   ]
H 2 rank95 3 L/R overlap 0.268 V energy in QK-left/right [0.212 0.111]
eigenvalues [-0.057+0.j    -0.007+0.003j -0.007-0.003j -0.003+0.001j -0.003-0.001j
 -0.002+0.j    -0.001+0.j    -0.001-0.j    -0.001+0.001j -0.001-0.001j
  0.001+0.001j  0.001-0.001j -0.   +0.001j -0.   -0.001j -0.001+0.j
  0.   +0.001j]
H 3 rank95 23 L/R overlap 0.799 V energy in QK-left/right [0.143 0.165]
eigenvalues [0.137+0.133j 0.137-0.133j 0.11 +0.089j 0.11 -0.089j 0.095+0.098j
 0.095-0.098j 0.084+0.104j 0.084-0.104j 0.064+0.114j 0.064-0.114j
 0.096+0.069j 0.096-0.069j 0.011+0.117j 0.011-0.117j 0.112+0.j
 0.056-0.07j ]
H 4 rank95 5 L/R overlap 0.137 V energy in QK-left/right [0.175 0.055]
eigenvalues [-0.015+0.j    -0.01 +0.j    -0.008+0.j    -0.003+0.j    -0.003-0.j
 -0.002+0.001j -0.002-0.001j -0.   +0.002j -0.   -0.002j -0.001+0.001j
 -0.001-0.001j -0.002+0.j    -0.001-0.001j -0.001+0.001j  0.001-0.001j
  0.001+0.001j]
H 5 rank95 10 L/R overlap 0.105 V energy in QK-left/right [0.347 0.038]
eigenvalues [-0.005+0.j     0.001+0.j    -0.001+0.j    -0.   +0.001j -0.   -0.001j
 -0.001+0.j    -0.001+0.j    -0.001-0.j     0.   +0.001j  0.   -0.001j
 -0.   +0.001j -0.   -0.001j -0.   +0.001j -0.   -0.001j  0.   +0.001j
  0.   -0.001j]

QK-OV composition: trace(A_lh @ B_earlier)/(|A_lh| |B_earlier|)
L1H0 [0.002 0.034 0.05  0.006 0.029 0.048]
L1H1 [0.    0.006 0.025 0.014 0.004 0.021]
L1H2 [-0.002  0.03   0.042  0.012  0.031  0.047]
L1H3 [0.001 0.028 0.045 0.005 0.024 0.043]
L1H4 [0.001 0.017 0.03  0.001 0.023 0.037]
L1H5 [-0.001  0.019  0.04   0.011  0.019  0.031]
L2H0 [-0.     0.038  0.058  0.004  0.023  0.067  0.001  0.007  0.004  0.009
 -0.007  0.002]
L2H1 [ 0.001  0.021  0.033  0.001  0.013  0.042 -0.004 -0.009 -0.014 -0.009
 -0.015 -0.01 ]
L2H2 [ 0.003  0.026  0.039  0.005  0.014  0.046 -0.001  0.003 -0.001 -0.002
 -0.007  0.001]
L2H3 [ 0.003  0.016  0.023  0.005  0.012  0.025  0.002  0.002 -0.002 -0.
 -0.007 -0.004]
L2H4 [-0.001  0.03   0.045  0.009  0.022  0.051 -0.     0.002 -0.012 -0.015
 -0.003  0.002]
L2H5 [ 0.001  0.021  0.036  0.001  0.014  0.047 -0.009 -0.    -0.008 -0.007
 -0.007 -0.009]
L3H0 [-0.002  0.008  0.013 -0.01   0.005  0.013 -0.01  -0.008 -0.018 -0.013
 -0.012 -0.014 -0.008 -0.014 -0.019 -0.016 -0.036 -0.02 ]
L3H1 [ 0.002  0.01   0.013 -0.002  0.004  0.014 -0.006  0.002  0.003 -0.001
 -0.003  0.002 -0.009 -0.    -0.004  0.003 -0.002 -0.002]
L3H2 [-0.     0.007  0.012  0.002  0.001  0.004 -0.007 -0.001  0.    -0.
 -0.002 -0.001 -0.003 -0.001 -0.011 -0.008 -0.01  -0.005]
L3H3 [-0.008  0.002  0.002  0.063  0.002 -0.002  0.031  0.021  0.001 -0.003
 -0.019  0.027  0.028  0.033  0.009  0.013  0.022  0.048]
L3H4 [ 0.005  0.009  0.009  0.006  0.01   0.009  0.     0.002  0.002 -0.001
  0.005  0.002  0.008  0.009  0.014  0.009  0.012  0.009]
L3H5 [-0.     0.002  0.007 -0.003  0.     0.009 -0.012 -0.007 -0.005 -0.009
 -0.007 -0.007 -0.015 -0.016 -0.013 -0.013 -0.012 -0.01 ]

Strongest composition positivity, with nonrandom comparison
L1H0 [('L0H2', np.float64(0.134), np.float64(0.009), np.float64(0.376)), ('L0H5', np.float64(0.103), np.float64(0.002), np.float64(0.467)), ('L0H3', np.float64(0.102), np.float64(0.013), np.float64(0.057)), ('L0H4', np.float64(0.096), np.float64(0.013), np.float64(0.304))]
L1H1 [('L0H3', np.float64(0.218), np.float64(0.016), np.float64(0.065)), ('L0H2', np.float64(0.065), np.float64(0.005), np.float64(0.387)), ('L0H5', np.float64(0.043), np.float64(0.004), np.float64(0.489)), ('L0H1', np.float64(0.017), np.float64(0.005), np.float64(0.371))]
L1H2 [('L0H3', np.float64(0.168), np.float64(0.017), np.float64(0.072)), ('L0H2', np.float64(0.106), np.float64(0.006), np.float64(0.396)), ('L0H4', np.float64(0.1), np.float64(0.011), np.float64(0.313)), ('L0H5', np.float64(0.092), np.float64(0.002), np.float64(0.509))]
L1H3 [('L0H2', np.float64(0.113), np.float64(0.008), np.float64(0.4)), ('L0H5', np.float64(0.085), np.float64(0.002), np.float64(0.508)), ('L0H3', np.float64(0.076), np.float64(0.014), np.float64(0.068)), ('L0H4', np.float64(0.075), np.float64(0.014), np.float64(0.321))]
L1H4 [('L0H2', np.float64(0.079), np.float64(-0.0), np.float64(0.375)), ('L0H4', np.float64(0.078), np.float64(0.004), np.float64(0.297)), ('L0H5', np.float64(0.075), np.float64(-0.001), np.float64(0.494)), ('L0H1', np.float64(0.046), np.float64(-0.002), np.float64(0.36))]
L1H5 [('L0H3', np.float64(0.2), np.float64(0.029), np.float64(0.056)), ('L0H2', np.float64(0.102), np.float64(0.007), np.float64(0.387)), ('L0H5', np.float64(0.064), np.float64(0.003), np.float64(0.478)), ('L0H4', np.float64(0.062), np.float64(0.021), np.float64(0.314))]
L2H0 [('L1H3', np.float64(0.206), np.float64(-0.001), np.float64(0.045)), ('L0H2', np.float64(0.196), np.float64(0.027), np.float64(0.298)), ('L0H5', np.float64(0.193), np.float64(0.016), np.float64(0.345)), ('L1H1', np.float64(0.163), np.float64(0.003), np.float64(0.043))]
L2H1 [('L0H5', np.float64(0.199), np.float64(0.014), np.float64(0.214)), ('L0H2', np.float64(0.179), np.float64(0.023), np.float64(0.186)), ('L0H1', np.float64(0.117), np.float64(0.022), np.float64(0.18)), ('L0H4', np.float64(0.08), np.float64(0.023), np.float64(0.161))]
L2H2 [('L0H5', np.float64(0.186), np.float64(0.017), np.float64(0.248)), ('L0H2', np.float64(0.182), np.float64(0.027), np.float64(0.214)), ('L0H1', np.float64(0.124), np.float64(0.024), np.float64(0.208)), ('L0H3', np.float64(0.1), np.float64(0.0), np.float64(0.053))]
L2H3 [('L0H2', np.float64(0.129), np.float64(0.012), np.float64(0.174)), ('L0H5', np.float64(0.112), np.float64(0.007), np.float64(0.22)), ('L0H1', np.float64(0.097), np.float64(0.008), np.float64(0.168)), ('L0H4', np.float64(0.086), np.float64(0.007), np.float64(0.141))]
L2H4 [('L0H2', np.float64(0.186), np.float64(0.025), np.float64(0.243)), ('L0H5', np.float64(0.182), np.float64(0.015), np.float64(0.281)), ('L0H3', np.float64(0.16), np.float64(0.009), np.float64(0.055)), ('L0H1', np.float64(0.128), np.float64(0.021), np.float64(0.233))]
L2H5 [('L0H5', np.float64(0.212), np.float64(0.018), np.float64(0.224)), ('L0H2', np.float64(0.188), np.float64(0.021), np.float64(0.193)), ('L0H1', np.float64(0.113), np.float64(0.021), np.float64(0.187)), ('L0H4', np.float64(0.081), np.float64(0.025), np.float64(0.167))]
L3H0 [('L0H2', np.float64(0.107), np.float64(0.015), np.float64(0.119)), ('L0H5', np.float64(0.087), np.float64(0.004), np.float64(0.15)), ('L0H1', np.float64(0.069), np.float64(0.01), np.float64(0.117)), ('L0H4', np.float64(0.048), np.float64(0.014), np.float64(0.103))]
L3H1 [('L0H2', np.float64(0.093), np.float64(0.013), np.float64(0.144)), ('L0H5', np.float64(0.077), np.float64(0.005), np.float64(0.182)), ('L1H2', np.float64(0.073), np.float64(0.0), np.float64(0.046)), ('L0H1', np.float64(0.07), np.float64(0.014), np.float64(0.14))]
L3H2 [('L0H2', np.float64(0.081), np.float64(0.015), np.float64(0.147)), ('L0H1', np.float64(0.048), np.float64(0.014), np.float64(0.145)), ('L0H3', np.float64(0.034), np.float64(0.006), np.float64(0.051)), ('L0H5', np.float64(0.019), np.float64(0.005), np.float64(0.188))]
L3H3 [('L0H3', np.float64(0.924), np.float64(0.067), np.float64(0.068)), ('L2H5', np.float64(0.809), np.float64(0.013), np.float64(0.06)), ('L2H1', np.float64(0.563), np.float64(0.002), np.float64(0.058)), ('L1H0', np.float64(0.515), np.float64(0.001), np.float64(0.059))]
L3H4 [('L2H2', np.float64(0.281), np.float64(0.002), np.float64(0.051)), ('L2H4', np.float64(0.273), np.float64(0.006), np.float64(0.045)), ('L2H5', np.float64(0.203), np.float64(0.001), np.float64(0.046)), ('L0H4', np.float64(0.196), np.float64(0.022), np.float64(0.053))]
L3H5 [('L0H2', np.float64(0.05), np.float64(0.004), np.float64(0.146)), ('L0H5', np.float64(0.048), np.float64(0.001), np.float64(0.185)), ('L0H1', np.float64(0.017), np.float64(0.004), np.float64(0.142)), ('L0H4', np.float64(0.0), np.float64(0.01), np.float64(0.12))]

L0 value-subspace sharing and query/key orthogonality
Combined value singular values [3.339 2.305 1.516 0.814 0.773 0.711 0.682 0.672 0.651 0.633 0.618 0.597
 0.574 0.561 0.558 0.537 0.525 0.508 0.498 0.487 0.476 0.469 0.461 0.45
 0.432 0.427 0.417 0.41  0.408 0.395 0.388 0.382 0.38  0.376 0.363 0.359
 0.356 0.348 0.342 0.334 0.333 0.326 0.317 0.308 0.307]
value basis rank 2
H 0 Q/K/V energy [0.234 0.308 0.003]
H 1 Q/K/V energy [0.249 0.056 0.524]
H 2 Q/K/V energy [0.31 0.08 0.52]
H 3 Q/K/V energy [0.044 0.198 0.003]
H 4 Q/K/V energy [0.14  0.045 0.339]
H 5 Q/K/V energy [0.449 0.007 0.721]
value basis rank 10
H 0 Q/K/V energy [0.409 0.381 0.268]
H 1 Q/K/V energy [0.54  0.18  0.678]
H 2 Q/K/V energy [0.473 0.176 0.631]
H 3 Q/K/V energy [0.091 0.243 0.214]
H 4 Q/K/V energy [0.38  0.135 0.467]
H 5 Q/K/V energy [0.527 0.096 0.891]
value basis rank 20
H 0 Q/K/V energy [0.459 0.44  0.514]
H 1 Q/K/V energy [0.575 0.28  0.712]
H 2 Q/K/V energy [0.503 0.256 0.667]
H 3 Q/K/V energy [0.125 0.275 0.51 ]
H 4 Q/K/V energy [0.414 0.197 0.504]
H 5 Q/K/V energy [0.548 0.15  0.924]
value basis rank 28
H 0 Q/K/V energy [0.499 0.489 0.617]
H 1 Q/K/V energy [0.595 0.356 0.737]
H 2 Q/K/V energy [0.527 0.318 0.697]
H 3 Q/K/V energy [0.175 0.324 0.651]
H 4 Q/K/V energy [0.44  0.247 0.549]
H 5 Q/K/V energy [0.573 0.198 0.943]
value basis rank 40
H 0 Q/K/V energy [0.569 0.576 0.711]
H 1 Q/K/V energy [0.641 0.419 0.789]
H 2 Q/K/V energy [0.573 0.383 0.754]
H 3 Q/K/V energy [0.31  0.467 0.774]
H 4 Q/K/V energy [0.509 0.317 0.628]
H 5 Q/K/V energy [0.61  0.275 0.958]

```
CLI OUTPUT IN EVENT ORDER
ERROR
Failed to read global AGENTS.md instructions from `<local-home>/.codex/AGENTS.md`: Operation not permitted (os error 1)

ERROR
Code Mode is unavailable because code-mode host is disabled. Code mode will fail closed; enable `features.code_mode_host` and install `codex-code-mode-host`.

AGENT_MESSAGE
```python
import numpy as np
from scipy.linalg import svd, svdvals
from threadpoolctl import threadpool_limits

with threadpool_limits(limits=2):
    print("Last-layer output singular spectra (indices start at 1)")
    for name in ["W_proj.3","W_o.3","W_proj.0"]:
        s=svdvals(W[name].astype(float))
        print(name)
        for start in range(0,80,20):
            print(start+1, np.round(s[start:start+20],3))
    T=np.concatenate([W["W_o.3"],W["W_proj.3"]],axis=1).astype(float)
    u,s,vt=svd(T,full_matrices=False)
    print("Combined final output spectrum",np.round(s[:70],3))
    print("Adjacent spectral ratios",[(i+1,round(s[i]/s[i+1],3))
          for i in np.argsort(s[:60]/s[1:61])[-12:][::-1]])
    print("\nL0 OV dominant input/output directions: largest coordinate loadings")
    for j in [0,1,2,3,4,5]:
        sl=slice(64*j,64*j+64)
        v=W["W_v.0"][sl].astype(float)*W["ln1_w.0"]
        v-=v.mean(1,keepdims=True)
        o=W["W_o.0"][:,sl].astype(float)
        uu,ss,vv=svd(o@v,full_matrices=False)
        print("H",j)
        for r in range(2):
            for tag,direction in [("in",vv[r]),("out",uu[:,r])]:
                ix=np.argsort(np.abs(direction))[-6:][::-1]
                print(r,tag,[(int(i),round(direction[i],3)) for i in ix],
                      "participation",round(1/np.sum(direction**4),1))
    print("\nFinal output common-subspace concentration")
    for r in [20,22,24,26,27,28,32,40]:
        U=u[:,:r]
        vals=[]
        for l in range(4):
            p=W[f"W_proj.{l}"].astype(float)
            vals.append(np.linalg.norm(U.T@p)**2/np.linalg.norm(p)**2)
        print("rank",r,"MLP projection energy L0..L3",np.round(vals,3))
    print("\nLayer0 FC input spectrum, additional indices")
    f=W["W_fc.0"].astype(float)*W["ln2_w.0"]
    s=svdvals(f)
    for start in range(0,100,20):
        print(start+1,np.round(s[start:start+20],3))
```


PERMITTED EXPERIMENT HARNESS RECORD: python
{
  "run": 4,
  "turn": "t004",
  "code": "import numpy as np\nfrom scipy.linalg import svd, svdvals\nfrom threadpoolctl import threadpool_limits\n\nwith threadpool_limits(limits=2):\n    print(\"Last-layer output singular spectra (indices start at 1)\")\n    for name in [\"W_proj.3\",\"W_o.3\",\"W_proj.0\"]:\n        s=svdvals(W[name].astype(float))\n        print(name)\n        for start in range(0,80,20):\n            print(start+1, np.round(s[start:start+20],3))\n    T=np.concatenate([W[\"W_o.3\"],W[\"W_proj.3\"]],axis=1).astype(float)\n    u,s,vt=svd(T,full_matrices=False)\n    print(\"Combined final output spectrum\",np.round(s[:70],3))\n    print(\"Adjacent spectral ratios\",[(i+1,round(s[i]/s[i+1],3))\n          for i in np.argsort(s[:60]/s[1:61])[-12:][::-1]])\n    print(\"\\nL0 OV dominant input/output directions: largest coordinate loadings\")\n    for j in [0,1,2,3,4,5]:\n        sl=slice(64*j,64*j+64)\n        v=W[\"W_v.0\"][sl].astype(float)*W[\"ln1_w.0\"]\n        v-=v.mean(1,keepdims=True)\n        o=W[\"W_o.0\"][:,sl].astype(float)\n        uu,ss,vv=svd(o@v,full_matrices=False)\n        print(\"H\",j)\n        for r in range(2):\n            for tag,direction in [(\"in\",vv[r]),(\"out\",uu[:,r])]:\n                ix=np.argsort(np.abs(direction))[-6:][::-1]\n                print(r,tag,[(int(i),round(direction[i],3)) for i in ix],\n                      \"participation\",round(1/np.sum(direction**4),1))\n    print(\"\\nFinal output common-subspace concentration\")\n    for r in [20,22,24,26,27,28,32,40]:\n        U=u[:,:r]\n        vals=[]\n        for l in range(4):\n            p=W[f\"W_proj.{l}\"].astype(float)\n            vals.append(np.linalg.norm(U.T@p)**2/np.linalg.norm(p)**2)\n        print(\"rank\",r,\"MLP projection energy L0..L3\",np.round(vals,3))\n    print(\"\\nLayer0 FC input spectrum, additional indices\")\n    f=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"]\n    s=svdvals(f)\n    for start in range(0,100,20):\n        print(start+1,np.round(s[start:start+20],3))",
  "out": "Last-layer output singular spectra (indices start at 1)\nW_proj.3\n1 [28.461 22.214 21.34  20.708 19.943 19.662 18.986 18.744 18.295 17.457\n 17.132 16.561 15.329 14.874 14.328 13.438 12.667 12.455 12.317 11.531]\n21 [11.047  9.084  8.353  8.24   6.37   5.836  4.626  4.583  3.777  3.61\n  3.252  3.183  3.086  2.941  2.865  2.801  2.639  2.564  2.538  2.466]\n41 [2.419 2.404 2.346 2.31  2.246 2.227 2.155 2.147 2.089 2.069 2.065 2.041\n 1.975 1.936 1.921 1.917 1.857 1.848 1.83  1.82 ]\n61 [1.798 1.779 1.764 1.737 1.729 1.719 1.709 1.692 1.68  1.661 1.645 1.635\n 1.619 1.594 1.589 1.583 1.565 1.55  1.541 1.52 ]\nW_o.3\n1 [10.477  7.357  5.323  5.294  5.177  5.124  5.049  4.959  4.775  4.751\n  4.625  4.565  4.462  4.442  4.262  4.246  4.188  4.105  4.067  4.035]\n21 [3.997 3.943 3.93  3.908 3.891 3.859 3.812 3.786 3.763 3.703 3.678 3.629\n 3.61  3.577 3.535 3.519 3.48  3.461 3.423 3.409]\n41 [3.378 3.356 3.293 3.263 3.23  3.219 3.206 3.18  3.146 3.13  3.116 3.082\n 3.065 3.025 3.002 2.975 2.954 2.933 2.915 2.896]\n61 [2.846 2.83  2.816 2.812 2.771 2.762 2.733 2.719 2.695 2.671 2.647 2.637\n 2.62  2.598 2.588 2.556 2.529 2.52  2.5   2.483]\nW_proj.0\n1 [10.899  7.702  7.173  6.638  6.541  6.288  6.201  6.133  5.941  5.917\n  5.758  5.641  5.552  5.476  5.393  5.363  5.259  5.206  5.171  5.153]\n21 [5.057 5.018 4.96  4.88  4.821 4.788 4.77  4.73  4.643 4.579 4.546 4.529\n 4.505 4.493 4.44  4.415 4.369 4.315 4.293 4.261]\n41 [4.243 4.185 4.134 4.104 4.064 4.049 4.026 3.988 3.967 3.95  3.933 3.901\n 3.857 3.804 3.778 3.754 3.74  3.713 3.692 3.683]\n61 [3.652 3.612 3.607 3.575 3.564 3.522 3.509 3.497 3.47  3.456 3.446 3.417\n 3.4   3.378 3.337 3.302 3.291 3.269 3.238 3.23 ]\nCombined final output spectrum [28.906 22.386 21.536 20.936 20.117 19.852 19.175 18.933 18.5   17.69\n 17.356 16.855 15.592 15.148 14.621 13.72  12.993 12.791 12.632 11.898\n 11.629 10.964  9.897  8.83   8.583  7.096  6.654  6.012  5.627  5.54\n  5.494  5.275  5.068  4.893  4.87   4.79   4.636  4.597  4.49   4.43\n  4.388  4.347  4.331  4.268  4.176  4.148  4.097  4.043  3.974  3.919\n  3.881  3.824  3.798  3.784  3.747  3.718  3.71   3.655  3.618  3.585\n  3.569  3.558  3.513  3.49   3.465  3.437  3.421  3.385  3.356  3.33 ]\nAdjacent spectral ratios [(np.int64(1), np.float64(1.291)), (np.int64(25), np.float64(1.209)), (np.int64(23), np.float64(1.121)), (np.int64(22), np.float64(1.108)), (np.int64(27), np.float64(1.107)), (np.int64(12), np.float64(1.081)), (np.int64(28), np.float64(1.068)), (np.int64(26), np.float64(1.067)), (np.int64(15), np.float64(1.066)), (np.int64(19), np.float64(1.062)), (np.int64(21), np.float64(1.061)), (np.int64(16), np.float64(1.056))]\n\nL0 OV dominant input/output directions: largest coordinate loadings\nH 0\n0 in [(373, np.float64(0.176)), (225, np.float64(-0.163)), (134, np.float64(-0.158)), (158, np.float64(-0.154)), (7, np.float64(0.153)), (51, np.float64(0.149))] participation 102.5\n0 out [(336, np.float64(0.193)), (96, np.float64(0.158)), (291, np.float64(-0.15)), (327, np.float64(0.149)), (203, np.float64(-0.14)), (202, np.float64(-0.128))] participation 116.1\n1 in [(226, np.float64(-0.167)), (301, np.float64(0.152)), (358, np.float64(-0.147)), (21, np.float64(-0.146)), (220, np.float64(-0.132)), (325, np.float64(-0.131))] participation 114.5\n1 out [(39, np.float64(-0.263)), (6, np.float64(-0.193)), (282, np.float64(0.186)), (156, np.float64(0.147)), (163, np.float64(0.137)), (152, np.float64(0.133))] participation 74.6\nH 1\n0 in [(184, np.float64(0.347)), (180, np.float64(0.315)), (99, np.float64(0.271)), (39, np.float64(0.267)), (56, np.float64(-0.254)), (317, np.float64(-0.239))] participation 19.1\n0 out [(39, np.float64(0.692)), (58, np.float64(-0.51)), (99, np.float64(0.358)), (21, np.float64(-0.212)), (184, np.float64(0.201)), (153, np.float64(-0.054))] participation 3.1\n1 in [(211, np.float64(0.34)), (223, np.float64(-0.262)), (228, np.float64(-0.244)), (65, np.float64(0.231)), (173, np.float64(-0.23)), (124, np.float64(-0.214))] participation 23.6\n1 out [(21, np.float64(0.961)), (39, np.float64(0.158)), (58, np.float64(-0.129)), (184, np.float64(0.072)), (306, np.float64(-0.032)), (173, np.float64(-0.029))] participation 1.2\nH 2\n0 in [(184, np.float64(-0.365)), (180, np.float64(-0.304)), (99, np.float64(-0.298)), (317, np.float64(0.248)), (56, np.float64(0.234)), (39, np.float64(-0.231))] participation 18.5\n0 out [(39, np.float64(-0.659)), (58, np.float64(0.494)), (21, np.float64(0.373)), (99, np.float64(-0.355)), (184, np.float64(-0.162)), (153, np.float64(0.045))] participation 3.5\n1 in [(211, np.float64(0.3)), (173, np.float64(-0.273)), (223, np.float64(-0.256)), (162, np.float64(0.227)), (256, np.float64(-0.225)), (65, np.float64(0.222))] participation 26.1\n1 out [(21, np.float64(0.91)), (39, np.float64(0.221)), (99, np.float64(0.207)), (58, np.float64(-0.201)), (184, np.float64(0.053)), (252, np.float64(-0.03))] participation 1.4\nH 3\n0 in [(223, np.float64(-0.225)), (26, np.float64(-0.196)), (200, np.float64(-0.17)), (48, np.float64(-0.167)), (359, np.float64(0.145)), (124, np.float64(0.142))] participation 77.7\n0 out [(92, np.float64(-0.179)), (86, np.float64(0.169)), (188, np.float64(-0.162)), (18, np.float64(0.16)), (131, np.float64(0.158)), (303, np.float64(0.156))] participation 93.5\n1 in [(200, np.float64(-0.229)), (124, np.float64(-0.181)), (53, np.float64(0.177)), (329, np.float64(-0.168)), (74, np.float64(0.167)), (105, np.float64(0.159))] participation 71.0\n1 out [(65, np.float64(0.19)), (125, np.float64(0.179)), (320, np.float64(-0.173)), (202, np.float64(-0.168)), (86, np.float64(-0.157)), (287, np.float64(-0.152))] participation 89.9\nH 4\n0 in [(184, np.float64(-0.413)), (180, np.float64(-0.289)), (256, np.float64(0.28)), (56, np.float64(0.243)), (100, np.float64(0.236)), (69, np.float64(-0.225))] participation 16.5\n0 out [(39, np.float64(-0.696)), (58, np.float64(0.511)), (99, np.float64(-0.32)), (184, np.float64(-0.227)), (21, np.float64(-0.182)), (153, np.float64(0.057))] participation 3.2\n1 in [(211, np.float64(0.352)), (228, np.float64(-0.274)), (124, np.float64(-0.219)), (65, np.float64(0.219)), (26, np.float64(0.214)), (319, np.float64(0.212))] participation 24.5\n1 out [(21, np.float64(0.942)), (99, np.float64(-0.24)), (39, np.float64(-0.097)), (58, np.float64(0.092)), (184, np.float64(0.042)), (148, np.float64(-0.033))] participation 1.3\nH 5\n0 in [(162, np.float64(-0.328)), (211, np.float64(-0.306)), (223, np.float64(0.278)), (65, np.float64(-0.235)), (354, np.float64(0.203)), (173, np.float64(0.201))] participation 22.4\n0 out [(21, np.float64(-0.864)), (99, np.float64(-0.357)), (58, np.float64(0.236)), (39, np.float64(-0.232)), (184, np.float64(0.024)), (153, np.float64(0.019))] participation 1.7\n1 in [(99, np.float64(-0.369)), (180, np.float64(-0.315)), (184, np.float64(-0.309)), (162, np.float64(-0.224)), (100, np.float64(0.209)), (317, np.float64(0.207))] participation 18.1\n1 out [(39, np.float64(-0.608)), (58, np.float64(0.486)), (21, np.float64(0.469)), (99, np.float64(-0.405)), (180, np.float64(-0.036)), (165, np.float64(-0.026))] participation 3.7\n\nFinal output common-subspace concentration\nrank 20 MLP projection energy L0..L3 [0.089 0.06  0.1   0.872]\nrank 22 MLP projection energy L0..L3 [0.099 0.064 0.106 0.894]\nrank 24 MLP projection energy L0..L3 [0.107 0.069 0.112 0.915]\nrank 26 MLP projection energy L0..L3 [0.114 0.074 0.118 0.929]\nrank 27 MLP projection energy L0..L3 [0.119 0.076 0.12  0.931]\nrank 28 MLP projection energy L0..L3 [0.121 0.079 0.123 0.933]\nrank 32 MLP projection energy L0..L3 [0.133 0.088 0.133 0.939]\nrank 40 MLP projection energy L0..L3 [0.154 0.107 0.154 0.943]\n\nLayer0 FC input spectrum, additional indices\n1 [17.584 13.477 11.766 10.188  9.613  9.54   9.344  9.149  8.754  8.681\n  8.593  8.39   8.008  7.926  7.84   7.731  7.517  7.386  7.159  7.084]\n21 [7.068 6.915 6.889 6.682 6.631 6.491 6.436 6.354 6.307 6.16  6.003 5.909\n 5.835 5.661 5.466 5.307 5.289 5.132 5.047 4.957]\n41 [4.895 4.443 4.367 4.111 4.038 3.8   3.63  3.408 3.226 3.154 2.964 2.947\n 2.817 2.635 2.605 2.501 2.481 2.393 2.351 2.276]\n61 [2.201 2.148 2.136 2.101 2.066 2.047 1.993 1.957 1.89  1.858 1.85  1.833\n 1.781 1.745 1.734 1.726 1.71  1.675 1.666 1.644]\n81 [1.625 1.603 1.579 1.555 1.55  1.533 1.518 1.506 1.492 1.464 1.457 1.437\n 1.428 1.414 1.404 1.398 1.381 1.374 1.372 1.362]\n",
  "seconds": 0.702,
  "rc": 0,
  "timed_out": false,
  "truncated": false,
  "code_sha256": "ca8f9e74acd6181531e8d0b500bcbecd0523e0832651c5f25a62d76afadc7348",
  "weights_sha256": "04ec0b300d207b26b92a1af6d49d56d452833e39b35826200bc1d821e5b7d930"
}

EXACT HARNESS FEEDBACK
Last-layer output singular spectra (indices start at 1)
W_proj.3
1 [28.461 22.214 21.34  20.708 19.943 19.662 18.986 18.744 18.295 17.457
 17.132 16.561 15.329 14.874 14.328 13.438 12.667 12.455 12.317 11.531]
21 [11.047  9.084  8.353  8.24   6.37   5.836  4.626  4.583  3.777  3.61
  3.252  3.183  3.086  2.941  2.865  2.801  2.639  2.564  2.538  2.466]
41 [2.419 2.404 2.346 2.31  2.246 2.227 2.155 2.147 2.089 2.069 2.065 2.041
 1.975 1.936 1.921 1.917 1.857 1.848 1.83  1.82 ]
61 [1.798 1.779 1.764 1.737 1.729 1.719 1.709 1.692 1.68  1.661 1.645 1.635
 1.619 1.594 1.589 1.583 1.565 1.55  1.541 1.52 ]
W_o.3
1 [10.477  7.357  5.323  5.294  5.177  5.124  5.049  4.959  4.775  4.751
  4.625  4.565  4.462  4.442  4.262  4.246  4.188  4.105  4.067  4.035]
21 [3.997 3.943 3.93  3.908 3.891 3.859 3.812 3.786 3.763 3.703 3.678 3.629
 3.61  3.577 3.535 3.519 3.48  3.461 3.423 3.409]
41 [3.378 3.356 3.293 3.263 3.23  3.219 3.206 3.18  3.146 3.13  3.116 3.082
 3.065 3.025 3.002 2.975 2.954 2.933 2.915 2.896]
61 [2.846 2.83  2.816 2.812 2.771 2.762 2.733 2.719 2.695 2.671 2.647 2.637
 2.62  2.598 2.588 2.556 2.529 2.52  2.5   2.483]
W_proj.0
1 [10.899  7.702  7.173  6.638  6.541  6.288  6.201  6.133  5.941  5.917
  5.758  5.641  5.552  5.476  5.393  5.363  5.259  5.206  5.171  5.153]
21 [5.057 5.018 4.96  4.88  4.821 4.788 4.77  4.73  4.643 4.579 4.546 4.529
 4.505 4.493 4.44  4.415 4.369 4.315 4.293 4.261]
41 [4.243 4.185 4.134 4.104 4.064 4.049 4.026 3.988 3.967 3.95  3.933 3.901
 3.857 3.804 3.778 3.754 3.74  3.713 3.692 3.683]
61 [3.652 3.612 3.607 3.575 3.564 3.522 3.509 3.497 3.47  3.456 3.446 3.417
 3.4   3.378 3.337 3.302 3.291 3.269 3.238 3.23 ]
Combined final output spectrum [28.906 22.386 21.536 20.936 20.117 19.852 19.175 18.933 18.5   17.69
 17.356 16.855 15.592 15.148 14.621 13.72  12.993 12.791 12.632 11.898
 11.629 10.964  9.897  8.83   8.583  7.096  6.654  6.012  5.627  5.54
  5.494  5.275  5.068  4.893  4.87   4.79   4.636  4.597  4.49   4.43
  4.388  4.347  4.331  4.268  4.176  4.148  4.097  4.043  3.974  3.919
  3.881  3.824  3.798  3.784  3.747  3.718  3.71   3.655  3.618  3.585
  3.569  3.558  3.513  3.49   3.465  3.437  3.421  3.385  3.356  3.33 ]
Adjacent spectral ratios [(np.int64(1), np.float64(1.291)), (np.int64(25), np.float64(1.209)), (np.int64(23), np.float64(1.121)), (np.int64(22), np.float64(1.108)), (np.int64(27), np.float64(1.107)), (np.int64(12), np.float64(1.081)), (np.int64(28), np.float64(1.068)), (np.int64(26), np.float64(1.067)), (np.int64(15), np.float64(1.066)), (np.int64(19), np.float64(1.062)), (np.int64(21), np.float64(1.061)), (np.int64(16), np.float64(1.056))]

L0 OV dominant input/output directions: largest coordinate loadings
H 0
0 in [(373, np.float64(0.176)), (225, np.float64(-0.163)), (134, np.float64(-0.158)), (158, np.float64(-0.154)), (7, np.float64(0.153)), (51, np.float64(0.149))] participation 102.5
0 out [(336, np.float64(0.193)), (96, np.float64(0.158)), (291, np.float64(-0.15)), (327, np.float64(0.149)), (203, np.float64(-0.14)), (202, np.float64(-0.128))] participation 116.1
1 in [(226, np.float64(-0.167)), (301, np.float64(0.152)), (358, np.float64(-0.147)), (21, np.float64(-0.146)), (220, np.float64(-0.132)), (325, np.float64(-0.131))] participation 114.5
1 out [(39, np.float64(-0.263)), (6, np.float64(-0.193)), (282, np.float64(0.186)), (156, np.float64(0.147)), (163, np.float64(0.137)), (152, np.float64(0.133))] participation 74.6
H 1
0 in [(184, np.float64(0.347)), (180, np.float64(0.315)), (99, np.float64(0.271)), (39, np.float64(0.267)), (56, np.float64(-0.254)), (317, np.float64(-0.239))] participation 19.1
0 out [(39, np.float64(0.692)), (58, np.float64(-0.51)), (99, np.float64(0.358)), (21, np.float64(-0.212)), (184, np.float64(0.201)), (153, np.float64(-0.054))] participation 3.1
1 in [(211, np.float64(0.34)), (223, np.float64(-0.262)), (228, np.float64(-0.244)), (65, np.float64(0.231)), (173, np.float64(-0.23)), (124, np.float64(-0.214))] participation 23.6
1 out [(21, np.float64(0.961)), (39, np.float64(0.158)), (58, np.float64(-0.129)), (184, np.float64(0.072)), (306, np.float64(-0.032)), (173, np.float64(-0.029))] participation 1.2
H 2
0 in [(184, np.float64(-0.365)), (180, np.float64(-0.304)), (99, np.float64(-0.298)), (317, np.float64(0.248)), (56, np.float64(0.234)), (39, np.float64(-0.231))] participation 18.5
0 out [(39, np.float64(-0.659)), (58, np.float64(0.494)), (21, np.float64(0.373)), (99, np.float64(-0.355)), (184, np.float64(-0.162)), (153, np.float64(0.045))] participation 3.5
1 in [(211, np.float64(0.3)), (173, np.float64(-0.273)), (223, np.float64(-0.256)), (162, np.float64(0.227)), (256, np.float64(-0.225)), (65, np.float64(0.222))] participation 26.1
1 out [(21, np.float64(0.91)), (39, np.float64(0.221)), (99, np.float64(0.207)), (58, np.float64(-0.201)), (184, np.float64(0.053)), (252, np.float64(-0.03))] participation 1.4
H 3
0 in [(223, np.float64(-0.225)), (26, np.float64(-0.196)), (200, np.float64(-0.17)), (48, np.float64(-0.167)), (359, np.float64(0.145)), (124, np.float64(0.142))] participation 77.7
0 out [(92, np.float64(-0.179)), (86, np.float64(0.169)), (188, np.float64(-0.162)), (18, np.float64(0.16)), (131, np.float64(0.158)), (303, np.float64(0.156))] participation 93.5
1 in [(200, np.float64(-0.229)), (124, np.float64(-0.181)), (53, np.float64(0.177)), (329, np.float64(-0.168)), (74, np.float64(0.167)), (105, np.float64(0.159))] participation 71.0
1 out [(65, np.float64(0.19)), (125, np.float64(0.179)), (320, np.float64(-0.173)), (202, np.float64(-0.168)), (86, np.float64(-0.157)), (287, np.float64(-0.152))] participation 89.9
H 4
0 in [(184, np.float64(-0.413)), (180, np.float64(-0.289)), (256, np.float64(0.28)), (56, np.float64(0.243)), (100, np.float64(0.236)), (69, np.float64(-0.225))] participation 16.5
0 out [(39, np.float64(-0.696)), (58, np.float64(0.511)), (99, np.float64(-0.32)), (184, np.float64(-0.227)), (21, np.float64(-0.182)), (153, np.float64(0.057))] participation 3.2
1 in [(211, np.float64(0.352)), (228, np.float64(-0.274)), (124, np.float64(-0.219)), (65, np.float64(0.219)), (26, np.float64(0.214)), (319, np.float64(0.212))] participation 24.5
1 out [(21, np.float64(0.942)), (99, np.float64(-0.24)), (39, np.float64(-0.097)), (58, np.float64(0.092)), (184, np.float64(0.042)), (148, np.float64(-0.033))] participation 1.3
H 5
0 in [(162, np.float64(-0.328)), (211, np.float64(-0.306)), (223, np.float64(0.278)), (65, np.float64(-0.235)), (354, np.float64(0.203)), (173, np.float64(0.201))] participation 22.4
0 out [(21, np.float64(-0.864)), (99, np.float64(-0.357)), (58, np.float64(0.236)), (39, np.float64(-0.232)), (184, np.float64(0.024)), (153, np.float64(0.019))] participation 1.7
1 in [(99, np.float64(-0.369)), (180, np.float64(-0.315)), (184, np.float64(-0.309)), (162, np.float64(-0.224)), (100, np.float64(0.209)), (317, np.float64(0.207))] participation 18.1
1 out [(39, np.float64(-0.608)), (58, np.float64(0.486)), (21, np.float64(0.469)), (99, np.float64(-0.405)), (180, np.float64(-0.036)), (165, np.float64(-0.026))] participation 3.7

Final output common-subspace concentration
rank 20 MLP projection energy L0..L3 [0.089 0.06  0.1   0.872]
rank 22 MLP projection energy L0..L3 [0.099 0.064 0.106 0.894]
rank 24 MLP projection energy L0..L3 [0.107 0.069 0.112 0.915]
rank 26 MLP projection energy L0..L3 [0.114 0.074 0.118 0.929]
rank 27 MLP projection energy L0..L3 [0.119 0.076 0.12  0.931]
rank 28 MLP projection energy L0..L3 [0.121 0.079 0.123 0.933]
rank 32 MLP projection energy L0..L3 [0.133 0.088 0.133 0.939]
rank 40 MLP projection energy L0..L3 [0.154 0.107 0.154 0.943]

Layer0 FC input spectrum, additional indices
1 [17.584 13.477 11.766 10.188  9.613  9.54   9.344  9.149  8.754  8.681
  8.593  8.39   8.008  7.926  7.84   7.731  7.517  7.386  7.159  7.084]
21 [7.068 6.915 6.889 6.682 6.631 6.491 6.436 6.354 6.307 6.16  6.003 5.909
 5.835 5.661 5.466 5.307 5.289 5.132 5.047 4.957]
41 [4.895 4.443 4.367 4.111 4.038 3.8   3.63  3.408 3.226 3.154 2.964 2.947
 2.817 2.635 2.605 2.501 2.481 2.393 2.351 2.276]
61 [2.201 2.148 2.136 2.101 2.066 2.047 1.993 1.957 1.89  1.858 1.85  1.833
 1.781 1.745 1.734 1.726 1.71  1.675 1.666 1.644]
81 [1.625 1.603 1.579 1.555 1.55  1.533 1.518 1.506 1.492 1.464 1.457 1.437
 1.428 1.414 1.404 1.398 1.381 1.374 1.372 1.362]


========================================================================
TURN t005
MESSAGE SENT TO CODEX
OUTPUT of run 4 of at most 100:
```
Last-layer output singular spectra (indices start at 1)
W_proj.3
1 [28.461 22.214 21.34  20.708 19.943 19.662 18.986 18.744 18.295 17.457
 17.132 16.561 15.329 14.874 14.328 13.438 12.667 12.455 12.317 11.531]
21 [11.047  9.084  8.353  8.24   6.37   5.836  4.626  4.583  3.777  3.61
  3.252  3.183  3.086  2.941  2.865  2.801  2.639  2.564  2.538  2.466]
41 [2.419 2.404 2.346 2.31  2.246 2.227 2.155 2.147 2.089 2.069 2.065 2.041
 1.975 1.936 1.921 1.917 1.857 1.848 1.83  1.82 ]
61 [1.798 1.779 1.764 1.737 1.729 1.719 1.709 1.692 1.68  1.661 1.645 1.635
 1.619 1.594 1.589 1.583 1.565 1.55  1.541 1.52 ]
W_o.3
1 [10.477  7.357  5.323  5.294  5.177  5.124  5.049  4.959  4.775  4.751
  4.625  4.565  4.462  4.442  4.262  4.246  4.188  4.105  4.067  4.035]
21 [3.997 3.943 3.93  3.908 3.891 3.859 3.812 3.786 3.763 3.703 3.678 3.629
 3.61  3.577 3.535 3.519 3.48  3.461 3.423 3.409]
41 [3.378 3.356 3.293 3.263 3.23  3.219 3.206 3.18  3.146 3.13  3.116 3.082
 3.065 3.025 3.002 2.975 2.954 2.933 2.915 2.896]
61 [2.846 2.83  2.816 2.812 2.771 2.762 2.733 2.719 2.695 2.671 2.647 2.637
 2.62  2.598 2.588 2.556 2.529 2.52  2.5   2.483]
W_proj.0
1 [10.899  7.702  7.173  6.638  6.541  6.288  6.201  6.133  5.941  5.917
  5.758  5.641  5.552  5.476  5.393  5.363  5.259  5.206  5.171  5.153]
21 [5.057 5.018 4.96  4.88  4.821 4.788 4.77  4.73  4.643 4.579 4.546 4.529
 4.505 4.493 4.44  4.415 4.369 4.315 4.293 4.261]
41 [4.243 4.185 4.134 4.104 4.064 4.049 4.026 3.988 3.967 3.95  3.933 3.901
 3.857 3.804 3.778 3.754 3.74  3.713 3.692 3.683]
61 [3.652 3.612 3.607 3.575 3.564 3.522 3.509 3.497 3.47  3.456 3.446 3.417
 3.4   3.378 3.337 3.302 3.291 3.269 3.238 3.23 ]
Combined final output spectrum [28.906 22.386 21.536 20.936 20.117 19.852 19.175 18.933 18.5   17.69
 17.356 16.855 15.592 15.148 14.621 13.72  12.993 12.791 12.632 11.898
 11.629 10.964  9.897  8.83   8.583  7.096  6.654  6.012  5.627  5.54
  5.494  5.275  5.068  4.893  4.87   4.79   4.636  4.597  4.49   4.43
  4.388  4.347  4.331  4.268  4.176  4.148  4.097  4.043  3.974  3.919
  3.881  3.824  3.798  3.784  3.747  3.718  3.71   3.655  3.618  3.585
  3.569  3.558  3.513  3.49   3.465  3.437  3.421  3.385  3.356  3.33 ]
Adjacent spectral ratios [(np.int64(1), np.float64(1.291)), (np.int64(25), np.float64(1.209)), (np.int64(23), np.float64(1.121)), (np.int64(22), np.float64(1.108)), (np.int64(27), np.float64(1.107)), (np.int64(12), np.float64(1.081)), (np.int64(28), np.float64(1.068)), (np.int64(26), np.float64(1.067)), (np.int64(15), np.float64(1.066)), (np.int64(19), np.float64(1.062)), (np.int64(21), np.float64(1.061)), (np.int64(16), np.float64(1.056))]

L0 OV dominant input/output directions: largest coordinate loadings
H 0
0 in [(373, np.float64(0.176)), (225, np.float64(-0.163)), (134, np.float64(-0.158)), (158, np.float64(-0.154)), (7, np.float64(0.153)), (51, np.float64(0.149))] participation 102.5
0 out [(336, np.float64(0.193)), (96, np.float64(0.158)), (291, np.float64(-0.15)), (327, np.float64(0.149)), (203, np.float64(-0.14)), (202, np.float64(-0.128))] participation 116.1
1 in [(226, np.float64(-0.167)), (301, np.float64(0.152)), (358, np.float64(-0.147)), (21, np.float64(-0.146)), (220, np.float64(-0.132)), (325, np.float64(-0.131))] participation 114.5
1 out [(39, np.float64(-0.263)), (6, np.float64(-0.193)), (282, np.float64(0.186)), (156, np.float64(0.147)), (163, np.float64(0.137)), (152, np.float64(0.133))] participation 74.6
H 1
0 in [(184, np.float64(0.347)), (180, np.float64(0.315)), (99, np.float64(0.271)), (39, np.float64(0.267)), (56, np.float64(-0.254)), (317, np.float64(-0.239))] participation 19.1
0 out [(39, np.float64(0.692)), (58, np.float64(-0.51)), (99, np.float64(0.358)), (21, np.float64(-0.212)), (184, np.float64(0.201)), (153, np.float64(-0.054))] participation 3.1
1 in [(211, np.float64(0.34)), (223, np.float64(-0.262)), (228, np.float64(-0.244)), (65, np.float64(0.231)), (173, np.float64(-0.23)), (124, np.float64(-0.214))] participation 23.6
1 out [(21, np.float64(0.961)), (39, np.float64(0.158)), (58, np.float64(-0.129)), (184, np.float64(0.072)), (306, np.float64(-0.032)), (173, np.float64(-0.029))] participation 1.2
H 2
0 in [(184, np.float64(-0.365)), (180, np.float64(-0.304)), (99, np.float64(-0.298)), (317, np.float64(0.248)), (56, np.float64(0.234)), (39, np.float64(-0.231))] participation 18.5
0 out [(39, np.float64(-0.659)), (58, np.float64(0.494)), (21, np.float64(0.373)), (99, np.float64(-0.355)), (184, np.float64(-0.162)), (153, np.float64(0.045))] participation 3.5
1 in [(211, np.float64(0.3)), (173, np.float64(-0.273)), (223, np.float64(-0.256)), (162, np.float64(0.227)), (256, np.float64(-0.225)), (65, np.float64(0.222))] participation 26.1
1 out [(21, np.float64(0.91)), (39, np.float64(0.221)), (99, np.float64(0.207)), (58, np.float64(-0.201)), (184, np.float64(0.053)), (252, np.float64(-0.03))] participation 1.4
H 3
0 in [(223, np.float64(-0.225)), (26, np.float64(-0.196)), (200, np.float64(-0.17)), (48, np.float64(-0.167)), (359, np.float64(0.145)), (124, np.float64(0.142))] participation 77.7
0 out [(92, np.float64(-0.179)), (86, np.float64(0.169)), (188, np.float64(-0.162)), (18, np.float64(0.16)), (131, np.float64(0.158)), (303, np.float64(0.156))] participation 93.5
1 in [(200, np.float64(-0.229)), (124, np.float64(-0.181)), (53, np.float64(0.177)), (329, np.float64(-0.168)), (74, np.float64(0.167)), (105, np.float64(0.159))] participation 71.0
1 out [(65, np.float64(0.19)), (125, np.float64(0.179)), (320, np.float64(-0.173)), (202, np.float64(-0.168)), (86, np.float64(-0.157)), (287, np.float64(-0.152))] participation 89.9
H 4
0 in [(184, np.float64(-0.413)), (180, np.float64(-0.289)), (256, np.float64(0.28)), (56, np.float64(0.243)), (100, np.float64(0.236)), (69, np.float64(-0.225))] participation 16.5
0 out [(39, np.float64(-0.696)), (58, np.float64(0.511)), (99, np.float64(-0.32)), (184, np.float64(-0.227)), (21, np.float64(-0.182)), (153, np.float64(0.057))] participation 3.2
1 in [(211, np.float64(0.352)), (228, np.float64(-0.274)), (124, np.float64(-0.219)), (65, np.float64(0.219)), (26, np.float64(0.214)), (319, np.float64(0.212))] participation 24.5
1 out [(21, np.float64(0.942)), (99, np.float64(-0.24)), (39, np.float64(-0.097)), (58, np.float64(0.092)), (184, np.float64(0.042)), (148, np.float64(-0.033))] participation 1.3
H 5
0 in [(162, np.float64(-0.328)), (211, np.float64(-0.306)), (223, np.float64(0.278)), (65, np.float64(-0.235)), (354, np.float64(0.203)), (173, np.float64(0.201))] participation 22.4
0 out [(21, np.float64(-0.864)), (99, np.float64(-0.357)), (58, np.float64(0.236)), (39, np.float64(-0.232)), (184, np.float64(0.024)), (153, np.float64(0.019))] participation 1.7
1 in [(99, np.float64(-0.369)), (180, np.float64(-0.315)), (184, np.float64(-0.309)), (162, np.float64(-0.224)), (100, np.float64(0.209)), (317, np.float64(0.207))] participation 18.1
1 out [(39, np.float64(-0.608)), (58, np.float64(0.486)), (21, np.float64(0.469)), (99, np.float64(-0.405)), (180, np.float64(-0.036)), (165, np.float64(-0.026))] participation 3.7

Final output common-subspace concentration
rank 20 MLP projection energy L0..L3 [0.089 0.06  0.1   0.872]
rank 22 MLP projection energy L0..L3 [0.099 0.064 0.106 0.894]
rank 24 MLP projection energy L0..L3 [0.107 0.069 0.112 0.915]
rank 26 MLP projection energy L0..L3 [0.114 0.074 0.118 0.929]
rank 27 MLP projection energy L0..L3 [0.119 0.076 0.12  0.931]
rank 28 MLP projection energy L0..L3 [0.121 0.079 0.123 0.933]
rank 32 MLP projection energy L0..L3 [0.133 0.088 0.133 0.939]
rank 40 MLP projection energy L0..L3 [0.154 0.107 0.154 0.943]

Layer0 FC input spectrum, additional indices
1 [17.584 13.477 11.766 10.188  9.613  9.54   9.344  9.149  8.754  8.681
  8.593  8.39   8.008  7.926  7.84   7.731  7.517  7.386  7.159  7.084]
21 [7.068 6.915 6.889 6.682 6.631 6.491 6.436 6.354 6.307 6.16  6.003 5.909
 5.835 5.661 5.466 5.307 5.289 5.132 5.047 4.957]
41 [4.895 4.443 4.367 4.111 4.038 3.8   3.63  3.408 3.226 3.154 2.964 2.947
 2.817 2.635 2.605 2.501 2.481 2.393 2.351 2.276]
61 [2.201 2.148 2.136 2.101 2.066 2.047 1.993 1.957 1.89  1.858 1.85  1.833
 1.781 1.745 1.734 1.726 1.71  1.675 1.666 1.644]
81 [1.625 1.603 1.579 1.555 1.55  1.533 1.518 1.506 1.492 1.464 1.457 1.437
 1.428 1.414 1.404 1.398 1.381 1.374 1.372 1.362]

```
CLI OUTPUT IN EVENT ORDER
ERROR
Failed to read global AGENTS.md instructions from `<local-home>/.codex/AGENTS.md`: Operation not permitted (os error 1)

ERROR
Code Mode is unavailable because code-mode host is disabled. Code mode will fail closed; enable `features.code_mode_host` and install `codex-code-mode-host`.

AGENT_MESSAGE
```python
import numpy as np
from scipy.linalg import svd, eigvals
from threadpoolctl import threadpool_limits

def cosine(a,b):
    return np.sum(a*b)/(np.linalg.norm(a)*np.linalg.norm(b)+1e-30)

with threadpool_limits(limits=2):
    A=[]; B=[]; KB=[]
    for l in range(4):
        g=W[f"ln1_w.{l}"].astype(float); b=W[f"ln1_b.{l}"].astype(float)
        for j in range(6):
            sl=slice(64*j,64*j+64)
            q=W[f"W_q.{l}"][sl].astype(float)
            k=W[f"W_k.{l}"][sl].astype(float)
            v=W[f"W_v.{l}"][sl].astype(float)
            qg=q*g; kg=k*g; vg=v*g
            for m in [qg,kg,vg]: m-=m.mean(1,keepdims=True)
            A.append(qg.T@kg/8)
            B.append(W[f"W_o.{l}"][:,sl].astype(float)@vg)
            KB.append(kg.T@(q@b)/8)
    print("L0H0 versus powers of L0H3 QK (weight products only)")
    C=np.eye(384)
    for power in range(1,7):
        C=C@A[3]
        C/=np.linalg.norm(C)
        print(power,round(cosine(A[0],C),4),round(cosine(A[0],C.T),4))
    u,s,vt=svd(A[3],full_matrices=False)
    Z=np.concatenate([u[:,:24],vt[:24].T],axis=1)
    z,sz,_=svd(Z,full_matrices=False)
    for rank in [16,24,32,40]:
        P=z[:,:rank]
        C3=P.T@A[3]@P; C0=P.T@A[0]@P
        print("QK subspace rank",rank,"H0/H3 captured energies",
              np.round([np.linalg.norm(C0)**2/np.linalg.norm(A[0])**2,
                        np.linalg.norm(C3)**2/np.linalg.norm(A[3])**2],3),
              "H0 vs H3^2",round(cosine(C0,C3@C3),3),
              "commutator relative",round(np.linalg.norm(C0@C3-C3@C0)/
                  (np.linalg.norm(C0@C3)+np.linalg.norm(C3@C0)),3))
    print("\nShared L0 low-rank output space")
    T=np.concatenate([B[j] for j in [1,2,4,5]],axis=1)
    U,ss,_=svd(T,full_matrices=False)
    print("singular values",np.round(ss[:12],3))
    C=U[:,:2]
    for i in range(24):
        a=A[i]; kb=KB[i]
        print("L%dH%d"%(i//6,i%6),
              "Q-side/K-side 2D energy",
              np.round([np.linalg.norm(C.T@a)**2/np.linalg.norm(a)**2,
                        np.linalg.norm(a@C)**2/np.linalg.norm(a)**2],3),
              "key-bias fraction",round(np.linalg.norm(C.T@kb)**2/(np.linalg.norm(kb)**2),3),
              "2x2",np.round(C.T@a@C,3).tolist(),
              "key-bias",np.round(C.T@kb,3))
    print("\nL0H3 value spectrum")
    v=W["W_v.0"][192:256].astype(float)*W["ln1_w.0"]
    v-=v.mean(1,keepdims=True)
    u,s,vt=svd(v,full_matrices=False)
    print(np.round(s,3))
    for rank in [16,20,24,28,32]:
        P=vt[:rank].T
        print("Token-candidate subspace rank",rank,
              "L3H3 QK@L0H3 OV trace/norm",
              round(np.trace(P.T@A[21]@B[3]@P)/np.linalg.norm(P.T@A[21]@B[3]@P),3))
```


PERMITTED EXPERIMENT HARNESS RECORD: python
{
  "run": 5,
  "turn": "t005",
  "code": "import numpy as np\nfrom scipy.linalg import svd, eigvals\nfrom threadpoolctl import threadpool_limits\n\ndef cosine(a,b):\n    return np.sum(a*b)/(np.linalg.norm(a)*np.linalg.norm(b)+1e-30)\n\nwith threadpool_limits(limits=2):\n    A=[]; B=[]; KB=[]\n    for l in range(4):\n        g=W[f\"ln1_w.{l}\"].astype(float); b=W[f\"ln1_b.{l}\"].astype(float)\n        for j in range(6):\n            sl=slice(64*j,64*j+64)\n            q=W[f\"W_q.{l}\"][sl].astype(float)\n            k=W[f\"W_k.{l}\"][sl].astype(float)\n            v=W[f\"W_v.{l}\"][sl].astype(float)\n            qg=q*g; kg=k*g; vg=v*g\n            for m in [qg,kg,vg]: m-=m.mean(1,keepdims=True)\n            A.append(qg.T@kg/8)\n            B.append(W[f\"W_o.{l}\"][:,sl].astype(float)@vg)\n            KB.append(kg.T@(q@b)/8)\n    print(\"L0H0 versus powers of L0H3 QK (weight products only)\")\n    C=np.eye(384)\n    for power in range(1,7):\n        C=C@A[3]\n        C/=np.linalg.norm(C)\n        print(power,round(cosine(A[0],C),4),round(cosine(A[0],C.T),4))\n    u,s,vt=svd(A[3],full_matrices=False)\n    Z=np.concatenate([u[:,:24],vt[:24].T],axis=1)\n    z,sz,_=svd(Z,full_matrices=False)\n    for rank in [16,24,32,40]:\n        P=z[:,:rank]\n        C3=P.T@A[3]@P; C0=P.T@A[0]@P\n        print(\"QK subspace rank\",rank,\"H0/H3 captured energies\",\n              np.round([np.linalg.norm(C0)**2/np.linalg.norm(A[0])**2,\n                        np.linalg.norm(C3)**2/np.linalg.norm(A[3])**2],3),\n              \"H0 vs H3^2\",round(cosine(C0,C3@C3),3),\n              \"commutator relative\",round(np.linalg.norm(C0@C3-C3@C0)/\n                  (np.linalg.norm(C0@C3)+np.linalg.norm(C3@C0)),3))\n    print(\"\\nShared L0 low-rank output space\")\n    T=np.concatenate([B[j] for j in [1,2,4,5]],axis=1)\n    U,ss,_=svd(T,full_matrices=False)\n    print(\"singular values\",np.round(ss[:12],3))\n    C=U[:,:2]\n    for i in range(24):\n        a=A[i]; kb=KB[i]\n        print(\"L%dH%d\"%(i//6,i%6),\n              \"Q-side/K-side 2D energy\",\n              np.round([np.linalg.norm(C.T@a)**2/np.linalg.norm(a)**2,\n                        np.linalg.norm(a@C)**2/np.linalg.norm(a)**2],3),\n              \"key-bias fraction\",round(np.linalg.norm(C.T@kb)**2/(np.linalg.norm(kb)**2),3),\n              \"2x2\",np.round(C.T@a@C,3).tolist(),\n              \"key-bias\",np.round(C.T@kb,3))\n    print(\"\\nL0H3 value spectrum\")\n    v=W[\"W_v.0\"][192:256].astype(float)*W[\"ln1_w.0\"]\n    v-=v.mean(1,keepdims=True)\n    u,s,vt=svd(v,full_matrices=False)\n    print(np.round(s,3))\n    for rank in [16,20,24,28,32]:\n        P=vt[:rank].T\n        print(\"Token-candidate subspace rank\",rank,\n              \"L3H3 QK@L0H3 OV trace/norm\",\n              round(np.trace(P.T@A[21]@B[3]@P)/np.linalg.norm(P.T@A[21]@B[3]@P),3))",
  "out": "L0H0 versus powers of L0H3 QK (weight products only)\n1 0.1374 -0.0574\n2 0.1115 -0.1454\n3 -0.0655 -0.2198\n4 -0.2895 -0.1894\n5 -0.3667 -0.0247\n6 -0.2073 0.1792\nQK subspace rank 16 H0/H3 captured energies [0.132 0.587] H0 vs H3^2 0.232 commutator relative 0.315\nQK subspace rank 24 H0/H3 captured energies [0.437 0.883] H0 vs H3^2 0.195 commutator relative 0.405\nQK subspace rank 32 H0/H3 captured energies [0.603 0.945] H0 vs H3^2 0.151 commutator relative 0.438\nQK subspace rank 40 H0/H3 captured energies [0.641 0.967] H0 vs H3^2 0.144 commutator relative 0.444\n\nShared L0 low-rank output space\nsingular values [16.477  9.756  3.151  1.143  1.082  0.768  0.561  0.544  0.443  0.424\n  0.319  0.281]\nL0H0 Q-side/K-side 2D energy [0.068 0.051] key-bias fraction 0.015 2x2 [[0.004, 0.01], [0.004, 0.014]] key-bias [ 0.005 -0.003]\nL0H1 Q-side/K-side 2D energy [0.019 0.007] key-bias fraction 0.019 2x2 [[-0.002, -0.001], [0.001, -0.001]] key-bias [0.001 0.001]\nL0H2 Q-side/K-side 2D energy [0.009 0.002] key-bias fraction 0.007 2x2 [[-0.001, 0.001], [0.0, -0.001]] key-bias [0.    0.001]\nL0H3 Q-side/K-side 2D energy [0.027 0.029] key-bias fraction 0.077 2x2 [[0.027, 0.025], [-0.003, 0.013]] key-bias [-0.01  -0.006]\nL0H4 Q-side/K-side 2D energy [0.039 0.011] key-bias fraction 0.012 2x2 [[-0.001, 0.001], [0.0, -0.0]] key-bias [ 0.001 -0.001]\nL0H5 Q-side/K-side 2D energy [0.113 0.007] key-bias fraction 0.007 2x2 [[-0.0, -0.0], [0.001, -0.0]] key-bias [0. 0.]\nL1H0 Q-side/K-side 2D energy [0.041 0.394] key-bias fraction 0.846 2x2 [[0.042, 0.208], [-0.264, 0.127]] key-bias [ 2.919 -2.202]\nL1H1 Q-side/K-side 2D energy [0.051 0.427] key-bias fraction 0.846 2x2 [[0.041, 0.213], [-0.278, 0.136]] key-bias [ 2.664 -2.1  ]\nL1H2 Q-side/K-side 2D energy [0.032 0.456] key-bias fraction 0.85 2x2 [[0.044, 0.167], [-0.209, 0.101]] key-bias [ 2.223 -1.723]\nL1H3 Q-side/K-side 2D energy [0.049 0.459] key-bias fraction 0.845 2x2 [[0.046, 0.203], [-0.262, 0.123]] key-bias [ 2.395 -1.996]\nL1H4 Q-side/K-side 2D energy [0.023 0.422] key-bias fraction 0.79 2x2 [[0.053, 0.114], [-0.151, 0.097]] key-bias [ 1.467 -1.46 ]\nL1H5 Q-side/K-side 2D energy [0.058 0.416] key-bias fraction 0.846 2x2 [[0.041, 0.23], [-0.302, 0.141]] key-bias [ 2.787 -2.252]\nL2H0 Q-side/K-side 2D energy [0.063 0.226] key-bias fraction 0.829 2x2 [[0.036, 0.228], [-0.272, 0.109]] key-bias [ 1.418 -1.172]\nL2H1 Q-side/K-side 2D energy [0.029 0.087] key-bias fraction 0.806 2x2 [[0.031, 0.207], [-0.244, 0.098]] key-bias [ 1.283 -1.098]\nL2H2 Q-side/K-side 2D energy [0.03  0.117] key-bias fraction 0.771 2x2 [[0.033, 0.168], [-0.196, 0.085]] key-bias [ 1.06  -0.933]\nL2H3 Q-side/K-side 2D energy [0.01  0.086] key-bias fraction 0.612 2x2 [[0.027, 0.087], [-0.103, 0.05]] key-bias [ 0.58  -0.593]\nL2H4 Q-side/K-side 2D energy [0.039 0.15 ] key-bias fraction 0.829 2x2 [[0.025, 0.25], [-0.298, 0.103]] key-bias [ 1.648 -1.301]\nL2H5 Q-side/K-side 2D energy [0.029 0.095] key-bias fraction 0.846 2x2 [[0.032, 0.217], [-0.255, 0.095]] key-bias [ 1.488 -1.118]\nL3H0 Q-side/K-side 2D energy [0.01  0.039] key-bias fraction 0.687 2x2 [[0.022, 0.114], [-0.117, 0.019]] key-bias [ 0.3   -0.286]\nL3H1 Q-side/K-side 2D energy [0.009 0.058] key-bias fraction 0.48 2x2 [[0.028, 0.059], [-0.065, 0.019]] key-bias [ 0.118 -0.153]\nL3H2 Q-side/K-side 2D energy [0.016 0.061] key-bias fraction 0.616 2x2 [[0.023, 0.104], [-0.107, 0.025]] key-bias [ 0.272 -0.278]\nL3H3 Q-side/K-side 2D energy [0.001 0.001] key-bias fraction 0.008 2x2 [[0.009, 0.0], [-0.0, 0.005]] key-bias [-0.018 -0.007]\nL3H4 Q-side/K-side 2D energy [0.005 0.008] key-bias fraction 0.038 2x2 [[0.003, 0.008], [-0.007, 0.0]] key-bias [ 0.024 -0.014]\nL3H5 Q-side/K-side 2D energy [0.01 0.06] key-bias fraction 0.724 2x2 [[0.016, 0.094], [-0.093, 0.013]] key-bias [ 0.323 -0.268]\n\nL0H3 value spectrum\n[0.57  0.513 0.504 0.472 0.47  0.45  0.44  0.434 0.425 0.411 0.39  0.383\n 0.379 0.367 0.359 0.342 0.339 0.336 0.324 0.297 0.286 0.276 0.273 0.266\n 0.254 0.248 0.245 0.241 0.237 0.231 0.225 0.223 0.22  0.21  0.206 0.204\n 0.197 0.194 0.183 0.18  0.173 0.169 0.16  0.151 0.15  0.138 0.133 0.132\n 0.124 0.121 0.116 0.11  0.108 0.107 0.103 0.101 0.097 0.093 0.09  0.087\n 0.085 0.081 0.077 0.072]\nToken-candidate subspace rank 16 L3H3 QK@L0H3 OV trace/norm 2.724\nToken-candidate subspace rank 20 L3H3 QK@L0H3 OV trace/norm 2.858\nToken-candidate subspace rank 24 L3H3 QK@L0H3 OV trace/norm 2.716\nToken-candidate subspace rank 28 L3H3 QK@L0H3 OV trace/norm 2.614\nToken-candidate subspace rank 32 L3H3 QK@L0H3 OV trace/norm 2.505\n",
  "seconds": 0.578,
  "rc": 0,
  "timed_out": false,
  "truncated": false,
  "code_sha256": "d51adcec839babb1205b859c37c4ab44e62d007d57ef1157874f353959fb21b4",
  "weights_sha256": "04ec0b300d207b26b92a1af6d49d56d452833e39b35826200bc1d821e5b7d930"
}

EXACT HARNESS FEEDBACK
L0H0 versus powers of L0H3 QK (weight products only)
1 0.1374 -0.0574
2 0.1115 -0.1454
3 -0.0655 -0.2198
4 -0.2895 -0.1894
5 -0.3667 -0.0247
6 -0.2073 0.1792
QK subspace rank 16 H0/H3 captured energies [0.132 0.587] H0 vs H3^2 0.232 commutator relative 0.315
QK subspace rank 24 H0/H3 captured energies [0.437 0.883] H0 vs H3^2 0.195 commutator relative 0.405
QK subspace rank 32 H0/H3 captured energies [0.603 0.945] H0 vs H3^2 0.151 commutator relative 0.438
QK subspace rank 40 H0/H3 captured energies [0.641 0.967] H0 vs H3^2 0.144 commutator relative 0.444

Shared L0 low-rank output space
singular values [16.477  9.756  3.151  1.143  1.082  0.768  0.561  0.544  0.443  0.424
  0.319  0.281]
L0H0 Q-side/K-side 2D energy [0.068 0.051] key-bias fraction 0.015 2x2 [[0.004, 0.01], [0.004, 0.014]] key-bias [ 0.005 -0.003]
L0H1 Q-side/K-side 2D energy [0.019 0.007] key-bias fraction 0.019 2x2 [[-0.002, -0.001], [0.001, -0.001]] key-bias [0.001 0.001]
L0H2 Q-side/K-side 2D energy [0.009 0.002] key-bias fraction 0.007 2x2 [[-0.001, 0.001], [0.0, -0.001]] key-bias [0.    0.001]
L0H3 Q-side/K-side 2D energy [0.027 0.029] key-bias fraction 0.077 2x2 [[0.027, 0.025], [-0.003, 0.013]] key-bias [-0.01  -0.006]
L0H4 Q-side/K-side 2D energy [0.039 0.011] key-bias fraction 0.012 2x2 [[-0.001, 0.001], [0.0, -0.0]] key-bias [ 0.001 -0.001]
L0H5 Q-side/K-side 2D energy [0.113 0.007] key-bias fraction 0.007 2x2 [[-0.0, -0.0], [0.001, -0.0]] key-bias [0. 0.]
L1H0 Q-side/K-side 2D energy [0.041 0.394] key-bias fraction 0.846 2x2 [[0.042, 0.208], [-0.264, 0.127]] key-bias [ 2.919 -2.202]
L1H1 Q-side/K-side 2D energy [0.051 0.427] key-bias fraction 0.846 2x2 [[0.041, 0.213], [-0.278, 0.136]] key-bias [ 2.664 -2.1  ]
L1H2 Q-side/K-side 2D energy [0.032 0.456] key-bias fraction 0.85 2x2 [[0.044, 0.167], [-0.209, 0.101]] key-bias [ 2.223 -1.723]
L1H3 Q-side/K-side 2D energy [0.049 0.459] key-bias fraction 0.845 2x2 [[0.046, 0.203], [-0.262, 0.123]] key-bias [ 2.395 -1.996]
L1H4 Q-side/K-side 2D energy [0.023 0.422] key-bias fraction 0.79 2x2 [[0.053, 0.114], [-0.151, 0.097]] key-bias [ 1.467 -1.46 ]
L1H5 Q-side/K-side 2D energy [0.058 0.416] key-bias fraction 0.846 2x2 [[0.041, 0.23], [-0.302, 0.141]] key-bias [ 2.787 -2.252]
L2H0 Q-side/K-side 2D energy [0.063 0.226] key-bias fraction 0.829 2x2 [[0.036, 0.228], [-0.272, 0.109]] key-bias [ 1.418 -1.172]
L2H1 Q-side/K-side 2D energy [0.029 0.087] key-bias fraction 0.806 2x2 [[0.031, 0.207], [-0.244, 0.098]] key-bias [ 1.283 -1.098]
L2H2 Q-side/K-side 2D energy [0.03  0.117] key-bias fraction 0.771 2x2 [[0.033, 0.168], [-0.196, 0.085]] key-bias [ 1.06  -0.933]
L2H3 Q-side/K-side 2D energy [0.01  0.086] key-bias fraction 0.612 2x2 [[0.027, 0.087], [-0.103, 0.05]] key-bias [ 0.58  -0.593]
L2H4 Q-side/K-side 2D energy [0.039 0.15 ] key-bias fraction 0.829 2x2 [[0.025, 0.25], [-0.298, 0.103]] key-bias [ 1.648 -1.301]
L2H5 Q-side/K-side 2D energy [0.029 0.095] key-bias fraction 0.846 2x2 [[0.032, 0.217], [-0.255, 0.095]] key-bias [ 1.488 -1.118]
L3H0 Q-side/K-side 2D energy [0.01  0.039] key-bias fraction 0.687 2x2 [[0.022, 0.114], [-0.117, 0.019]] key-bias [ 0.3   -0.286]
L3H1 Q-side/K-side 2D energy [0.009 0.058] key-bias fraction 0.48 2x2 [[0.028, 0.059], [-0.065, 0.019]] key-bias [ 0.118 -0.153]
L3H2 Q-side/K-side 2D energy [0.016 0.061] key-bias fraction 0.616 2x2 [[0.023, 0.104], [-0.107, 0.025]] key-bias [ 0.272 -0.278]
L3H3 Q-side/K-side 2D energy [0.001 0.001] key-bias fraction 0.008 2x2 [[0.009, 0.0], [-0.0, 0.005]] key-bias [-0.018 -0.007]
L3H4 Q-side/K-side 2D energy [0.005 0.008] key-bias fraction 0.038 2x2 [[0.003, 0.008], [-0.007, 0.0]] key-bias [ 0.024 -0.014]
L3H5 Q-side/K-side 2D energy [0.01 0.06] key-bias fraction 0.724 2x2 [[0.016, 0.094], [-0.093, 0.013]] key-bias [ 0.323 -0.268]

L0H3 value spectrum
[0.57  0.513 0.504 0.472 0.47  0.45  0.44  0.434 0.425 0.411 0.39  0.383
 0.379 0.367 0.359 0.342 0.339 0.336 0.324 0.297 0.286 0.276 0.273 0.266
 0.254 0.248 0.245 0.241 0.237 0.231 0.225 0.223 0.22  0.21  0.206 0.204
 0.197 0.194 0.183 0.18  0.173 0.169 0.16  0.151 0.15  0.138 0.133 0.132
 0.124 0.121 0.116 0.11  0.108 0.107 0.103 0.101 0.097 0.093 0.09  0.087
 0.085 0.081 0.077 0.072]
Token-candidate subspace rank 16 L3H3 QK@L0H3 OV trace/norm 2.724
Token-candidate subspace rank 20 L3H3 QK@L0H3 OV trace/norm 2.858
Token-candidate subspace rank 24 L3H3 QK@L0H3 OV trace/norm 2.716
Token-candidate subspace rank 28 L3H3 QK@L0H3 OV trace/norm 2.614
Token-candidate subspace rank 32 L3H3 QK@L0H3 OV trace/norm 2.505


========================================================================
TURN t006
MESSAGE SENT TO CODEX
OUTPUT of run 5 of at most 100:
```
L0H0 versus powers of L0H3 QK (weight products only)
1 0.1374 -0.0574
2 0.1115 -0.1454
3 -0.0655 -0.2198
4 -0.2895 -0.1894
5 -0.3667 -0.0247
6 -0.2073 0.1792
QK subspace rank 16 H0/H3 captured energies [0.132 0.587] H0 vs H3^2 0.232 commutator relative 0.315
QK subspace rank 24 H0/H3 captured energies [0.437 0.883] H0 vs H3^2 0.195 commutator relative 0.405
QK subspace rank 32 H0/H3 captured energies [0.603 0.945] H0 vs H3^2 0.151 commutator relative 0.438
QK subspace rank 40 H0/H3 captured energies [0.641 0.967] H0 vs H3^2 0.144 commutator relative 0.444

Shared L0 low-rank output space
singular values [16.477  9.756  3.151  1.143  1.082  0.768  0.561  0.544  0.443  0.424
  0.319  0.281]
L0H0 Q-side/K-side 2D energy [0.068 0.051] key-bias fraction 0.015 2x2 [[0.004, 0.01], [0.004, 0.014]] key-bias [ 0.005 -0.003]
L0H1 Q-side/K-side 2D energy [0.019 0.007] key-bias fraction 0.019 2x2 [[-0.002, -0.001], [0.001, -0.001]] key-bias [0.001 0.001]
L0H2 Q-side/K-side 2D energy [0.009 0.002] key-bias fraction 0.007 2x2 [[-0.001, 0.001], [0.0, -0.001]] key-bias [0.    0.001]
L0H3 Q-side/K-side 2D energy [0.027 0.029] key-bias fraction 0.077 2x2 [[0.027, 0.025], [-0.003, 0.013]] key-bias [-0.01  -0.006]
L0H4 Q-side/K-side 2D energy [0.039 0.011] key-bias fraction 0.012 2x2 [[-0.001, 0.001], [0.0, -0.0]] key-bias [ 0.001 -0.001]
L0H5 Q-side/K-side 2D energy [0.113 0.007] key-bias fraction 0.007 2x2 [[-0.0, -0.0], [0.001, -0.0]] key-bias [0. 0.]
L1H0 Q-side/K-side 2D energy [0.041 0.394] key-bias fraction 0.846 2x2 [[0.042, 0.208], [-0.264, 0.127]] key-bias [ 2.919 -2.202]
L1H1 Q-side/K-side 2D energy [0.051 0.427] key-bias fraction 0.846 2x2 [[0.041, 0.213], [-0.278, 0.136]] key-bias [ 2.664 -2.1  ]
L1H2 Q-side/K-side 2D energy [0.032 0.456] key-bias fraction 0.85 2x2 [[0.044, 0.167], [-0.209, 0.101]] key-bias [ 2.223 -1.723]
L1H3 Q-side/K-side 2D energy [0.049 0.459] key-bias fraction 0.845 2x2 [[0.046, 0.203], [-0.262, 0.123]] key-bias [ 2.395 -1.996]
L1H4 Q-side/K-side 2D energy [0.023 0.422] key-bias fraction 0.79 2x2 [[0.053, 0.114], [-0.151, 0.097]] key-bias [ 1.467 -1.46 ]
L1H5 Q-side/K-side 2D energy [0.058 0.416] key-bias fraction 0.846 2x2 [[0.041, 0.23], [-0.302, 0.141]] key-bias [ 2.787 -2.252]
L2H0 Q-side/K-side 2D energy [0.063 0.226] key-bias fraction 0.829 2x2 [[0.036, 0.228], [-0.272, 0.109]] key-bias [ 1.418 -1.172]
L2H1 Q-side/K-side 2D energy [0.029 0.087] key-bias fraction 0.806 2x2 [[0.031, 0.207], [-0.244, 0.098]] key-bias [ 1.283 -1.098]
L2H2 Q-side/K-side 2D energy [0.03  0.117] key-bias fraction 0.771 2x2 [[0.033, 0.168], [-0.196, 0.085]] key-bias [ 1.06  -0.933]
L2H3 Q-side/K-side 2D energy [0.01  0.086] key-bias fraction 0.612 2x2 [[0.027, 0.087], [-0.103, 0.05]] key-bias [ 0.58  -0.593]
L2H4 Q-side/K-side 2D energy [0.039 0.15 ] key-bias fraction 0.829 2x2 [[0.025, 0.25], [-0.298, 0.103]] key-bias [ 1.648 -1.301]
L2H5 Q-side/K-side 2D energy [0.029 0.095] key-bias fraction 0.846 2x2 [[0.032, 0.217], [-0.255, 0.095]] key-bias [ 1.488 -1.118]
L3H0 Q-side/K-side 2D energy [0.01  0.039] key-bias fraction 0.687 2x2 [[0.022, 0.114], [-0.117, 0.019]] key-bias [ 0.3   -0.286]
L3H1 Q-side/K-side 2D energy [0.009 0.058] key-bias fraction 0.48 2x2 [[0.028, 0.059], [-0.065, 0.019]] key-bias [ 0.118 -0.153]
L3H2 Q-side/K-side 2D energy [0.016 0.061] key-bias fraction 0.616 2x2 [[0.023, 0.104], [-0.107, 0.025]] key-bias [ 0.272 -0.278]
L3H3 Q-side/K-side 2D energy [0.001 0.001] key-bias fraction 0.008 2x2 [[0.009, 0.0], [-0.0, 0.005]] key-bias [-0.018 -0.007]
L3H4 Q-side/K-side 2D energy [0.005 0.008] key-bias fraction 0.038 2x2 [[0.003, 0.008], [-0.007, 0.0]] key-bias [ 0.024 -0.014]
L3H5 Q-side/K-side 2D energy [0.01 0.06] key-bias fraction 0.724 2x2 [[0.016, 0.094], [-0.093, 0.013]] key-bias [ 0.323 -0.268]

L0H3 value spectrum
[0.57  0.513 0.504 0.472 0.47  0.45  0.44  0.434 0.425 0.411 0.39  0.383
 0.379 0.367 0.359 0.342 0.339 0.336 0.324 0.297 0.286 0.276 0.273 0.266
 0.254 0.248 0.245 0.241 0.237 0.231 0.225 0.223 0.22  0.21  0.206 0.204
 0.197 0.194 0.183 0.18  0.173 0.169 0.16  0.151 0.15  0.138 0.133 0.132
 0.124 0.121 0.116 0.11  0.108 0.107 0.103 0.101 0.097 0.093 0.09  0.087
 0.085 0.081 0.077 0.072]
Token-candidate subspace rank 16 L3H3 QK@L0H3 OV trace/norm 2.724
Token-candidate subspace rank 20 L3H3 QK@L0H3 OV trace/norm 2.858
Token-candidate subspace rank 24 L3H3 QK@L0H3 OV trace/norm 2.716
Token-candidate subspace rank 28 L3H3 QK@L0H3 OV trace/norm 2.614
Token-candidate subspace rank 32 L3H3 QK@L0H3 OV trace/norm 2.505

```
CLI OUTPUT IN EVENT ORDER
ERROR
Failed to read global AGENTS.md instructions from `<local-home>/.codex/AGENTS.md`: Operation not permitted (os error 1)

ERROR
Code Mode is unavailable because code-mode host is disabled. Code mode will fail closed; enable `features.code_mode_host` and install `codex-code-mode-host`.

AGENT_MESSAGE
```python
import numpy as np
from scipy.linalg import svd, eigh
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
from threadpoolctl import threadpool_limits

def unitrows(x):
    return x/(np.linalg.norm(x,axis=1,keepdims=True)+1e-12)

with threadpool_limits(limits=2):
    g=W["ln1_w.0"].astype(float)
    q=W["W_q.0"][192:256].astype(float)*g
    k=W["W_k.0"][192:256].astype(float)*g
    v=W["W_v.0"][192:256].astype(float)*g
    for m in [q,k,v]: m-=m.mean(1,keepdims=True)
    B=W["W_o.0"][:,192:256].astype(float)@v
    ui,si,vi=svd(B,full_matrices=False)
    uq,sq,vq=svd(q.T@k,full_matrices=False)
    f=W["W_fc.0"].astype(float)*W["ln2_w.0"]
    f-=f.mean(1,keepdims=True)

    # All rows below are weight directions or linear products of weights.
    # No inputs, layer execution, activation functions, or attention distributions.
    nuisance=np.concatenate([ui[:,:28],uq[:,:24],vq[:24].T,
                              np.ones((384,1))/np.sqrt(384)],axis=1)
    un,sn,_=svd(nuisance,full_matrices=False)
    N=un[:,sn>1e-8]
    candidates=vi[:28].T
    candidates-=N@(N.T@candidates)
    X,_,_=svd(candidates,full_matrices=False)
    X=X[:,:28]
    C0=f@X
    C1=f@B@X
    C0-=C0.mean(0); C1-=C1.mean(0)
    C0/=np.linalg.norm(C0)
    C1/=np.linalg.norm(C1)
    covariance=(C0.T@C0+C1.T@C1)/2
    ev,U=eigh(covariance)
    whitening=(U/np.sqrt(np.maximum(ev,ev[-1]*.015)))@U.T
    D0=C0@whitening
    D1=C1@whitening
    cross=(D0.T@D1+D1.T@D0)/2
    print("Symmetric, whitened FC/FC-OV direction covariance eigenvalues:")
    print(np.round(eigh(cross,eigvals_only=True),3))

    Z=np.concatenate([unitrows(D0),unitrows(D1)])
    print("\nShared clustering of current/OV-composed FC weight directions")
    for nc in [20,24,28,32]:
        km=KMeans(n_clusters=nc,n_init=10,random_state=42).fit(Z)
        labels=km.labels_
        cent=unitrows(km.cluster_centers_)
        confidence=np.sum(Z*cent[labels],axis=1)
        pairs=np.zeros((nc,nc))
        for i in range(1536):
            pairs[labels[i],labels[i+1536]]+=confidence[i]*confidence[i+1536]
        pairs=(pairs+pairs.T)/2
        degree=pairs.sum(1)
        norm=pairs/np.sqrt(degree[:,None]*degree[None,:]+1e-12)
        eig=eigh(norm,eigvals_only=True)
        print("k",nc,"silhouette",
              round(silhouette_score(Z,labels,sample_size=1500,random_state=42),3),
              "confidence median",round(float(np.median(confidence)),3),
              "pair-graph bottom eigenvalues",np.round(eig[:5],3),
              "cluster counts",sorted(np.bincount(labels).tolist(),reverse=True))

    print("\nFinal MLP output-weight clustering")
    p=W["W_proj.3"].astype(float).T
    _,s,vt=svd(p,full_matrices=False)
    Z=unitrows(p@vt[:28].T)
    for nc in [20,24,28,32]:
        km=KMeans(n_clusters=nc,n_init=10,random_state=42).fit(Z)
        print("k",nc,"silhouette",
              round(silhouette_score(Z,km.labels_,sample_size=1500,random_state=42),3),
              "counts",sorted(np.bincount(km.labels_).tolist(),reverse=True))
```


PERMITTED EXPERIMENT HARNESS RECORD: python
{
  "run": 6,
  "turn": "t006",
  "code": "import numpy as np\nfrom scipy.linalg import svd, eigh\nfrom sklearn.cluster import KMeans\nfrom sklearn.metrics import silhouette_score\nfrom threadpoolctl import threadpool_limits\n\ndef unitrows(x):\n    return x/(np.linalg.norm(x,axis=1,keepdims=True)+1e-12)\n\nwith threadpool_limits(limits=2):\n    g=W[\"ln1_w.0\"].astype(float)\n    q=W[\"W_q.0\"][192:256].astype(float)*g\n    k=W[\"W_k.0\"][192:256].astype(float)*g\n    v=W[\"W_v.0\"][192:256].astype(float)*g\n    for m in [q,k,v]: m-=m.mean(1,keepdims=True)\n    B=W[\"W_o.0\"][:,192:256].astype(float)@v\n    ui,si,vi=svd(B,full_matrices=False)\n    uq,sq,vq=svd(q.T@k,full_matrices=False)\n    f=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"]\n    f-=f.mean(1,keepdims=True)\n\n    # All rows below are weight directions or linear products of weights.\n    # No inputs, layer execution, activation functions, or attention distributions.\n    nuisance=np.concatenate([ui[:,:28],uq[:,:24],vq[:24].T,\n                              np.ones((384,1))/np.sqrt(384)],axis=1)\n    un,sn,_=svd(nuisance,full_matrices=False)\n    N=un[:,sn>1e-8]\n    candidates=vi[:28].T\n    candidates-=N@(N.T@candidates)\n    X,_,_=svd(candidates,full_matrices=False)\n    X=X[:,:28]\n    C0=f@X\n    C1=f@B@X\n    C0-=C0.mean(0); C1-=C1.mean(0)\n    C0/=np.linalg.norm(C0)\n    C1/=np.linalg.norm(C1)\n    covariance=(C0.T@C0+C1.T@C1)/2\n    ev,U=eigh(covariance)\n    whitening=(U/np.sqrt(np.maximum(ev,ev[-1]*.015)))@U.T\n    D0=C0@whitening\n    D1=C1@whitening\n    cross=(D0.T@D1+D1.T@D0)/2\n    print(\"Symmetric, whitened FC/FC-OV direction covariance eigenvalues:\")\n    print(np.round(eigh(cross,eigvals_only=True),3))\n\n    Z=np.concatenate([unitrows(D0),unitrows(D1)])\n    print(\"\\nShared clustering of current/OV-composed FC weight directions\")\n    for nc in [20,24,28,32]:\n        km=KMeans(n_clusters=nc,n_init=10,random_state=42).fit(Z)\n        labels=km.labels_\n        cent=unitrows(km.cluster_centers_)\n        confidence=np.sum(Z*cent[labels],axis=1)\n        pairs=np.zeros((nc,nc))\n        for i in range(1536):\n            pairs[labels[i],labels[i+1536]]+=confidence[i]*confidence[i+1536]\n        pairs=(pairs+pairs.T)/2\n        degree=pairs.sum(1)\n        norm=pairs/np.sqrt(degree[:,None]*degree[None,:]+1e-12)\n        eig=eigh(norm,eigvals_only=True)\n        print(\"k\",nc,\"silhouette\",\n              round(silhouette_score(Z,labels,sample_size=1500,random_state=42),3),\n              \"confidence median\",round(float(np.median(confidence)),3),\n              \"pair-graph bottom eigenvalues\",np.round(eig[:5],3),\n              \"cluster counts\",sorted(np.bincount(labels).tolist(),reverse=True))\n\n    print(\"\\nFinal MLP output-weight clustering\")\n    p=W[\"W_proj.3\"].astype(float).T\n    _,s,vt=svd(p,full_matrices=False)\n    Z=unitrows(p@vt[:28].T)\n    for nc in [20,24,28,32]:\n        km=KMeans(n_clusters=nc,n_init=10,random_state=42).fit(Z)\n        print(\"k\",nc,\"silhouette\",\n              round(silhouette_score(Z,km.labels_,sample_size=1500,random_state=42),3),\n              \"counts\",sorted(np.bincount(km.labels_).tolist(),reverse=True))",
  "out": "Symmetric, whitened FC/FC-OV direction covariance eigenvalues:\n[-0.336 -0.299 -0.226 -0.205 -0.172 -0.151 -0.115 -0.095 -0.07  -0.021\n -0.007  0.002  0.026  0.066  0.078  0.108  0.158  0.179  0.222  0.23\n  0.28   0.289  0.346  0.361  0.372  0.404  0.479  0.507]\n\nShared clustering of current/OV-composed FC weight directions\nk 20 silhouette 0.048 confidence median 0.503 pair-graph bottom eigenvalues [-0.7   -0.107 -0.08  -0.069 -0.028] cluster counts [224, 216, 213, 185, 179, 178, 175, 159, 154, 153, 152, 150, 139, 138, 123, 117, 112, 109, 99, 97]\nk 24 silhouette 0.051 confidence median 0.518 pair-graph bottom eigenvalues [-0.691 -0.153 -0.122 -0.089 -0.071] cluster counts [268, 206, 164, 160, 154, 150, 145, 143, 138, 133, 126, 124, 122, 113, 111, 108, 108, 106, 95, 93, 87, 85, 82, 51]\nk 28 silhouette 0.056 confidence median 0.539 pair-graph bottom eigenvalues [-0.692 -0.148 -0.132 -0.119 -0.096] cluster counts [215, 172, 171, 169, 160, 154, 138, 128, 127, 125, 120, 114, 104, 98, 96, 95, 92, 89, 85, 81, 78, 78, 70, 67, 65, 64, 59, 58]\nk 32 silhouette 0.054 confidence median 0.556 pair-graph bottom eigenvalues [-0.699 -0.187 -0.148 -0.139 -0.102] cluster counts [147, 137, 135, 129, 127, 123, 121, 121, 120, 118, 107, 106, 104, 102, 101, 101, 98, 96, 91, 89, 83, 78, 74, 72, 68, 68, 66, 65, 60, 58, 56, 51]\n\nFinal MLP output-weight clustering\nk 20 silhouette 0.055 counts [137, 108, 82, 81, 80, 80, 79, 79, 79, 75, 75, 69, 69, 68, 67, 64, 62, 61, 61, 60]\nk 24 silhouette 0.054 counts [88, 85, 84, 77, 72, 70, 68, 67, 67, 66, 65, 64, 64, 60, 58, 57, 57, 57, 56, 56, 56, 56, 47, 39]\nk 28 silhouette 0.055 counts [97, 71, 68, 65, 65, 61, 60, 58, 58, 58, 56, 56, 56, 55, 55, 55, 55, 53, 52, 48, 46, 46, 46, 46, 45, 43, 32, 30]\nk 32 silhouette 0.054 counts [78, 69, 61, 61, 60, 59, 57, 56, 56, 55, 52, 52, 49, 48, 47, 45, 44, 44, 43, 43, 42, 42, 42, 42, 42, 41, 40, 37, 36, 33, 33, 27]\n",
  "seconds": 1.673,
  "rc": 0,
  "timed_out": false,
  "truncated": false,
  "code_sha256": "5ded82b621871776ac5988f71dbe9cfa56fcd91535179a02174bccbe92514168",
  "weights_sha256": "04ec0b300d207b26b92a1af6d49d56d452833e39b35826200bc1d821e5b7d930"
}

EXACT HARNESS FEEDBACK
Symmetric, whitened FC/FC-OV direction covariance eigenvalues:
[-0.336 -0.299 -0.226 -0.205 -0.172 -0.151 -0.115 -0.095 -0.07  -0.021
 -0.007  0.002  0.026  0.066  0.078  0.108  0.158  0.179  0.222  0.23
  0.28   0.289  0.346  0.361  0.372  0.404  0.479  0.507]

Shared clustering of current/OV-composed FC weight directions
k 20 silhouette 0.048 confidence median 0.503 pair-graph bottom eigenvalues [-0.7   -0.107 -0.08  -0.069 -0.028] cluster counts [224, 216, 213, 185, 179, 178, 175, 159, 154, 153, 152, 150, 139, 138, 123, 117, 112, 109, 99, 97]
k 24 silhouette 0.051 confidence median 0.518 pair-graph bottom eigenvalues [-0.691 -0.153 -0.122 -0.089 -0.071] cluster counts [268, 206, 164, 160, 154, 150, 145, 143, 138, 133, 126, 124, 122, 113, 111, 108, 108, 106, 95, 93, 87, 85, 82, 51]
k 28 silhouette 0.056 confidence median 0.539 pair-graph bottom eigenvalues [-0.692 -0.148 -0.132 -0.119 -0.096] cluster counts [215, 172, 171, 169, 160, 154, 138, 128, 127, 125, 120, 114, 104, 98, 96, 95, 92, 89, 85, 81, 78, 78, 70, 67, 65, 64, 59, 58]
k 32 silhouette 0.054 confidence median 0.556 pair-graph bottom eigenvalues [-0.699 -0.187 -0.148 -0.139 -0.102] cluster counts [147, 137, 135, 129, 127, 123, 121, 121, 120, 118, 107, 106, 104, 102, 101, 101, 98, 96, 91, 89, 83, 78, 74, 72, 68, 68, 66, 65, 60, 58, 56, 51]

Final MLP output-weight clustering
k 20 silhouette 0.055 counts [137, 108, 82, 81, 80, 80, 79, 79, 79, 75, 75, 69, 69, 68, 67, 64, 62, 61, 61, 60]
k 24 silhouette 0.054 counts [88, 85, 84, 77, 72, 70, 68, 67, 67, 66, 65, 64, 64, 60, 58, 57, 57, 57, 56, 56, 56, 56, 47, 39]
k 28 silhouette 0.055 counts [97, 71, 68, 65, 65, 61, 60, 58, 58, 58, 56, 56, 56, 55, 55, 55, 55, 53, 52, 48, 46, 46, 46, 46, 45, 43, 32, 30]
k 32 silhouette 0.054 counts [78, 69, 61, 61, 60, 59, 57, 56, 56, 55, 52, 52, 49, 48, 47, 45, 44, 44, 43, 43, 42, 42, 42, 42, 42, 41, 40, 37, 36, 33, 33, 27]


========================================================================
TURN t007
MESSAGE SENT TO CODEX
OUTPUT of run 6 of at most 100:
```
Symmetric, whitened FC/FC-OV direction covariance eigenvalues:
[-0.336 -0.299 -0.226 -0.205 -0.172 -0.151 -0.115 -0.095 -0.07  -0.021
 -0.007  0.002  0.026  0.066  0.078  0.108  0.158  0.179  0.222  0.23
  0.28   0.289  0.346  0.361  0.372  0.404  0.479  0.507]

Shared clustering of current/OV-composed FC weight directions
k 20 silhouette 0.048 confidence median 0.503 pair-graph bottom eigenvalues [-0.7   -0.107 -0.08  -0.069 -0.028] cluster counts [224, 216, 213, 185, 179, 178, 175, 159, 154, 153, 152, 150, 139, 138, 123, 117, 112, 109, 99, 97]
k 24 silhouette 0.051 confidence median 0.518 pair-graph bottom eigenvalues [-0.691 -0.153 -0.122 -0.089 -0.071] cluster counts [268, 206, 164, 160, 154, 150, 145, 143, 138, 133, 126, 124, 122, 113, 111, 108, 108, 106, 95, 93, 87, 85, 82, 51]
k 28 silhouette 0.056 confidence median 0.539 pair-graph bottom eigenvalues [-0.692 -0.148 -0.132 -0.119 -0.096] cluster counts [215, 172, 171, 169, 160, 154, 138, 128, 127, 125, 120, 114, 104, 98, 96, 95, 92, 89, 85, 81, 78, 78, 70, 67, 65, 64, 59, 58]
k 32 silhouette 0.054 confidence median 0.556 pair-graph bottom eigenvalues [-0.699 -0.187 -0.148 -0.139 -0.102] cluster counts [147, 137, 135, 129, 127, 123, 121, 121, 120, 118, 107, 106, 104, 102, 101, 101, 98, 96, 91, 89, 83, 78, 74, 72, 68, 68, 66, 65, 60, 58, 56, 51]

Final MLP output-weight clustering
k 20 silhouette 0.055 counts [137, 108, 82, 81, 80, 80, 79, 79, 79, 75, 75, 69, 69, 68, 67, 64, 62, 61, 61, 60]
k 24 silhouette 0.054 counts [88, 85, 84, 77, 72, 70, 68, 67, 67, 66, 65, 64, 64, 60, 58, 57, 57, 57, 56, 56, 56, 56, 47, 39]
k 28 silhouette 0.055 counts [97, 71, 68, 65, 65, 61, 60, 58, 58, 58, 56, 56, 56, 55, 55, 55, 55, 53, 52, 48, 46, 46, 46, 46, 45, 43, 32, 30]
k 32 silhouette 0.054 counts [78, 69, 61, 61, 60, 59, 57, 56, 56, 55, 52, 52, 49, 48, 47, 45, 44, 44, 43, 43, 42, 42, 42, 42, 42, 41, 40, 37, 36, 33, 33, 27]

```
CLI OUTPUT IN EVENT ORDER
ERROR
Failed to read global AGENTS.md instructions from `<local-home>/.codex/AGENTS.md`: Operation not permitted (os error 1)

ERROR
Code Mode is unavailable because code-mode host is disabled. Code mode will fail closed; enable `features.code_mode_host` and install `codex-code-mode-host`.

AGENT_MESSAGE
```python
import numpy as np
from scipy.linalg import svd,eigh
from sklearn.cluster import KMeans
from threadpoolctl import threadpool_limits

def unitrows(x):
    return x/(np.linalg.norm(x,axis=1,keepdims=True)+1e-12)

with threadpool_limits(limits=2):
    g=W["ln1_w.0"].astype(float)
    q=W["W_q.0"][192:256].astype(float)*g
    k=W["W_k.0"][192:256].astype(float)*g
    v=W["W_v.0"][192:256].astype(float)*g
    for m in [q,k,v]:m-=m.mean(1,keepdims=True)
    B=W["W_o.0"][:,192:256].astype(float)@v
    u,s,vt=svd(B,full_matrices=False)
    uq,sq,vq=svd(q.T@k,full_matrices=False)
    f=W["W_fc.0"].astype(float)*W["ln2_w.0"]
    f-=f.mean(1,keepdims=True)
    for mode in ["plain","remove_output","remove_output_and_qk"]:
        candidates=vt[:28].T.copy()
        if mode!="plain":
            nuisance=u[:,:28]
            if mode=="remove_output_and_qk":
                nuisance=np.concatenate([nuisance,uq[:,:24],vq[:24].T,
                                          np.ones((384,1))/np.sqrt(384)],axis=1)
            un,sn,_=svd(nuisance,full_matrices=False)
            N=un[:,sn>1e-8]
            candidates-=N@(N.T@candidates)
        X,_,_=svd(candidates,full_matrices=False)
        C0=f@X; C1=f@B@X
        C0-=C0.mean(0); C1-=C1.mean(0)
        C0/=np.linalg.norm(C0); C1/=np.linalg.norm(C1)
        ev,U=eigh((C0.T@C0+C1.T@C1)/2)
        whitening=(U/np.sqrt(np.maximum(ev,ev[-1]*.015)))@U.T
        Z=np.concatenate([unitrows(C0@whitening),unitrows(C1@whitening)])
        km=KMeans(n_clusters=24,n_init=15,random_state=42).fit(Z)
        lab=km.labels_
        n0=np.bincount(lab[:1536],minlength=24)
        n1=np.bincount(lab[1536:],minlength=24)
        pairs=np.zeros((24,24))
        for i in range(1536):pairs[lab[i],lab[i+1536]]+=1
        pairs=(pairs+pairs.T)/2
        deg=pairs.sum(1)
        norm=pairs/np.sqrt(deg[:,None]*deg[None,:]+1e-12)
        ev,evec=eigh(norm)
        origin=(n0-n1)/(n0+n1+1e-12)
        graphaxis=evec[:,0]/np.sqrt(deg+1e-12)
        print("\nMode",mode)
        print("bottom graph eigenvalues",np.round(ev[:5],3))
        print("origin imbalance RMS",round(float(np.sqrt(np.mean(origin**2))),3),
              "correlation of bipartition with sample origin",
              round(float(np.corrcoef(origin,graphaxis)[0,1]),3))
        print("cluster: current-count, composed-count, graph-axis sign")
        print([(i,int(n0[i]),int(n1[i]),int(np.sign(graphaxis[i]))) for i in range(24)])
```


PERMITTED EXPERIMENT HARNESS RECORD: python
{
  "run": 7,
  "turn": "t007",
  "code": "import numpy as np\nfrom scipy.linalg import svd,eigh\nfrom sklearn.cluster import KMeans\nfrom threadpoolctl import threadpool_limits\n\ndef unitrows(x):\n    return x/(np.linalg.norm(x,axis=1,keepdims=True)+1e-12)\n\nwith threadpool_limits(limits=2):\n    g=W[\"ln1_w.0\"].astype(float)\n    q=W[\"W_q.0\"][192:256].astype(float)*g\n    k=W[\"W_k.0\"][192:256].astype(float)*g\n    v=W[\"W_v.0\"][192:256].astype(float)*g\n    for m in [q,k,v]:m-=m.mean(1,keepdims=True)\n    B=W[\"W_o.0\"][:,192:256].astype(float)@v\n    u,s,vt=svd(B,full_matrices=False)\n    uq,sq,vq=svd(q.T@k,full_matrices=False)\n    f=W[\"W_fc.0\"].astype(float)*W[\"ln2_w.0\"]\n    f-=f.mean(1,keepdims=True)\n    for mode in [\"plain\",\"remove_output\",\"remove_output_and_qk\"]:\n        candidates=vt[:28].T.copy()\n        if mode!=\"plain\":\n            nuisance=u[:,:28]\n            if mode==\"remove_output_and_qk\":\n                nuisance=np.concatenate([nuisance,uq[:,:24],vq[:24].T,\n                                          np.ones((384,1))/np.sqrt(384)],axis=1)\n            un,sn,_=svd(nuisance,full_matrices=False)\n            N=un[:,sn>1e-8]\n            candidates-=N@(N.T@candidates)\n        X,_,_=svd(candidates,full_matrices=False)\n        C0=f@X; C1=f@B@X\n        C0-=C0.mean(0); C1-=C1.mean(0)\n        C0/=np.linalg.norm(C0); C1/=np.linalg.norm(C1)\n        ev,U=eigh((C0.T@C0+C1.T@C1)/2)\n        whitening=(U/np.sqrt(np.maximum(ev,ev[-1]*.015)))@U.T\n        Z=np.concatenate([unitrows(C0@whitening),unitrows(C1@whitening)])\n        km=KMeans(n_clusters=24,n_init=15,random_state=42).fit(Z)\n        lab=km.labels_\n        n0=np.bincount(lab[:1536],minlength=24)\n        n1=np.bincount(lab[1536:],minlength=24)\n        pairs=np.zeros((24,24))\n        for i in range(1536):pairs[lab[i],lab[i+1536]]+=1\n        pairs=(pairs+pairs.T)/2\n        deg=pairs.sum(1)\n        norm=pairs/np.sqrt(deg[:,None]*deg[None,:]+1e-12)\n        ev,evec=eigh(norm)\n        origin=(n0-n1)/(n0+n1+1e-12)\n        graphaxis=evec[:,0]/np.sqrt(deg+1e-12)\n        print(\"\\nMode\",mode)\n        print(\"bottom graph eigenvalues\",np.round(ev[:5],3))\n        print(\"origin imbalance RMS\",round(float(np.sqrt(np.mean(origin**2))),3),\n              \"correlation of bipartition with sample origin\",\n              round(float(np.corrcoef(origin,graphaxis)[0,1]),3))\n        print(\"cluster: current-count, composed-count, graph-axis sign\")\n        print([(i,int(n0[i]),int(n1[i]),int(np.sign(graphaxis[i]))) for i in range(24)])",
  "out": "\nMode plain\nbottom graph eigenvalues [-0.551 -0.197 -0.185 -0.132 -0.101]\norigin imbalance RMS 0.523 correlation of bipartition with sample origin 0.841\ncluster: current-count, composed-count, graph-axis sign\n[(0, 34, 104, -1), (1, 116, 24, 1), (2, 45, 31, 1), (3, 163, 10, 1), (4, 133, 14, 1), (5, 33, 135, -1), (6, 147, 17, 1), (7, 43, 56, -1), (8, 38, 78, -1), (9, 55, 57, 1), (10, 19, 59, -1), (11, 30, 53, 1), (12, 111, 51, 1), (13, 124, 17, 1), (14, 45, 68, 1), (15, 62, 23, -1), (16, 52, 158, -1), (17, 23, 61, 1), (18, 35, 66, 1), (19, 42, 140, -1), (20, 82, 29, 1), (21, 51, 62, -1), (22, 48, 45, 1), (23, 5, 178, -1)]\n\nMode remove_output\nbottom graph eigenvalues [-0.603 -0.192 -0.129 -0.103 -0.086]\norigin imbalance RMS 0.613 correlation of bipartition with sample origin -0.882\ncluster: current-count, composed-count, graph-axis sign\n[(0, 32, 56, -1), (1, 28, 64, 1), (2, 160, 12, -1), (3, 138, 22, -1), (4, 37, 118, 1), (5, 25, 70, 1), (6, 161, 4, -1), (7, 24, 87, 1), (8, 14, 177, 1), (9, 58, 71, -1), (10, 15, 180, 1), (11, 28, 7, 1), (12, 46, 31, -1), (13, 47, 94, 1), (14, 54, 65, 1), (15, 150, 8, -1), (16, 50, 71, -1), (17, 98, 5, -1), (18, 45, 24, -1), (19, 18, 161, 1), (20, 62, 31, -1), (21, 29, 103, -1), (22, 43, 73, 1), (23, 174, 2, -1)]\n\nMode remove_output_and_qk\nbottom graph eigenvalues [-0.626 -0.15  -0.122 -0.078 -0.069]\norigin imbalance RMS 0.647 correlation of bipartition with sample origin -0.941\ncluster: current-count, composed-count, graph-axis sign\n[(0, 141, 4, -1), (1, 3, 265, 1), (2, 164, 0, -1), (3, 100, 8, -1), (4, 141, 2, -1), (5, 131, 2, -1), (6, 49, 157, 1), (7, 135, 3, -1), (8, 27, 84, 1), (9, 49, 75, 1), (10, 40, 55, -1), (11, 109, 13, -1), (12, 6, 144, 1), (13, 25, 88, 1), (14, 46, 41, -1), (15, 36, 70, 1), (16, 31, 54, 1), (17, 22, 86, 1), (18, 29, 22, 1), (19, 53, 73, 1), (20, 25, 57, 1), (21, 53, 101, 1), (22, 72, 21, -1), (23, 49, 111, 1)]\n",
  "seconds": 1.433,
  "rc": 0,
  "timed_out": false,
  "truncated": false,
  "code_sha256": "9f145975555c45a2a939fcf0e2eddb8fde8407800e69e3c3982914ecd485bf68",
  "weights_sha256": "04ec0b300d207b26b92a1af6d49d56d452833e39b35826200bc1d821e5b7d930"
}

EXACT HARNESS FEEDBACK

Mode plain
bottom graph eigenvalues [-0.551 -0.197 -0.185 -0.132 -0.101]
origin imbalance RMS 0.523 correlation of bipartition with sample origin 0.841
cluster: current-count, composed-count, graph-axis sign
[(0, 34, 104, -1), (1, 116, 24, 1), (2, 45, 31, 1), (3, 163, 10, 1), (4, 133, 14, 1), (5, 33, 135, -1), (6, 147, 17, 1), (7, 43, 56, -1), (8, 38, 78, -1), (9, 55, 57, 1), (10, 19, 59, -1), (11, 30, 53, 1), (12, 111, 51, 1), (13, 124, 17, 1), (14, 45, 68, 1), (15, 62, 23, -1), (16, 52, 158, -1), (17, 23, 61, 1), (18, 35, 66, 1), (19, 42, 140, -1), (20, 82, 29, 1), (21, 51, 62, -1), (22, 48, 45, 1), (23, 5, 178, -1)]

Mode remove_output
bottom graph eigenvalues [-0.603 -0.192 -0.129 -0.103 -0.086]
origin imbalance RMS 0.613 correlation of bipartition with sample origin -0.882
cluster: current-count, composed-count, graph-axis sign
[(0, 32, 56, -1), (1, 28, 64, 1), (2, 160, 12, -1), (3, 138, 22, -1), (4, 37, 118, 1), (5, 25, 70, 1), (6, 161, 4, -1), (7, 24, 87, 1), (8, 14, 177, 1), (9, 58, 71, -1), (10, 15, 180, 1), (11, 28, 7, 1), (12, 46, 31, -1), (13, 47, 94, 1), (14, 54, 65, 1), (15, 150, 8, -1), (16, 50, 71, -1), (17, 98, 5, -1), (18, 45, 24, -1), (19, 18, 161, 1), (20, 62, 31, -1), (21, 29, 103, -1), (22, 43, 73, 1), (23, 174, 2, -1)]

Mode remove_output_and_qk
bottom graph eigenvalues [-0.626 -0.15  -0.122 -0.078 -0.069]
origin imbalance RMS 0.647 correlation of bipartition with sample origin -0.941
cluster: current-count, composed-count, graph-axis sign
[(0, 141, 4, -1), (1, 3, 265, 1), (2, 164, 0, -1), (3, 100, 8, -1), (4, 141, 2, -1), (5, 131, 2, -1), (6, 49, 157, 1), (7, 135, 3, -1), (8, 27, 84, 1), (9, 49, 75, 1), (10, 40, 55, -1), (11, 109, 13, -1), (12, 6, 144, 1), (13, 25, 88, 1), (14, 46, 41, -1), (15, 36, 70, 1), (16, 31, 54, 1), (17, 22, 86, 1), (18, 29, 22, 1), (19, 53, 73, 1), (20, 25, 57, 1), (21, 53, 101, 1), (22, 72, 21, -1), (23, 49, 111, 1)]


========================================================================
TURN t008
MESSAGE SENT TO CODEX
OUTPUT of run 7 of at most 100:
```

Mode plain
bottom graph eigenvalues [-0.551 -0.197 -0.185 -0.132 -0.101]
origin imbalance RMS 0.523 correlation of bipartition with sample origin 0.841
cluster: current-count, composed-count, graph-axis sign
[(0, 34, 104, -1), (1, 116, 24, 1), (2, 45, 31, 1), (3, 163, 10, 1), (4, 133, 14, 1), (5, 33, 135, -1), (6, 147, 17, 1), (7, 43, 56, -1), (8, 38, 78, -1), (9, 55, 57, 1), (10, 19, 59, -1), (11, 30, 53, 1), (12, 111, 51, 1), (13, 124, 17, 1), (14, 45, 68, 1), (15, 62, 23, -1), (16, 52, 158, -1), (17, 23, 61, 1), (18, 35, 66, 1), (19, 42, 140, -1), (20, 82, 29, 1), (21, 51, 62, -1), (22, 48, 45, 1), (23, 5, 178, -1)]

Mode remove_output
bottom graph eigenvalues [-0.603 -0.192 -0.129 -0.103 -0.086]
origin imbalance RMS 0.613 correlation of bipartition with sample origin -0.882
cluster: current-count, composed-count, graph-axis sign
[(0, 32, 56, -1), (1, 28, 64, 1), (2, 160, 12, -1), (3, 138, 22, -1), (4, 37, 118, 1), (5, 25, 70, 1), (6, 161, 4, -1), (7, 24, 87, 1), (8, 14, 177, 1), (9, 58, 71, -1), (10, 15, 180, 1), (11, 28, 7, 1), (12, 46, 31, -1), (13, 47, 94, 1), (14, 54, 65, 1), (15, 150, 8, -1), (16, 50, 71, -1), (17, 98, 5, -1), (18, 45, 24, -1), (19, 18, 161, 1), (20, 62, 31, -1), (21, 29, 103, -1), (22, 43, 73, 1), (23, 174, 2, -1)]

Mode remove_output_and_qk
bottom graph eigenvalues [-0.626 -0.15  -0.122 -0.078 -0.069]
origin imbalance RMS 0.647 correlation of bipartition with sample origin -0.941
cluster: current-count, composed-count, graph-axis sign
[(0, 141, 4, -1), (1, 3, 265, 1), (2, 164, 0, -1), (3, 100, 8, -1), (4, 141, 2, -1), (5, 131, 2, -1), (6, 49, 157, 1), (7, 135, 3, -1), (8, 27, 84, 1), (9, 49, 75, 1), (10, 40, 55, -1), (11, 109, 13, -1), (12, 6, 144, 1), (13, 25, 88, 1), (14, 46, 41, -1), (15, 36, 70, 1), (16, 31, 54, 1), (17, 22, 86, 1), (18, 29, 22, 1), (19, 53, 73, 1), (20, 25, 57, 1), (21, 53, 101, 1), (22, 72, 21, -1), (23, 49, 111, 1)]

```
CLI OUTPUT IN EVENT ORDER
ERROR
Failed to read global AGENTS.md instructions from `<local-home>/.codex/AGENTS.md`: Operation not permitted (os error 1)

ERROR
Code Mode is unavailable because code-mode host is disabled. Code mode will fail closed; enable `features.code_mode_host` and install `codex-code-mode-host`.

AGENT_MESSAGE
```python
import numpy as np
from scipy.linalg import svd
from threadpoolctl import threadpool_limits

with threadpool_limits(limits=2):
    A=[]; B=[]; bases=[]
    for l in range(4):
        g=W[f"ln1_w.{l}"].astype(float)
        for j in range(6):
            sl=slice(64*j,64*j+64)
            q=W[f"W_q.{l}"][sl].astype(float)*g
            k=W[f"W_k.{l}"][sl].astype(float)*g
            v=W[f"W_v.{l}"][sl].astype(float)*g
            for m in [q,k,v]:m-=m.mean(1,keepdims=True)
            A.append(q.T@k/8)
            B.append(W[f"W_o.{l}"][:,sl].astype(float)@v)
            bases.append(svd(v,full_matrices=False)[2][:20].T)

    print("Weight-only matching diagnostic:")
    print("trace(P.T @ QK_lh @ OV_source @ P) / Frobenius norm;")
    print("P = top 20 right singular directions of source V.")
    for i in range(6,24):
        scores=[]
        syms=[]
        for j in range((i//6)*6):
            P=bases[j]
            C=P.T@A[i]@B[j]@P
            n=np.linalg.norm(C)
            scores.append(np.trace(C)/n)
            syms.append(np.sum(C*C.T)/(n*n))
        best=np.argsort(scores)[::-1][:3]
        print("L%dH%d"%(i//6,i%6),
              "L0-source scores",np.round(scores[:6],3),
              "best",[
                  ("L%dH%d"%(j//6,j%6),round(scores[j],3),round(syms[j],3))
                  for j in best])

    rng=np.random.default_rng(874)
    P=bases[3]
    left=P.T@A[21]
    right=B[3]@P
    C=left@right
    observed=np.trace(C)/np.linalg.norm(C)
    null=[]
    for _ in range(1000):
        signs=rng.choice([-1.,1.],size=384)
        D=(left*signs)@right
        null.append(np.trace(D)/np.linalg.norm(D))
    print("\nL3H3 <- L0H3 matching score:",round(observed,4))
    print("Coordinate-sign scrambling of the weight connection, null quantiles:",
          np.round(np.quantile(null,[0,.01,.5,.99,1]),4))

    print("\nSelected literal LayerNorm weights")
    for name,inds in [
        ("ln1_b.1",[39,58,99,21]),
        ("ln1_b.2",[39,58,99,21]),
        ("ln1_w.0",[180,184,162,99,211])]:
        print(name,[(i,float(W[name][i])) for i in inds])
```


PERMITTED EXPERIMENT HARNESS RECORD: python
{
  "run": 8,
  "turn": "t008",
  "code": "import numpy as np\nfrom scipy.linalg import svd\nfrom threadpoolctl import threadpool_limits\n\nwith threadpool_limits(limits=2):\n    A=[]; B=[]; bases=[]\n    for l in range(4):\n        g=W[f\"ln1_w.{l}\"].astype(float)\n        for j in range(6):\n            sl=slice(64*j,64*j+64)\n            q=W[f\"W_q.{l}\"][sl].astype(float)*g\n            k=W[f\"W_k.{l}\"][sl].astype(float)*g\n            v=W[f\"W_v.{l}\"][sl].astype(float)*g\n            for m in [q,k,v]:m-=m.mean(1,keepdims=True)\n            A.append(q.T@k/8)\n            B.append(W[f\"W_o.{l}\"][:,sl].astype(float)@v)\n            bases.append(svd(v,full_matrices=False)[2][:20].T)\n\n    print(\"Weight-only matching diagnostic:\")\n    print(\"trace(P.T @ QK_lh @ OV_source @ P) / Frobenius norm;\")\n    print(\"P = top 20 right singular directions of source V.\")\n    for i in range(6,24):\n        scores=[]\n        syms=[]\n        for j in range((i//6)*6):\n            P=bases[j]\n            C=P.T@A[i]@B[j]@P\n            n=np.linalg.norm(C)\n            scores.append(np.trace(C)/n)\n            syms.append(np.sum(C*C.T)/(n*n))\n        best=np.argsort(scores)[::-1][:3]\n        print(\"L%dH%d\"%(i//6,i%6),\n              \"L0-source scores\",np.round(scores[:6],3),\n              \"best\",[\n                  (\"L%dH%d\"%(j//6,j%6),round(scores[j],3),round(syms[j],3))\n                  for j in best])\n\n    rng=np.random.default_rng(874)\n    P=bases[3]\n    left=P.T@A[21]\n    right=B[3]@P\n    C=left@right\n    observed=np.trace(C)/np.linalg.norm(C)\n    null=[]\n    for _ in range(1000):\n        signs=rng.choice([-1.,1.],size=384)\n        D=(left*signs)@right\n        null.append(np.trace(D)/np.linalg.norm(D))\n    print(\"\\nL3H3 <- L0H3 matching score:\",round(observed,4))\n    print(\"Coordinate-sign scrambling of the weight connection, null quantiles:\",\n          np.round(np.quantile(null,[0,.01,.5,.99,1]),4))\n\n    print(\"\\nSelected literal LayerNorm weights\")\n    for name,inds in [\n        (\"ln1_b.1\",[39,58,99,21]),\n        (\"ln1_b.2\",[39,58,99,21]),\n        (\"ln1_w.0\",[180,184,162,99,211])]:\n        print(name,[(i,float(W[name][i])) for i in inds])",
  "out": "Weight-only matching diagnostic:\ntrace(P.T @ QK_lh @ OV_source @ P) / Frobenius norm;\nP = top 20 right singular directions of source V.\nL1H0 L0-source scores [0.214 0.281 0.413 0.329 0.387 0.387] best [('L0H2', np.float64(0.413), np.float64(0.084)), ('L0H5', np.float64(0.387), np.float64(0.025)), ('L0H4', np.float64(0.387), np.float64(0.222))]\nL1H1 L0-source scores [0.106 0.052 0.221 0.632 0.048 0.149] best [('L0H3', np.float64(0.632), np.float64(0.126)), ('L0H2', np.float64(0.221), np.float64(0.067)), ('L0H5', np.float64(0.149), np.float64(0.043))]\nL1H2 L0-source scores [-0.225  0.256  0.348  0.482  0.377  0.326] best [('L0H3', np.float64(0.482), np.float64(0.175)), ('L0H4', np.float64(0.377), np.float64(0.156)), ('L0H2', np.float64(0.348), np.float64(0.065))]\nL1H3 L0-source scores [0.196 0.206 0.38  0.164 0.277 0.29 ] best [('L0H2', np.float64(0.38), np.float64(0.09)), ('L0H5', np.float64(0.29), np.float64(0.025)), ('L0H4', np.float64(0.277), np.float64(0.177))]\nL1H4 L0-source scores [0.05  0.149 0.294 0.157 0.374 0.239] best [('L0H4', np.float64(0.374), np.float64(0.084)), ('L0H2', np.float64(0.294), np.float64(-0.002)), ('L0H5', np.float64(0.239), np.float64(-0.008))]\nL1H5 L0-source scores [-0.149  0.147  0.301  0.518  0.205  0.201] best [('L0H3', np.float64(0.518), np.float64(0.211)), ('L0H2', np.float64(0.301), np.float64(0.06)), ('L0H4', np.float64(0.205), np.float64(0.265))]\nL2H0 L0-source scores [-0.065  0.328  0.58   0.282  0.297  0.51 ] best [('L1H3', np.float64(0.743), np.float64(-0.011)), ('L1H1', np.float64(0.669), np.float64(0.024)), ('L0H2', np.float64(0.58), np.float64(0.235))]\nL2H1 L0-source scores [0.145 0.273 0.541 0.107 0.258 0.505] best [('L0H2', np.float64(0.541), np.float64(0.21)), ('L0H5', np.float64(0.505), np.float64(0.087)), ('L0H1', np.float64(0.273), np.float64(0.12))]\nL2H2 L0-source scores [0.244 0.307 0.567 0.349 0.249 0.523] best [('L0H2', np.float64(0.567), np.float64(0.269)), ('L0H5', np.float64(0.523), np.float64(0.136)), ('L0H3', np.float64(0.349), np.float64(0.024))]\nL2H3 L0-source scores [0.324 0.329 0.493 0.434 0.357 0.469] best [('L0H2', np.float64(0.493), np.float64(0.18)), ('L0H5', np.float64(0.469), np.float64(0.116)), ('L0H3', np.float64(0.434), np.float64(0.145))]\nL2H4 L0-source scores [-0.132  0.341  0.661  0.708  0.325  0.581] best [('L0H3', np.float64(0.708), np.float64(0.191)), ('L0H2', np.float64(0.661), np.float64(0.323)), ('L0H5', np.float64(0.581), np.float64(0.155))]\nL2H5 L0-source scores [ 0.098  0.274  0.519 -0.03   0.25   0.571] best [('L0H5', np.float64(0.571), np.float64(0.131)), ('L0H2', np.float64(0.519), np.float64(0.159)), ('L0H1', np.float64(0.274), np.float64(0.121))]\nL3H0 L0-source scores [-0.263  0.218  0.391 -0.629  0.19   0.278] best [('L0H2', np.float64(0.391), np.float64(0.196)), ('L0H5', np.float64(0.278), np.float64(0.039)), ('L0H1', np.float64(0.218), np.float64(0.097))]\nL3H1 L0-source scores [ 0.121  0.208  0.388 -0.214  0.14   0.307] best [('L0H2', np.float64(0.388), np.float64(0.225)), ('L0H5', np.float64(0.307), np.float64(0.082)), ('L1H2', np.float64(0.238), np.float64(0.002))]\nL3H2 L0-source scores [-0.028  0.138  0.282  0.202  0.043  0.061] best [('L0H2', np.float64(0.282), np.float64(0.187)), ('L0H3', np.float64(0.202), np.float64(0.105)), ('L0H1', np.float64(0.138), np.float64(0.12))]\nL3H3 L0-source scores [-0.59   0.275  0.352  2.858  0.388 -0.173] best [('L0H3', np.float64(2.858), np.float64(0.591)), ('L2H5', np.float64(1.86), np.float64(0.226)), ('L1H5', np.float64(1.361), np.float64(0.183))]\nL3H4 L0-source scores [0.246 0.606 0.763 0.682 0.693 0.586] best [('L2H4', np.float64(1.023), np.float64(0.161)), ('L0H2', np.float64(0.763), np.float64(0.349)), ('L2H0', np.float64(0.718), np.float64(0.092))]\nL3H5 L0-source scores [-0.048  0.06   0.241 -0.126  0.011  0.187] best [('L0H2', np.float64(0.241), np.float64(0.077)), ('L0H5', np.float64(0.187), np.float64(0.015)), ('L0H1', np.float64(0.06), np.float64(0.047))]\n\nL3H3 <- L0H3 matching score: 2.858\nCoordinate-sign scrambling of the weight connection, null quantiles: [-1.0762 -0.8702  0.0232  0.8891  1.0625]\n\nSelected literal LayerNorm weights\nln1_b.1 [(39, -1.5675644874572754), (58, 1.36513352394104), (99, -1.3355246782302856), (21, -0.4298906922340393)]\nln1_b.2 [(39, -1.1991313695907593), (58, 1.331817865371704), (99, -1.6588826179504395), (21, -0.4534468650817871)]\nln1_w.0 [(180, 0.9784557819366455), (184, 0.9740331768989563), (162, 0.9703823924064636), (99, 0.9171200394630432), (211, 0.8959937691688538)]\n",
  "seconds": 0.534,
  "rc": 0,
  "timed_out": false,
  "truncated": false,
  "code_sha256": "d4461a679d9b7439e3c5db6d0e8c994aa14e665f4f3d65bde385b4dba4b0f4d2",
  "weights_sha256": "04ec0b300d207b26b92a1af6d49d56d452833e39b35826200bc1d821e5b7d930"
}

EXACT HARNESS FEEDBACK
Weight-only matching diagnostic:
trace(P.T @ QK_lh @ OV_source @ P) / Frobenius norm;
P = top 20 right singular directions of source V.
L1H0 L0-source scores [0.214 0.281 0.413 0.329 0.387 0.387] best [('L0H2', np.float64(0.413), np.float64(0.084)), ('L0H5', np.float64(0.387), np.float64(0.025)), ('L0H4', np.float64(0.387), np.float64(0.222))]
L1H1 L0-source scores [0.106 0.052 0.221 0.632 0.048 0.149] best [('L0H3', np.float64(0.632), np.float64(0.126)), ('L0H2', np.float64(0.221), np.float64(0.067)), ('L0H5', np.float64(0.149), np.float64(0.043))]
L1H2 L0-source scores [-0.225  0.256  0.348  0.482  0.377  0.326] best [('L0H3', np.float64(0.482), np.float64(0.175)), ('L0H4', np.float64(0.377), np.float64(0.156)), ('L0H2', np.float64(0.348), np.float64(0.065))]
L1H3 L0-source scores [0.196 0.206 0.38  0.164 0.277 0.29 ] best [('L0H2', np.float64(0.38), np.float64(0.09)), ('L0H5', np.float64(0.29), np.float64(0.025)), ('L0H4', np.float64(0.277), np.float64(0.177))]
L1H4 L0-source scores [0.05  0.149 0.294 0.157 0.374 0.239] best [('L0H4', np.float64(0.374), np.float64(0.084)), ('L0H2', np.float64(0.294), np.float64(-0.002)), ('L0H5', np.float64(0.239), np.float64(-0.008))]
L1H5 L0-source scores [-0.149  0.147  0.301  0.518  0.205  0.201] best [('L0H3', np.float64(0.518), np.float64(0.211)), ('L0H2', np.float64(0.301), np.float64(0.06)), ('L0H4', np.float64(0.205), np.float64(0.265))]
L2H0 L0-source scores [-0.065  0.328  0.58   0.282  0.297  0.51 ] best [('L1H3', np.float64(0.743), np.float64(-0.011)), ('L1H1', np.float64(0.669), np.float64(0.024)), ('L0H2', np.float64(0.58), np.float64(0.235))]
L2H1 L0-source scores [0.145 0.273 0.541 0.107 0.258 0.505] best [('L0H2', np.float64(0.541), np.float64(0.21)), ('L0H5', np.float64(0.505), np.float64(0.087)), ('L0H1', np.float64(0.273), np.float64(0.12))]
L2H2 L0-source scores [0.244 0.307 0.567 0.349 0.249 0.523] best [('L0H2', np.float64(0.567), np.float64(0.269)), ('L0H5', np.float64(0.523), np.float64(0.136)), ('L0H3', np.float64(0.349), np.float64(0.024))]
L2H3 L0-source scores [0.324 0.329 0.493 0.434 0.357 0.469] best [('L0H2', np.float64(0.493), np.float64(0.18)), ('L0H5', np.float64(0.469), np.float64(0.116)), ('L0H3', np.float64(0.434), np.float64(0.145))]
L2H4 L0-source scores [-0.132  0.341  0.661  0.708  0.325  0.581] best [('L0H3', np.float64(0.708), np.float64(0.191)), ('L0H2', np.float64(0.661), np.float64(0.323)), ('L0H5', np.float64(0.581), np.float64(0.155))]
L2H5 L0-source scores [ 0.098  0.274  0.519 -0.03   0.25   0.571] best [('L0H5', np.float64(0.571), np.float64(0.131)), ('L0H2', np.float64(0.519), np.float64(0.159)), ('L0H1', np.float64(0.274), np.float64(0.121))]
L3H0 L0-source scores [-0.263  0.218  0.391 -0.629  0.19   0.278] best [('L0H2', np.float64(0.391), np.float64(0.196)), ('L0H5', np.float64(0.278), np.float64(0.039)), ('L0H1', np.float64(0.218), np.float64(0.097))]
L3H1 L0-source scores [ 0.121  0.208  0.388 -0.214  0.14   0.307] best [('L0H2', np.float64(0.388), np.float64(0.225)), ('L0H5', np.float64(0.307), np.float64(0.082)), ('L1H2', np.float64(0.238), np.float64(0.002))]
L3H2 L0-source scores [-0.028  0.138  0.282  0.202  0.043  0.061] best [('L0H2', np.float64(0.282), np.float64(0.187)), ('L0H3', np.float64(0.202), np.float64(0.105)), ('L0H1', np.float64(0.138), np.float64(0.12))]
L3H3 L0-source scores [-0.59   0.275  0.352  2.858  0.388 -0.173] best [('L0H3', np.float64(2.858), np.float64(0.591)), ('L2H5', np.float64(1.86), np.float64(0.226)), ('L1H5', np.float64(1.361), np.float64(0.183))]
L3H4 L0-source scores [0.246 0.606 0.763 0.682 0.693 0.586] best [('L2H4', np.float64(1.023), np.float64(0.161)), ('L0H2', np.float64(0.763), np.float64(0.349)), ('L2H0', np.float64(0.718), np.float64(0.092))]
L3H5 L0-source scores [-0.048  0.06   0.241 -0.126  0.011  0.187] best [('L0H2', np.float64(0.241), np.float64(0.077)), ('L0H5', np.float64(0.187), np.float64(0.015)), ('L0H1', np.float64(0.06), np.float64(0.047))]

L3H3 <- L0H3 matching score: 2.858
Coordinate-sign scrambling of the weight connection, null quantiles: [-1.0762 -0.8702  0.0232  0.8891  1.0625]

Selected literal LayerNorm weights
ln1_b.1 [(39, -1.5675644874572754), (58, 1.36513352394104), (99, -1.3355246782302856), (21, -0.4298906922340393)]
ln1_b.2 [(39, -1.1991313695907593), (58, 1.331817865371704), (99, -1.6588826179504395), (21, -0.4534468650817871)]
ln1_w.0 [(180, 0.9784557819366455), (184, 0.9740331768989563), (162, 0.9703823924064636), (99, 0.9171200394630432), (211, 0.8959937691688538)]


========================================================================
TURN t009
MESSAGE SENT TO CODEX
OUTPUT of run 8 of at most 100:
```
Weight-only matching diagnostic:
trace(P.T @ QK_lh @ OV_source @ P) / Frobenius norm;
P = top 20 right singular directions of source V.
L1H0 L0-source scores [0.214 0.281 0.413 0.329 0.387 0.387] best [('L0H2', np.float64(0.413), np.float64(0.084)), ('L0H5', np.float64(0.387), np.float64(0.025)), ('L0H4', np.float64(0.387), np.float64(0.222))]
L1H1 L0-source scores [0.106 0.052 0.221 0.632 0.048 0.149] best [('L0H3', np.float64(0.632), np.float64(0.126)), ('L0H2', np.float64(0.221), np.float64(0.067)), ('L0H5', np.float64(0.149), np.float64(0.043))]
L1H2 L0-source scores [-0.225  0.256  0.348  0.482  0.377  0.326] best [('L0H3', np.float64(0.482), np.float64(0.175)), ('L0H4', np.float64(0.377), np.float64(0.156)), ('L0H2', np.float64(0.348), np.float64(0.065))]
L1H3 L0-source scores [0.196 0.206 0.38  0.164 0.277 0.29 ] best [('L0H2', np.float64(0.38), np.float64(0.09)), ('L0H5', np.float64(0.29), np.float64(0.025)), ('L0H4', np.float64(0.277), np.float64(0.177))]
L1H4 L0-source scores [0.05  0.149 0.294 0.157 0.374 0.239] best [('L0H4', np.float64(0.374), np.float64(0.084)), ('L0H2', np.float64(0.294), np.float64(-0.002)), ('L0H5', np.float64(0.239), np.float64(-0.008))]
L1H5 L0-source scores [-0.149  0.147  0.301  0.518  0.205  0.201] best [('L0H3', np.float64(0.518), np.float64(0.211)), ('L0H2', np.float64(0.301), np.float64(0.06)), ('L0H4', np.float64(0.205), np.float64(0.265))]
L2H0 L0-source scores [-0.065  0.328  0.58   0.282  0.297  0.51 ] best [('L1H3', np.float64(0.743), np.float64(-0.011)), ('L1H1', np.float64(0.669), np.float64(0.024)), ('L0H2', np.float64(0.58), np.float64(0.235))]
L2H1 L0-source scores [0.145 0.273 0.541 0.107 0.258 0.505] best [('L0H2', np.float64(0.541), np.float64(0.21)), ('L0H5', np.float64(0.505), np.float64(0.087)), ('L0H1', np.float64(0.273), np.float64(0.12))]
L2H2 L0-source scores [0.244 0.307 0.567 0.349 0.249 0.523] best [('L0H2', np.float64(0.567), np.float64(0.269)), ('L0H5', np.float64(0.523), np.float64(0.136)), ('L0H3', np.float64(0.349), np.float64(0.024))]
L2H3 L0-source scores [0.324 0.329 0.493 0.434 0.357 0.469] best [('L0H2', np.float64(0.493), np.float64(0.18)), ('L0H5', np.float64(0.469), np.float64(0.116)), ('L0H3', np.float64(0.434), np.float64(0.145))]
L2H4 L0-source scores [-0.132  0.341  0.661  0.708  0.325  0.581] best [('L0H3', np.float64(0.708), np.float64(0.191)), ('L0H2', np.float64(0.661), np.float64(0.323)), ('L0H5', np.float64(0.581), np.float64(0.155))]
L2H5 L0-source scores [ 0.098  0.274  0.519 -0.03   0.25   0.571] best [('L0H5', np.float64(0.571), np.float64(0.131)), ('L0H2', np.float64(0.519), np.float64(0.159)), ('L0H1', np.float64(0.274), np.float64(0.121))]
L3H0 L0-source scores [-0.263  0.218  0.391 -0.629  0.19   0.278] best [('L0H2', np.float64(0.391), np.float64(0.196)), ('L0H5', np.float64(0.278), np.float64(0.039)), ('L0H1', np.float64(0.218), np.float64(0.097))]
L3H1 L0-source scores [ 0.121  0.208  0.388 -0.214  0.14   0.307] best [('L0H2', np.float64(0.388), np.float64(0.225)), ('L0H5', np.float64(0.307), np.float64(0.082)), ('L1H2', np.float64(0.238), np.float64(0.002))]
L3H2 L0-source scores [-0.028  0.138  0.282  0.202  0.043  0.061] best [('L0H2', np.float64(0.282), np.float64(0.187)), ('L0H3', np.float64(0.202), np.float64(0.105)), ('L0H1', np.float64(0.138), np.float64(0.12))]
L3H3 L0-source scores [-0.59   0.275  0.352  2.858  0.388 -0.173] best [('L0H3', np.float64(2.858), np.float64(0.591)), ('L2H5', np.float64(1.86), np.float64(0.226)), ('L1H5', np.float64(1.361), np.float64(0.183))]
L3H4 L0-source scores [0.246 0.606 0.763 0.682 0.693 0.586] best [('L2H4', np.float64(1.023), np.float64(0.161)), ('L0H2', np.float64(0.763), np.float64(0.349)), ('L2H0', np.float64(0.718), np.float64(0.092))]
L3H5 L0-source scores [-0.048  0.06   0.241 -0.126  0.011  0.187] best [('L0H2', np.float64(0.241), np.float64(0.077)), ('L0H5', np.float64(0.187), np.float64(0.015)), ('L0H1', np.float64(0.06), np.float64(0.047))]

L3H3 <- L0H3 matching score: 2.858
Coordinate-sign scrambling of the weight connection, null quantiles: [-1.0762 -0.8702  0.0232  0.8891  1.0625]

Selected literal LayerNorm weights
ln1_b.1 [(39, -1.5675644874572754), (58, 1.36513352394104), (99, -1.3355246782302856), (21, -0.4298906922340393)]
ln1_b.2 [(39, -1.1991313695907593), (58, 1.331817865371704), (99, -1.6588826179504395), (21, -0.4534468650817871)]
ln1_w.0 [(180, 0.9784557819366455), (184, 0.9740331768989563), (162, 0.9703823924064636), (99, 0.9171200394630432), (211, 0.8959937691688538)]

```
CLI OUTPUT IN EVENT ORDER
ERROR
Failed to read global AGENTS.md instructions from `<local-home>/.codex/AGENTS.md`: Operation not permitted (os error 1)

ERROR
Code Mode is unavailable because code-mode host is disabled. Code mode will fail closed; enable `features.code_mode_host` and install `codex-code-mode-host`.

AGENT_MESSAGE
## Observations

**The strongest evidence concerns order and circuitry, not corpus identity.** These are weight-only hypotheses; no attention patterns were measured.

Below, \(A\) denotes a head’s QK product, including the learned LN scale and centering projection; \(B\) denotes its corresponding OV product.

- **L0H3 looks like a positional-shift head.** Its QK eigenvalues include \(0.137\pm0.133i\), \(0.110\pm0.089i\), and \(0.095\pm0.098i\). These rotation-like pairs suggest positional displacement, although they do not establish an exact one-character offset.
- **L3H3 has a distinctive induction-compatible connection to L0H3.** Restricted to L0H3’s leading 20 value-reading directions, the normalized trace of \(A_{\mathrm{L3H3}}B_{\mathrm{L0H3}}\) is **2.858**. Scrambling coordinate signs in that connection gave values between **−1.076 and 1.063** across 1,000 trials. This supports matching information written by the earlier head.
- **L0H1/H2/H4/H5 share low-dimensional machinery.** Their OV effective ranks are approximately **2.0, 2.1, 2.5, 2.0**. L0H1 and L0H2’s OV matrices have cosine similarity **0.925**. This looks more like shared structural bookkeeping than four independent character-copying channels.
- **Middle layers strongly read that shared machinery.** Its leading two output directions capture **79–85%** of L1’s key-bias-vector energy. Literal supporting weights include `ln1_b.1[39] = −1.56756`, `[58] = 1.36513`, and `[99] = −1.33552`. A positional/recency interpretation is plausible, but not established.

## Heads

Labels are tentative, especially **local versus broad**. “Key bias” below means the key-dependent linear term induced by `ln1_b`, not an observed attention bias.

L0H0: **local** — substantial overlap with L0H3’s candidate positional subspace; weaker displacement-like structure.  
L0H1: **unclear** — nearly rank-two QK/OV machinery; its spatial range is unidentified.  
L0H2: **unclear** — closely shares L0H1’s low-dimensional output; no identifiable offset.  
L0H3: **previous** — rotation-like QK spectrum plus the strong downstream matching connection; exact offset remains uncertain.  
L0H4: **unclear** — another shared structural channel; OV effective rank 2.5.  
L0H5: **broad** — best pooling candidate: QK Frobenius norm only 0.034, versus OV norm 18.812.

L1H0: **local** — strong shared positional-candidate reading; key-bias norm 3.975.  
L1H1: **local** — same dominant structural connection; key-bias norm 3.689.  
L1H2: **local** — strongest shared-subspace QK key-side concentration, approximately 46%.  
L1H3: **local** — approximately 46% key-side concentration; key-bias norm 3.390.  
L1H4: **local** — approximately 42% concentration; weaker key bias, 2.329.  
L1H5: **local** — approximately 42% concentration and strong key bias, 3.895.

L2H0: **local** — retains the strongest shared structural QK component in this layer, approximately 23%.  
L2H1: **unclear** — much more distributed QK structure; shared machinery does not determine range.  
L2H2: **local** — retains the common structural bias; norm 1.608, but assignment is weak.  
L2H3: **unclear** — weaker structural bias and no standout induction connection.  
L2H4: **local** — comparatively strong structural component and key-bias norm 2.305.  
L2H5: **unclear** — distributed content-reading structure; insufficient evidence for a particular distance.

L3H0: **unclear** — weak remaining structural bias; neither distance nor induction is established.  
L3H1: **unclear** — small key bias, 0.280; this alone cannot establish broad attention.  
L3H2: **unclear** — content-dependent QK structure without a diagnostic earlier-head connection.  
L3H3: **copy** — standout L0H3-to-QK matching score, 2.858; strongest induction candidate.  
L3H4: **broad** — plausible pooling head: relatively weak QK norm 0.622, strong OV norm 49.234.  
L3H5: **unclear** — distributed QK structure; no convincing displacement or induction signature.

## Reasoning

The displacement-like early head and selective downstream matching connection favor **as-is text**: preserving character order makes previous-character transport and induction useful. Shuffling would substantially weaken their utility, although it would not eliminate all contextual structure.

**English is my low-confidence corpus choice.** The weights suggest rich local processing and repetition-sensitive retrieval, but these also fit Python and romaji. I recovered neither labeled character features nor a convincing corpus-specific signature. Consequently, the corpus probabilities are deliberately much less decisive than the order probabilities.

corpus: english  
order: as is  
probabilities: python=0.35 romaji=0.23 english=0.42; as is=0.95 shuffled=0.05

SAVED FINAL ANSWER
## Observations

**The strongest evidence concerns order and circuitry, not corpus identity.** These are weight-only hypotheses; no attention patterns were measured.

Below, \(A\) denotes a head’s QK product, including the learned LN scale and centering projection; \(B\) denotes its corresponding OV product.

- **L0H3 looks like a positional-shift head.** Its QK eigenvalues include \(0.137\pm0.133i\), \(0.110\pm0.089i\), and \(0.095\pm0.098i\). These rotation-like pairs suggest positional displacement, although they do not establish an exact one-character offset.
- **L3H3 has a distinctive induction-compatible connection to L0H3.** Restricted to L0H3’s leading 20 value-reading directions, the normalized trace of \(A_{\mathrm{L3H3}}B_{\mathrm{L0H3}}\) is **2.858**. Scrambling coordinate signs in that connection gave values between **−1.076 and 1.063** across 1,000 trials. This supports matching information written by the earlier head.
- **L0H1/H2/H4/H5 share low-dimensional machinery.** Their OV effective ranks are approximately **2.0, 2.1, 2.5, 2.0**. L0H1 and L0H2’s OV matrices have cosine similarity **0.925**. This looks more like shared structural bookkeeping than four independent character-copying channels.
- **Middle layers strongly read that shared machinery.** Its leading two output directions capture **79–85%** of L1’s key-bias-vector energy. Literal supporting weights include `ln1_b.1[39] = −1.56756`, `[58] = 1.36513`, and `[99] = −1.33552`. A positional/recency interpretation is plausible, but not established.

## Heads

Labels are tentative, especially **local versus broad**. “Key bias” below means the key-dependent linear term induced by `ln1_b`, not an observed attention bias.

L0H0: **local** — substantial overlap with L0H3’s candidate positional subspace; weaker displacement-like structure.  
L0H1: **unclear** — nearly rank-two QK/OV machinery; its spatial range is unidentified.  
L0H2: **unclear** — closely shares L0H1’s low-dimensional output; no identifiable offset.  
L0H3: **previous** — rotation-like QK spectrum plus the strong downstream matching connection; exact offset remains uncertain.  
L0H4: **unclear** — another shared structural channel; OV effective rank 2.5.  
L0H5: **broad** — best pooling candidate: QK Frobenius norm only 0.034, versus OV norm 18.812.

L1H0: **local** — strong shared positional-candidate reading; key-bias norm 3.975.  
L1H1: **local** — same dominant structural connection; key-bias norm 3.689.  
L1H2: **local** — strongest shared-subspace QK key-side concentration, approximately 46%.  
L1H3: **local** — approximately 46% key-side concentration; key-bias norm 3.390.  
L1H4: **local** — approximately 42% concentration; weaker key bias, 2.329.  
L1H5: **local** — approximately 42% concentration and strong key bias, 3.895.

L2H0: **local** — retains the strongest shared structural QK component in this layer, approximately 23%.  
L2H1: **unclear** — much more distributed QK structure; shared machinery does not determine range.  
L2H2: **local** — retains the common structural bias; norm 1.608, but assignment is weak.  
L2H3: **unclear** — weaker structural bias and no standout induction connection.  
L2H4: **local** — comparatively strong structural component and key-bias norm 2.305.  
L2H5: **unclear** — distributed content-reading structure; insufficient evidence for a particular distance.

L3H0: **unclear** — weak remaining structural bias; neither distance nor induction is established.  
L3H1: **unclear** — small key bias, 0.280; this alone cannot establish broad attention.  
L3H2: **unclear** — content-dependent QK structure without a diagnostic earlier-head connection.  
L3H3: **copy** — standout L0H3-to-QK matching score, 2.858; strongest induction candidate.  
L3H4: **broad** — plausible pooling head: relatively weak QK norm 0.622, strong OV norm 49.234.  
L3H5: **unclear** — distributed QK structure; no convincing displacement or induction signature.

## Reasoning

The displacement-like early head and selective downstream matching connection favor **as-is text**: preserving character order makes previous-character transport and induction useful. Shuffling would substantially weaken their utility, although it would not eliminate all contextual structure.

**English is my low-confidence corpus choice.** The weights suggest rich local processing and repetition-sensitive retrieval, but these also fit Python and romaji. I recovered neither labeled character features nor a convincing corpus-specific signature. Consequently, the corpus probabilities are deliberately much less decisive than the order probabilities.

corpus: english  
order: as is  
probabilities: python=0.35 romaji=0.23 english=0.42; as is=0.95 shuffled=0.05
