{"type":"thread.started","thread_id":"id-be6fd769"}
{"type":"item.completed","item":{"id":"item_0","type":"error","message":"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`."}}
{"type":"turn.started"}
{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"## Observations:\n\nAll measurements below are **weight-only**, not forward passes. Head labels are hypotheses; attention distances cannot be verified without the missing embeddings and activations.\n\nFor compactness, define\n\\[\nA=G W_q^\\top W_kG/8,\\qquad B=W_oW_vG,\\qquad\nr=G W_k^\\top W_q\\,\\mathrm{ln1_b}/8,\n\\]\nwhere \\(G=\\operatorname{diag}(\\mathrm{ln1_w})\\), using each head’s slices. Thus \\(A\\) is its bilinear score matrix, \\(B\\) its value/output product, and \\(r\\) a key-dependent affine coefficient.\n\n- **L0H3 stands out as a directional positional head.** Its \\(W_q,W_k\\) norms are **14.141, 14.661**, substantially above the other L0 heads. Its unscaled QK product has complex eigenvalues including **\\(0.724\\pm0.691i\\)** and **\\(0.446\\pm0.842i\\)**. The leading 16-dimensional Q/K subspaces overlap strongly (**0.620**), whereas Q/V overlap is only **0.0177**. This supports position-controlled transport of different, likely character-related information.\n- **Several L0 heads construct shared low-dimensional signals.** Coordinates **21,39,58,99,184** contain **94.0%, 94.2%, 87.8%, 97.0%** of \\(B\\)’s squared norm for H1,H2,H4,H5. These coordinates have no intrinsic semantic labels.\n- **Later heads strongly read those shared signals.** For example, `ln1_b.1[39]=-1.5676`, `[58]=1.3651`, and `[99]=-1.3355`. All six L1 heads have positive \\(r_{21}\\), ranging from **2.008 to 3.627**. This is consistent with a shared positional/recency mechanism, although it does not establish its meaning conclusively.\n- **L3H3 has a distinctive induction-compatible connection to L0H3.** Let \\(T\\) contain the leading 20 right-singular directions of L0H3’s scaled value matrix. For\n  \\[\n  C=T^\\top A_{3,3}B_{0,3}T,\n  \\]\n  \\(\\operatorname{tr}(C)/\\|C\\|_F=\\mathbf{2.860}\\). Signed/permuted-coordinate controls had standard deviation **0.234** and maximum **0.682** across 1,000 trials. This is strong evidence of learned matching through the earlier transport circuit.\n- **The corpus-specific evidence is weaker.** The leading 24 singular directions of `W_proj.3` contain **92.14%** of its squared norm; directions 25–28 add only **1.62%**. This is compatible with a comparatively restricted frequently used alphabet, but is **not** a recovered character count.\n\n## Heads:\n\nThe “local” assignments below largely depend on the tentative recency interpretation of the shared channel.\n\nL0H0: **local** — Its positional-subspace score matrix resembles a higher power of L0H3’s directional factor more than the first power; compatible with a longer short offset.\n\nL0H1: **unclear** — Almost rank-two score/output structure; 94.0% of output-product energy enters the shared coordinates. Boundary selection and positional bookkeeping remain alternatives.\n\nL0H2: **unclear** — One score singular mode carries 90.8% of energy; 94.2% of output energy enters the shared coordinates. Distance is unresolved.\n\nL0H3: **previous** — Strongest predecessor candidate: high-rank directional QK structure, separated positional and value subspaces, and the downstream induction-compatible connection.\n\nL0H4: **unclear** — Dominant rank-one score component and 87.8% shared-coordinate output concentration; insufficient evidence for a particular attention distance.\n\nL0H5: **broad** — Very weak score product, with leading singular value **0.032**, but strong low-rank value transport (**16.282, 8.786**); consistent with context aggregation.\n\nL1H0: **local** — Strong shared-channel preference: \\(r_{21}=3.627\\); key column 21 contains 30.1% of score-product energy.\n\nL1H1: **local** — \\(r_{21}=3.352\\), with 32.5% key-column-21 energy; closely resembles the other L1 recency candidates.\n\nL1H2: **local** — \\(r_{21}=2.769\\), with 36.4% key-column-21 energy.\n\nL1H3: **local** — \\(r_{21}=3.079\\), with 36.4% key-column-21 energy.\n\nL1H4: **local** — \\(r_{21}=2.008\\), with 34.8% key-column-21 energy; weaker shared preference than most L1 heads.\n\nL1H5: **local** — \\(r_{21}=3.563\\), with 31.9% key-column-21 energy.\n\nL2H0: **local** — Retains the shared mechanism strongly: \\(r_{21}=1.815\\), with 15.4% key-column-21 energy.\n\nL2H1: **local** — \\(r_{21}=1.682\\); substantial shared-channel preference, but more distributed content-sensitive score structure.\n\nL2H2: **local** — \\(r_{21}=1.411\\); compatible with content-conditioned local retrieval.\n\nL2H3: **local** — Lower-confidence assignment: the shared preference remains, \\(r_{21}=0.803\\), but is weaker.\n\nL2H4: **local** — Strongest L2 shared-channel preference, \\(r_{21}=2.069\\); supports recency-sensitive retrieval.\n\nL2H5: **local** — \\(r_{21}=1.859\\), without a distinctive positive L0H3 matching composition.\n\nL3H0: **local** — Residual shared-channel preference, \\(r_{21}=0.408\\); the tested predecessor-matching composition is negative, unlike L3H3.\n\nL3H1: **unclear** — Weaker shared-channel preference, \\(r_{21}=0.181\\), and no strong tested induction signature; local versus broader retrieval remains unresolved.\n\nL3H2: **local** — \\(r_{21}=0.382\\); retains the common positional mechanism without L3H3’s matching signature.\n\nL3H3: **copy** — Strong positive matching through L0H3: projected composition trace/norm **2.860**, far beyond the coordinate-randomization controls.\n\nL3H4: **broad** — Little shared-channel preference, \\(r_{21}=0.028\\), combined with large value/output singular values **21.271, 17.680**; favors an aggregation interpretation.\n\nL3H5: **local** — \\(r_{21}=0.416\\), with no comparable positive predecessor-matching signature.\n\n## Reasoning:\n\n**Intact order is strongly favored.** A directional character-transport circuit followed by an induction-compatible matching circuit is useful for ordered sequences and repetition. Randomly shuffling each line largely removes those predictive relationships, although it preserves line-level composition and boundaries.\n\n**Romaji is my best, less-confident corpus judgment.** The comparatively concentrated character-related geometry and substantial short-context machinery fit a restricted, regular romanized orthography. English remains a serious alternative; the spectra do not identify letters, vowels, words, or language directly. I find less positive evidence specifically favoring Python.\n\ncorpus: romaji  \norder: as is  \nprobabilities: python=0.11 romaji=0.62 english=0.27; as is=0.99 shuffled=0.01"}}
{"type":"turn.completed","usage":{"input_tokens":278463,"cached_input_tokens":231680,"cache_write_input_tokens":0,"output_tokens":17376,"reasoning_output_tokens":10325}}