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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nfrom scipy.stats import kurtosis\nfrom sklearn.decomposition import FastICA\nfrom threadpoolctl import threadpool_limits\nimport warnings\nthreadpool_limits(2)\nnp.set_printoptions(precision=3, suppress=True, linewidth=180)\n\nA={};B={}\nfor l in range(4):\n    g=W[f\"ln1_w.{l}\"].astype(float)\n    for j in range(6):\n        sl=slice(j*64,j*64+64)\n        q=W[f\"W_q.{l}\"][sl].astype(float)*g\n        k=W[f\"W_k.{l}\"][sl].astype(float)*g\n        A[l,j]=q.T@k/8\n        B[l,j]=W[f\"W_o.{l}\"][:,sl].astype(float)@(W[f\"W_v.{l}\"][sl].astype(float)*g)\n\nb=B[0,3]\n_,_,vt=np.linalg.svd(W[\"W_v.0\"][192:256].astype(float)*W[\"ln1_w.0\"],full_matrices=False)\nT=vt[:24].T\n\ndef diagnostic(c):\n    n=np.linalg.norm(c)\n    sym=(c+c.T)/2\n    return [np.trace(c)/n,np.linalg.norm(sym)/n]\n\nprint(\"MATCHING-PATH DIAGNOSTICS\")\nprint(\"Each pair is trace/F, symmetric_fraction.\")\nprint(\"00=direct/direct; 01=direct/earlier-OV; 10=earlier-OV/direct; 11=earlier-OV/both.\")\nfor l in range(1,4):\n    for j in range(6):\n        a=A[l,j]\n        cs=[a,a@b,b.T@a,b.T@a@b]\n        full=[diagnostic(c) for c in cs]\n        sub=[diagnostic(T.T@c@T) for c in cs]\n        print(f\"L{l}H{j} full\",np.round(full,3),\"V-subspace\",np.round(sub,3))\n\nprint(\"\\nL0H3 PATH TO L3H3: POSITIVE/NEGATIVE SYMMETRIC ENERGY\")\nfor label,c in [\n    (\"direct\",A[3,3]),\n    (\"key via H3\",A[3,3]@b),\n    (\"query via H3\",b.T@A[3,3]),\n    (\"both via H3\",b.T@A[3,3]@b)\n]:\n    e=np.linalg.eigvalsh((c+c.T)/2)\n    print(label,\"positive squared-eigenvalue fraction\",np.sum(e[e>0]**2)/np.sum(e**2),\n          \"top positive\",e[-8:],\"most negative\",e[:8])\n\nprint(\"\\nICA OF FINAL MLP OUTPUT COLUMNS (weights only; no neural computation)\")\nX=W[\"W_proj.3\"].astype(float).T\nfor n in [22,24,27,30]:\n    with warnings.catch_warnings(record=True) as ws:\n        ica=FastICA(n_components=n,whiten=\"unit-variance\",random_state=0,max_iter=3000,tol=1e-4)\n        Z=ica.fit_transform(X)\n    ku=kurtosis(Z,axis=0,fisher=True)\n    norms=np.linalg.norm(ica.mixing_,axis=0)\n    order=np.argsort(norms)[::-1]\n    print(\"components\",n,\"iterations\",ica.n_iter_,\"warnings\",len(ws))\n    print(\"mixing norm, excess kurtosis:\",np.round(np.column_stack([norms[order],ku[order]]),3))\n\nprint(\"\\nCLOCK-REGISTER WRITE STRENGTHS\")\nfor j in range(6):\n    mat=B[0,j]\n    print(f\"L0H{j}: row21 norm={np.linalg.norm(mat[21]):.3f}\",\n          f\"row21 energy fraction={np.sum(mat[21]**2)/np.sum(mat**2):.3f}\",\n          f\"rows21,39,58,99 combined fraction={np.sum(mat[[21,39,58,99]]**2)/np.sum(mat**2):.3f}\")\nprint(\"Exact LayerNorm gains at coordinate 21:\",\n      {f\"{name}.{l}\":float(W[f\"{name}.{l}\"][21]) for l in range(4) for name in [\"ln1_w\",\"ln2_w\"]})\n```\n"}}
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