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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nfrom threadpoolctl import threadpool_limits\nthreadpool_limits(4)\n\ng0=W[\"ln1_w.0\"].astype(float)\nV0=W[\"W_v.0\"][192:256].astype(float)*g0\nT=np.linalg.svd(V0,full_matrices=False)[2][:20].T\nB0=W[\"W_o.0\"][:,192:256].astype(float)@V0\nUout=np.linalg.svd(W[\"W_proj.3\"].astype(float),full_matrices=False)[0][:,:24]\n\nprint(\"Final heads: weight-only token-to-output and matching diagnostics\")\nfor j in range(6):\n    s=slice(j*64,(j+1)*64)\n    g=W[\"ln1_w.3\"].astype(float)\n    A=(W[\"W_q.3\"][s]*g).T@(W[\"W_k.3\"][s]*g)/8\n    B=W[\"W_o.3\"][:,s].astype(float)@(W[\"W_v.3\"][s]*g)\n    D=B@T\n    C=T.T@A@B0@T\n    print(\"L3H%d\"%j,\n          \"OV token-map norm %.3f output-subspace energy %.3f\"%\n          (np.linalg.norm(D),np.linalg.norm(Uout.T@D)**2/np.linalg.norm(D)**2),\n          \"matching trace/norm %.3f\"%(np.trace(C)/np.linalg.norm(C)),\n          \"matching eig real\",np.round(np.sort(np.linalg.eigvals(C).real)[-6:],4))\n\nprint(\"\\nCoordinate concentration of L0 OV output (rows 21,39,58,99,184)\")\nix=[21,39,58,99,184]\nfor j in range(6):\n    s=slice(j*64,(j+1)*64)\n    B=W[\"W_o.0\"][:,s].astype(float)@(W[\"W_v.0\"][s]*g0)\n    print(\"L0H%d\"%j,round(np.sum(B[ix]**2)/np.sum(B**2),4))\n\nprint(\"\\nInduction matching control: signed/permuted head-output coordinates\")\nrng=np.random.default_rng(1022)\ns=slice(192,256);g=W[\"ln1_w.3\"].astype(float)\nA=(W[\"W_q.3\"][s]*g).T@(W[\"W_k.3\"][s]*g)/8\nleft=T.T@A\nright=B0@T\nactual=left@right\nnull=[]\nfor _ in range(1000):\n    perm=rng.permutation(384)\n    sign=rng.choice([-1.,1.],384)\n    C=(left*sign)@right[perm]\n    null.append(np.trace(C)/np.linalg.norm(C))\nprint(\"observed\",np.trace(actual)/np.linalg.norm(actual),\n      \"null mean/std\",np.mean(null),np.std(null),\n      \"null 1/99 percentiles\",np.percentile(null,[1,99]),\n      \"null max\",max(null))\n```\n"}}
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