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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nimport scipy.linalg as la\nfrom threadpoolctl import threadpool_limits\nnp.set_printoptions(precision=4, suppress=True, linewidth=180)\n\ndef svd(a):\n    return la.svd(a,full_matrices=False,lapack_driver=\"gesvd\")\ndef cos(a,b):\n    return np.sum(a*b)/(la.norm(a)*la.norm(b)+1e-30)\n\nwith threadpool_limits(limits=2):\n    A,B={},{}\n    for l in range(4):\n        g=np.asarray(W[f\"ln1_w.{l}\"],dtype=float)\n        for h in range(6):\n            sl=slice(h*64,h*64+64)\n            q=np.asarray(W[f\"W_q.{l}\"][sl],dtype=float)*g\n            k=np.asarray(W[f\"W_k.{l}\"][sl],dtype=float)*g\n            A[l,h]=q.T@k/8\n            B[l,h]=(np.asarray(W[f\"W_o.{l}\"][:,sl],dtype=float)@np.asarray(W[f\"W_v.{l}\"][sl],dtype=float))*g\n\n    prev=B[0,2]\n    _,_,vt=svd(prev)\n    T=vt[:24].T\n    U=prev@T\n    print(\"DIRECT SHIFTED-MATCH SIGNATURES\")\n    print(\"tracecos=tr(A B)/(sqrt(384)||A B||F); positive_real_mass uses eigenvalues of A B.\")\n    for l in range(1,4):\n        for h in range(6):\n            a=A[l,h]\n            c=a@prev\n            e=la.eigvals(c)\n            real_mass=np.maximum(e.real,0).sum()/(abs(e.real).sum()+1e-30)\n            r=T.T@a@U\n            match=np.trace(r)/(np.sqrt(24)*la.norm(r)+1e-30)\n            print(f\"L{l}H{h}: tracecos={np.trace(c)/(np.sqrt(384)*la.norm(c)):.4f}, \"\n                  f\"positive_real_mass={real_mass:.4f}, \"\n                  f\"token24_tracecos={match:.4f}, token24_symfrac={la.norm((r+r.T)/2)/(la.norm(r)+1e-30):.4f}\")\n\n    print(\"\\nCIRCUIT TRACE-COSINES FOR ALL EARLIER HEADS\")\n    for l in (2,3):\n        print(\"target layer\",l,\"columns\", [f\"L{m}H{h}\" for m in range(l) for h in range(6)])\n        for j in range(6):\n            vals=[]\n            for m in range(l):\n                for h in range(6):\n                    c=A[l,j]@B[m,h]\n                    vals.append(np.trace(c)/(np.sqrt(384)*la.norm(c)+1e-30))\n            print(f\"L{l}H{j}\",np.round(vals,4))\n\n    print(\"\\nHEAD VALUE-PATH ALIGNMENTS\")\n    print(\"Cosines among final-layer OV products:\")\n    print(np.array([[cos(B[3,i],B[3,j]) for j in range(6)] for i in range(6)]))\n    print(\"Earlier OV products most aligned with each final-layer OV (direct tensor cosine):\")\n    for j in range(6):\n        vals=sorted([(cos(B[3,j],B[l,h]),l,h) for l in range(3) for h in range(6)],reverse=True)\n        print(f\"L3H{j}\",[(f\"L{l}H{h}\",round(v,4)) for v,l,h in vals[:4]])\n\n    print(\"\\nPOSITIONAL-CANDIDATE QK GEOMETRY OF L0 HEADS\")\n    _,_,v=svd(np.vstack([\n        np.asarray(W[\"W_q.0\"][128:192],dtype=float)*W[\"ln1_w.0\"],\n        np.asarray(W[\"W_k.0\"][128:192],dtype=float)*W[\"ln1_w.0\"]]))\n    P=v[:32].T\n    for j in range(6):\n        a=A[0,j]\n        print(f\"L0H{j}: fraction_in_QK32={la.norm(P.T@a@P)**2/la.norm(a)**2:.4f}; \"\n              f\"cosine_to_H2={cos(a,A[0,2]):.4f}\")\n```"}}
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