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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nfrom scipy.linalg import svd, svdvals, eigvals\nfrom threadpoolctl import threadpool_limits\nnp.set_printoptions(precision=3, suppress=True, linewidth=180)\n\ndef center_columns(a):\n    return a-a.mean(axis=1,keepdims=True)\ndef center_output(a):\n    return a-a.mean(axis=0,keepdims=True)\n\nwith threadpool_limits(limits=4):\n    A, B = {}, {}\n    for l in range(4):\n        g=W[f\"ln1_w.{l}\"]\n        for j in range(6):\n            s=slice(j*64,(j+1)*64)\n            q=center_columns(W[f\"W_q.{l}\"][s]*g)\n            k=center_columns(W[f\"W_k.{l}\"][s]*g)\n            v=center_columns(W[f\"W_v.{l}\"][s]*g)\n            o=center_output(W[f\"W_o.{l}\"][:,s])\n            A[l,j]=q.T@k/8\n            B[l,j]=o@v\n    s=slice(128,192)\n    pos_basis=svd(np.vstack([center_columns(W[\"W_q.0\"][s]*W[\"ln1_w.0\"]),\n                            center_columns(W[\"W_k.0\"][s]*W[\"ln1_w.0\"])]),full_matrices=False)[2].T\n    vmat=center_columns(W[\"W_v.0\"][s]*W[\"ln1_w.0\"])\n    char_basis=svd(vmat,full_matrices=False)[2].T[:,:28]\n    print(\"L0H2 gain-weighted V spectrum\",svdvals(vmat)[:40])\n    print(\"POSITION-CANDIDATE OVERLAP WITH V0H2 TOP28:\",\n          [(r,round(float(np.linalg.norm(pos_basis[:,:r].T@char_basis)**2/28),3)) for r in [16,24,32,40,48,64]])\n    p=pos_basis[:,:32]\n    print(\"\\nHEAD PRODUCT ENERGY IN CANDIDATE POSITION SPACE\")\n    for l in range(4):\n        for j in range(6):\n            a=A[l,j]\n            den=np.linalg.norm(a)**2\n            print(f\"L{l}H{j}\", \"query\",round(float(np.linalg.norm(p.T@a)**2/den),3),\n                  \"key\",round(float(np.linalg.norm(a@p)**2/den),3),\n                  \"both\",round(float(np.linalg.norm(p.T@a@p)**2/den),3))\n    print(\"\\nCOMPOSITION WITH EACH L0 OV: tr(A @ B) / (||A||F ||B||F)\")\n    for l in range(1,4):\n        for j in range(6):\n            a=A[l,j]\n            scores=[np.trace(a@B[0,k])/(np.linalg.norm(a)*np.linalg.norm(B[0,k])) for k in range(6)]\n            scores_rev=[np.trace(a.T@B[0,k])/(np.linalg.norm(a)*np.linalg.norm(B[0,k])) for k in range(6)]\n            print(f\"L{l}H{j}\", \"key-path\",np.array(scores),\"query-path\",np.array(scores_rev))\n    print(\"\\nCOMPOSITION SPECTRA WITH L0H2 OV\")\n    for l in range(1,4):\n        for j in range(6):\n            c=A[l,j]@B[0,2]\n            ss=svdvals(c)\n            cc=char_basis.T@c@char_basis\n            sc=svdvals(cc)\n            es=eigvals(cc)\n            print(f\"L{l}H{j}\",\n                  \"trace\",round(float(np.trace(c)),3),\n                  \"trace/nuclear\",round(float(np.trace(c)/ss.sum()),3),\n                  \"char trace/nuclear\",round(float(np.trace(cc)/sc.sum()),3),\n                  \"char positive-real eig\",int(np.sum(es.real>0)), \"char eig top\",es[np.argsort(abs(es))[-5:][::-1]])\n```\n"}}
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