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{"type":"item.completed","item":{"id":"item_1","type":"agent_message","text":"```python\nimport numpy as np\nimport torch\nfrom scipy.linalg import eig\ntorch.set_num_threads(4)\ntorch.set_default_dtype(torch.float64)\nT=lambda a: torch.as_tensor(np.asarray(a),dtype=torch.float64)\nP=torch.eye(384)-torch.ones((384,384))/384\ng=T(W[\"ln1_w.0\"])\nm={}\nfor j in [1,5]:\n    sl=slice(64*j,64*(j+1))\n    q=(T(W[\"W_q.0\"])[sl]*g)@P\n    k=(T(W[\"W_k.0\"])[sl]*g)@P\n    m[j]=q.T@k/8\nc=sum(a@a.T+a.T@a for a in m.values())\n_,u=torch.linalg.eigh(c)\nu=u.flip(1)\n\nprint(\"Relative-shift diagnostic using only generalized eigenvectors of QK weight products.\")\nprint(\"For shared rotational modes, phase(H1) approximately k*phase(H5) would suggest a lag ratio k.\")\nfor r in [12,16,20,24,28,32,40]:\n    z=u[:,:r]\n    a=(z.T@m[1]@z).numpy()\n    b=(z.T@m[5]@z).numpy()\n    ev,vec=eig(b.T,b)\n    rows=[]\n    for i,x in enumerate(ev):\n        if not np.isfinite(x) or x.imag<=1e-5 or abs(abs(x)-1)>.12:\n            continue\n        v=vec[:,i]\n        av=a@v\n        atv=a.T@v\n        overlap=np.vdot(av,atv)/(np.linalg.norm(av)*np.linalg.norm(atv)+1e-15)\n        rows.append((float(np.angle(x)),float(np.angle(overlap)),float(abs(overlap))))\n    print(\"\\nrank\",r,\"(H5 phase,H1 phase,mode agreement)\",np.round(rows,3).tolist())\n    if rows:\n        p,q,w=np.array(rows).T\n        print(\"phase agreement for H1/H5 lag ratios -3,-2,-1,1,2,3,4:\",\n              [(k,round(float(np.average(np.cos(q-k*p),weights=w**4)),3))\n               for k in [-3,-2,-1,1,2,3,4]])\n```\n"}}
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