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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\n\n# Replace local safety propagation with two-colour liberty reachability.\n# A genuine one-liberty group cannot have liberties in both checkerboard\n# classes. Two immediate liberties seed both classes, even if same-coloured.\n# All steps are fixed Boolean ReLU circuits; no positions are evaluated here.\np = {n: load(n) for n in NAMES}\ndef u(ch,q): return ch*81+q\nadj=[]\nrings={k:[] for k in (\"diag\",\"axial2\",\"knight\",\"axial3\")}\ndeltas={\n    \"diag\":[(a,b) for a in (-1,1) for b in (-1,1)],\n    \"axial2\":[(-2,0),(2,0),(0,-2),(0,2)],\n    \"knight\":[(a,b) for a in (-2,-1,1,2) for b in (-2,-1,1,2)\n              if abs(a)+abs(b)==3],\n    \"axial3\":[(-3,0),(3,0),(0,-3),(0,3)]}\nfor q in range(81):\n    r,c=divmod(q,9)\n    adj.append([rr*9+cc for rr,cc in ((r-1,c),(r+1,c),(r,c-1),(r,c+1))\n                if 0<=rr<9 and 0<=cc<9])\n    for k,ds in deltas.items():\n        rings[k].append([(r+a)*9+c+b for a,b in ds\n                         if 0<=r+a<9 and 0<=c+b<9])\n\nfor k in (2,3,4,5,6):\n    p[f\"L{k}.W\"][:]=0\n    p[f\"L{k}.b\"][:]=0\n    for j in range(486,493):\n        p[f\"L{k}.W\"][j,j]=1\n\nw=p[\"L2.W\"]\nfor q in range(81):\n    for co in (0,1): w[u(co,q),u(co,q)]=1\n    for co,old_d,old_z,new_start in ((0,2,3,2),(1,4,5,4)):\n        for cls in (0,1):\n            dest=u(new_start+cls,q)\n            w[u(co,q),dest]+=1\n            # Remove the \"unreached\" flag when a connected stone has\n            # two immediate liberties.\n            for v in [q]+adj[q]:\n                w[u(co,v),dest]-=1\n                w[u(old_d,v),dest]+=1\n                w[u(old_z,v),dest]-=1\n                r,c=divmod(v,9)\n                if (r+c+1)%2==cls:\n                    # ownership-Z is the exact has-a-liberty indicator.\n                    w[u(co,v),dest]-=1\n                    w[u(old_z,v),dest]+=1\n\nfor k in (3,4):\n    w=p[f\"L{k}.W\"]\n    for q in range(81):\n        for co in (0,1): w[u(co,q),u(co,q)]=1\n        for co,start in ((0,2),(1,4)):\n            for cls in (0,1):\n                ch=start+cls\n                w[u(ch,q),u(ch,q)]=1\n                for v in adj[q]:\n                    w[u(co,v),u(ch,q)]-=1\n                    w[u(ch,v),u(ch,q)]+=1\n\nw=p[\"L5.W\"]; b=p[\"L5.b\"]\nfor q in range(81):\n    r,c=divmod(q,9)\n    edge=min(r,c,8-r,8-c)\n    b[u(0,q)]=32+.20*min(edge,2)-(.20 if edge==0 else 0)\n    w[490,u(0,q)]=.55*min(edge,2)+.15*(1-(abs(r-4)+abs(c-4))/8)\n    for pts,own,enemy in (\n        (adj[q],.25,.05),\n        (rings[\"diag\"][q],.60,.10),\n        (rings[\"axial2\"][q],.85,.05),\n        (rings[\"knight\"][q],.45,.04),\n        (rings[\"axial3\"][q],.20,0)):\n        for v in pts:\n            w[u(0,v),u(0,q)]+=own\n            w[u(1,v),u(0,q)]+=enemy\n\n    other_class=1-((r+c)%2)\n    own_unreached=2+other_class\n    enemy_unreached=4+other_class\n    for v in adj[q]:\n        w[u(enemy_unreached,v),u(1,q)]+=1\n        w[u(own_unreached,v),u(2,q)]+=1\n\n    b[u(3,q)]=2-len(adj[q])\n    for v in adj[q]:\n        w[u(1,v),u(3,q)]+=1\n        w[u(own_unreached,v),u(3,q)]+=1\n        w[u(enemy_unreached,v),u(3,q)]-=1\n\n    b[u(4,q)]=1-len(adj[q])\n    for v in adj[q]: w[u(0,v),u(4,q)]+=1\n    for v in rings[\"diag\"][q]:\n        w[u(1,v),u(4,q)]-=1 if edge==0 else .5\n\n    b[u(5,q)]=-1.30\n    for pts,weight in (\n        (adj[q],1.0),(rings[\"diag\"][q],.65),\n        (rings[\"axial2\"][q],.30),(rings[\"knight\"][q],.15)):\n        for v in pts:\n            w[u(0,v),u(5,q)]+=weight\n            w[u(1,v),u(5,q)]-=.55*weight\n\nw=p[\"L6.W\"]\nfor q in range(81):\n    for ch in range(6): w[u(ch,q),u(ch,q)]=1\n    w[u(3,q),u(2,q)]-=2\n    w[u(4,q),u(2,q)]-=2\n\np[\"out.W\"][:]=0\np[\"out.b\"][:]=0\nscale=3.6\nfor q in range(81):\n    for ch,coef in enumerate((1,3.2,2.4,-4.5,-8,-2)):\n        p[\"out.W\"][u(ch,q),q]=scale*coef\n    p[\"out.b\"][q]=-32*scale\np[\"out.b\"][PASS]=-2.7*scale\nfor n in NAMES: save(n,p[n])\nprint(\"Installed checkerboard-liberty propagation and revised shape circuit.\")\n```\n"}}
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