{"abstract":"Collapsing any edge of a tetrahedron is accepted and produces a degenerate surface.","category":"Mesh topology invariants","checks":7,"contract":"Input [faces, a, b] for a triangle mesh. Collapsing edge (a,b) is checked in order: missing edge -> [false,\"no-edge\"]; common neighbours of a and b must equal the opposite vertices of the triangles on the edge -> else [false,\"link\"]; if a and b are both boundary vertices the edge itself must be a boundary edge -> else [false,\"boundary\"]; a closed mesh with 4 or fewer vertices -> [false,\"minimal\"]; otherwise [true,\"ok\"].","evaluation_group":"w2-mesh_topology_invariants-edge-collapse-link","failed_approach":"Dropping the closed-mesh condition refuses collapses on small open patches.","family":"w2-mesh_topology_invariants-edge-collapse-link-minimal-closed-mesh","id":"FA-88496","implementations":{"attempt":{"sha256":"75bdc3255117debd62a176d9c206bdc7bcd615badea39d86e3b1893ee0de373f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    faces,a,b=x\n    adj={}\n    opp=[]\n    ecount={}\n    for f in faces:\n        for i in range(3):\n            u,v=f[i],f[(i+1)%3]\n            adj.setdefault(u,set()).add(v)\n            adj.setdefault(v,set()).add(u)\n            k=(min(u,v),max(u,v))\n            ecount[k]=ecount.get(k,0)+1\n        if a in f and b in f:\n            opp.append([w for w in f if w!=a and w!=b][0])\n    k=(min(a,b),max(a,b))\n    if k not in ecount: return [False,'no-edge']\n    if (adj[a]&adj[b])!=set(opp): return [False,'link']\n    bnd=set()\n    for (u,v),c in ecount.items():\n        if c==1: bnd.update((u,v))\n    if a in bnd and b in bnd and ecount[k]!=1: return [False,'boundary']\n    if len(adj)<=4: return [False,'minimal']\n    return [True,'ok']\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['disk spoke', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 0, 1]], [True, 'ok']], ['disk rim', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 1, 2]], [True, 'ok']], ['fan interior edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 0, 2]], [False, 'boundary']], ['fan missing edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 1, 3]], [False, 'no-edge']], ['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['octahedron edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 1], [5, 2, 1], [5, 3, 2], [5, 4, 3], [5, 1, 4]], 0, 1]], [True, 'ok']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']]], [['fan missing edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 1, 3]], [False, 'no-edge']], ['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['octahedron edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 1], [5, 2, 1], [5, 3, 2], [5, 4, 3], [5, 1, 4]], 0, 1]], [True, 'ok']], ['octahedron reversed', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 1], [5, 2, 1], [5, 3, 2], [5, 4, 3], [5, 1, 4]], 5, 2]], [True, 'ok']], ['open tetra cap', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1]], 1, 2]], [False, 'link']], ['two triangles shared edge', [[[[0, 1, 2], [2, 1, 3]], 1, 2]], [False, 'boundary']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']]], [['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['open tetra cap', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1]], 1, 2]], [False, 'link']], ['two triangles shared edge', [[[[0, 1, 2], [2, 1, 3]], 1, 2]], [False, 'boundary']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']], ['torus edge', [[[[0, 3, 4], [0, 4, 1], [1, 4, 5], [1, 5, 2], [2, 5, 3], [2, 3, 0], [3, 6, 7], [3, 7, 4], [4, 7, 8], [4, 8, 5], [5, 8, 6], [5, 6, 3], [6, 0, 1], [6, 1, 7], [7, 1, 2], [7, 2, 8], [8, 2, 0], [8, 0, 6]], 0, 1]], [False, 'link']], ['cylinder rung', [[[[0, 1, 5], [0, 5, 4], [1, 2, 6], [1, 6, 5], [2, 3, 7], [2, 7, 6], [3, 0, 4], [3, 4, 7]], 0, 5]], [False, 'boundary']], ['strip over-constrained', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1], [1, 3, 4]], 1, 3]], [False, 'link']]], [['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']], ['cylinder rung', [[[[0, 1, 5], [0, 5, 4], [1, 2, 6], [1, 6, 5], [2, 3, 7], [2, 7, 6], [3, 0, 4], [3, 4, 7]], 0, 5]], [False, 'boundary']], ['strip over-constrained', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1], [1, 3, 4]], 1, 3]], [False, 'link']], ['grid diagonal', [[[[0, 1, 4], [0, 4, 3], [1, 2, 5], [1, 5, 4], [3, 4, 7], [3, 7, 6], [4, 5, 8], [4, 8, 7]], 0, 4]], [True, 'ok']], ['grid interior spoke', [[[[0, 1, 4], [0, 4, 3], [1, 2, 5], [1, 5, 4], [3, 4, 7], [3, 7, 6], [4, 5, 8], [4, 8, 7]], 4, 5]], [True, 'ok']], ['rotated face order', [[[[2, 0, 1], [3, 0, 2]], 0, 2]], [False, 'boundary']]], [['disk spoke', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 0, 1]], [True, 'ok']], ['disk rim', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 1, 2]], [True, 'ok']], ['fan interior edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 0, 2]], [False, 'boundary']], ['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']], ['grid interior spoke', [[[[0, 1, 4], [0, 4, 3], [1, 2, 5], [1, 5, 4], [3, 4, 7], [3, 7, 6], [4, 5, 8], [4, 8, 7]], 4, 5]], [True, 'ok']], ['rotated face order', [[[[2, 0, 1], [3, 0, 2]], 0, 2]], [False, 'boundary']]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"7eeeb864b1d2a25c8e8a4ff911b064049a17199e5aca5db230ebef1826ca7ec0","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    faces,a,b=x\n    adj={}\n    opp=[]\n    ecount={}\n    for f in faces:\n        for i in range(3):\n            u,v=f[i],f[(i+1)%3]\n            adj.setdefault(u,set()).add(v)\n            adj.setdefault(v,set()).add(u)\n            k=(min(u,v),max(u,v))\n            ecount[k]=ecount.get(k,0)+1\n        if a in f and b in f:\n            opp.append([w for w in f if w!=a and w!=b][0])\n    k=(min(a,b),max(a,b))\n    if k not in ecount: return [False,'no-edge']\n    if (adj[a]&adj[b])!=set(opp): return [False,'link']\n    bnd=set()\n    for (u,v),c in ecount.items():\n        if c==1: bnd.update((u,v))\n    if a in bnd and b in bnd and ecount[k]!=1: return [False,'boundary']\n    if not bnd and len(adj)<4: return [False,'minimal']\n    return [True,'ok']\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['disk spoke', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 0, 1]], [True, 'ok']], ['disk rim', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 1, 2]], [True, 'ok']], ['fan interior edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 0, 2]], [False, 'boundary']], ['fan missing edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 1, 3]], [False, 'no-edge']], ['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['octahedron edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 1], [5, 2, 1], [5, 3, 2], [5, 4, 3], [5, 1, 4]], 0, 1]], [True, 'ok']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']]], [['fan missing edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 1, 3]], [False, 'no-edge']], ['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['octahedron edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 1], [5, 2, 1], [5, 3, 2], [5, 4, 3], [5, 1, 4]], 0, 1]], [True, 'ok']], ['octahedron reversed', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 1], [5, 2, 1], [5, 3, 2], [5, 4, 3], [5, 1, 4]], 5, 2]], [True, 'ok']], ['open tetra cap', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1]], 1, 2]], [False, 'link']], ['two triangles shared edge', [[[[0, 1, 2], [2, 1, 3]], 1, 2]], [False, 'boundary']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']]], [['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['open tetra cap', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1]], 1, 2]], [False, 'link']], ['two triangles shared edge', [[[[0, 1, 2], [2, 1, 3]], 1, 2]], [False, 'boundary']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']], ['torus edge', [[[[0, 3, 4], [0, 4, 1], [1, 4, 5], [1, 5, 2], [2, 5, 3], [2, 3, 0], [3, 6, 7], [3, 7, 4], [4, 7, 8], [4, 8, 5], [5, 8, 6], [5, 6, 3], [6, 0, 1], [6, 1, 7], [7, 1, 2], [7, 2, 8], [8, 2, 0], [8, 0, 6]], 0, 1]], [False, 'link']], ['cylinder rung', [[[[0, 1, 5], [0, 5, 4], [1, 2, 6], [1, 6, 5], [2, 3, 7], [2, 7, 6], [3, 0, 4], [3, 4, 7]], 0, 5]], [False, 'boundary']], ['strip over-constrained', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1], [1, 3, 4]], 1, 3]], [False, 'link']]], [['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']], ['cylinder rung', [[[[0, 1, 5], [0, 5, 4], [1, 2, 6], [1, 6, 5], [2, 3, 7], [2, 7, 6], [3, 0, 4], [3, 4, 7]], 0, 5]], [False, 'boundary']], ['strip over-constrained', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1], [1, 3, 4]], 1, 3]], [False, 'link']], ['grid diagonal', [[[[0, 1, 4], [0, 4, 3], [1, 2, 5], [1, 5, 4], [3, 4, 7], [3, 7, 6], [4, 5, 8], [4, 8, 7]], 0, 4]], [True, 'ok']], ['grid interior spoke', [[[[0, 1, 4], [0, 4, 3], [1, 2, 5], [1, 5, 4], [3, 4, 7], [3, 7, 6], [4, 5, 8], [4, 8, 7]], 4, 5]], [True, 'ok']], ['rotated face order', [[[[2, 0, 1], [3, 0, 2]], 0, 2]], [False, 'boundary']]], [['disk spoke', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 0, 1]], [True, 'ok']], ['disk rim', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 1, 2]], [True, 'ok']], ['fan interior edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 0, 2]], [False, 'boundary']], ['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']], ['grid interior spoke', [[[[0, 1, 4], [0, 4, 3], [1, 2, 5], [1, 5, 4], [3, 4, 7], [3, 7, 6], [4, 5, 8], [4, 8, 7]], 4, 5]], [True, 'ok']], ['rotated face order', [[[[2, 0, 1], [3, 0, 2]], 0, 2]], [False, 'boundary']]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"335f06d621537f9d1315ea6995109e8fa1afb795234086ef6a1d403ea12fa4ca","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    faces,a,b=x\n    adj={}\n    opp=[]\n    ecount={}\n    for f in faces:\n        for i in range(3):\n            u,v=f[i],f[(i+1)%3]\n            adj.setdefault(u,set()).add(v)\n            adj.setdefault(v,set()).add(u)\n            k=(min(u,v),max(u,v))\n            ecount[k]=ecount.get(k,0)+1\n        if a in f and b in f:\n            opp.append([w for w in f if w!=a and w!=b][0])\n    k=(min(a,b),max(a,b))\n    if k not in ecount: return [False,'no-edge']\n    if (adj[a]&adj[b])!=set(opp): return [False,'link']\n    bnd=set()\n    for (u,v),c in ecount.items():\n        if c==1: bnd.update((u,v))\n    if a in bnd and b in bnd and ecount[k]!=1: return [False,'boundary']\n    if not bnd and len(adj)<=4: return [False,'minimal']\n    return [True,'ok']\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['disk spoke', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 0, 1]], [True, 'ok']], ['disk rim', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 1, 2]], [True, 'ok']], ['fan interior edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 0, 2]], [False, 'boundary']], ['fan missing edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 1, 3]], [False, 'no-edge']], ['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['octahedron edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 1], [5, 2, 1], [5, 3, 2], [5, 4, 3], [5, 1, 4]], 0, 1]], [True, 'ok']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']]], [['fan missing edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 1, 3]], [False, 'no-edge']], ['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['octahedron edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 1], [5, 2, 1], [5, 3, 2], [5, 4, 3], [5, 1, 4]], 0, 1]], [True, 'ok']], ['octahedron reversed', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 1], [5, 2, 1], [5, 3, 2], [5, 4, 3], [5, 1, 4]], 5, 2]], [True, 'ok']], ['open tetra cap', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1]], 1, 2]], [False, 'link']], ['two triangles shared edge', [[[[0, 1, 2], [2, 1, 3]], 1, 2]], [False, 'boundary']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']]], [['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['open tetra cap', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1]], 1, 2]], [False, 'link']], ['two triangles shared edge', [[[[0, 1, 2], [2, 1, 3]], 1, 2]], [False, 'boundary']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']], ['torus edge', [[[[0, 3, 4], [0, 4, 1], [1, 4, 5], [1, 5, 2], [2, 5, 3], [2, 3, 0], [3, 6, 7], [3, 7, 4], [4, 7, 8], [4, 8, 5], [5, 8, 6], [5, 6, 3], [6, 0, 1], [6, 1, 7], [7, 1, 2], [7, 2, 8], [8, 2, 0], [8, 0, 6]], 0, 1]], [False, 'link']], ['cylinder rung', [[[[0, 1, 5], [0, 5, 4], [1, 2, 6], [1, 6, 5], [2, 3, 7], [2, 7, 6], [3, 0, 4], [3, 4, 7]], 0, 5]], [False, 'boundary']], ['strip over-constrained', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1], [1, 3, 4]], 1, 3]], [False, 'link']]], [['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']], ['cylinder rung', [[[[0, 1, 5], [0, 5, 4], [1, 2, 6], [1, 6, 5], [2, 3, 7], [2, 7, 6], [3, 0, 4], [3, 4, 7]], 0, 5]], [False, 'boundary']], ['strip over-constrained', [[[[0, 1, 2], [0, 2, 3], [0, 3, 1], [1, 3, 4]], 1, 3]], [False, 'link']], ['grid diagonal', [[[[0, 1, 4], [0, 4, 3], [1, 2, 5], [1, 5, 4], [3, 4, 7], [3, 7, 6], [4, 5, 8], [4, 8, 7]], 0, 4]], [True, 'ok']], ['grid interior spoke', [[[[0, 1, 4], [0, 4, 3], [1, 2, 5], [1, 5, 4], [3, 4, 7], [3, 7, 6], [4, 5, 8], [4, 8, 7]], 4, 5]], [True, 'ok']], ['rotated face order', [[[[2, 0, 1], [3, 0, 2]], 0, 2]], [False, 'boundary']]], [['disk spoke', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 0, 1]], [True, 'ok']], ['disk rim', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4], [0, 4, 5], [0, 5, 1]], 1, 2]], [True, 'ok']], ['fan interior edge', [[[[0, 1, 2], [0, 2, 3], [0, 3, 4]], 0, 2]], [False, 'boundary']], ['tetrahedron edge', [[[[0, 2, 1], [0, 1, 3], [1, 2, 3], [0, 3, 2]], 0, 1]], [False, 'minimal']], ['two triangles rim edge', [[[[0, 1, 2], [2, 1, 3]], 0, 1]], [True, 'ok']], ['grid interior spoke', [[[[0, 1, 4], [0, 4, 3], [1, 2, 5], [1, 5, 4], [3, 4, 7], [3, 7, 6], [4, 5, 8], [4, 8, 7]], 4, 5]], [True, 'ok']], ['rotated face order', [[[[2, 0, 1], [3, 0, 2]], 0, 2]], [False, 'boundary']]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Pure combinatorial teaching model over integer face lists with a stipulated contract; no geometry kernel or file format is implied. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-mesh_topology_invariants-edge-collapse-link-minimal-closed-mesh","generated_at":"2026-09-29T14:51:08.784251+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Mesh processing pipelines (remeshing, export, simulation, printing) trust these topological counts and adjacency answers; a wrong invariant silently accepts broken meshes or rejects valid ones.","repair":"Refuse collapses on closed meshes with 4 or fewer vertices.","root_cause":"The minimal-mesh test uses < 4 vertices instead of <= 4.","sha256":"dfe0be94d281fc04ac418d4e7a44d628045a306eccb7ecaebd4ab43cac052539","title":"Tetrahedron edge collapse is allowed · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.965,"exit_code":1,"observations":[{"actual":[true,"ok"],"check":"disk spoke","expected":[true,"ok"],"passed":true},{"actual":[true,"ok"],"check":"disk rim","expected":[true,"ok"],"passed":true},{"actual":[false,"boundary"],"check":"fan interior edge","expected":[false,"boundary"],"passed":true},{"actual":[false,"no-edge"],"check":"fan missing edge","expected":[false,"no-edge"],"passed":true},{"actual":[false,"minimal"],"check":"tetrahedron edge","expected":[false,"minimal"],"passed":true},{"actual":[true,"ok"],"check":"octahedron edge","expected":[true,"ok"],"passed":true},{"actual":[false,"minimal"],"check":"two triangles rim edge","expected":[true,"ok"],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"disk spoke\", \"actual\": [true, \"ok\"], \"expected\": [true, \"ok\"], \"passed\": true}, {\"check\": \"disk rim\", \"actual\": [true, \"ok\"], \"expected\": [true, \"ok\"], \"passed\": true}, {\"check\": \"fan interior edge\", \"actual\": [false, \"boundary\"], \"expected\": [false, \"boundary\"], \"passed\": true}, {\"check\": \"fan missing edge\", \"actual\": [false, \"no-edge\"], \"expected\": [false, \"no-edge\"], \"passed\": true}, {\"check\": \"tetrahedron edge\", \"actual\": [false, \"minimal\"], \"expected\": [false, \"minimal\"], \"passed\": true}, {\"check\": \"octahedron edge\", \"actual\": [true, \"ok\"], \"expected\": [true, \"ok\"], \"passed\": true}, {\"check\": \"two triangles rim edge\", \"actual\": [false, \"minimal\"], \"expected\": [true, \"ok\"], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.601,"exit_code":1,"observations":[{"actual":[true,"ok"],"check":"disk spoke","expected":[true,"ok"],"passed":true},{"actual":[true,"ok"],"check":"disk rim","expected":[true,"ok"],"passed":true},{"actual":[false,"boundary"],"check":"fan 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