{"abstract":"Parallel arcs enclosing a face are merged and the face disappears.","category":"GIS polygon topology","checks":8,"contract":"Input [nodes, arcs] for a planar, fully noded arc-node graph. arcs are [arc_id, from, to]; the same arc_id may be listed more than once (once per adjacent polygon) and counts once, while distinct ids between the same nodes are distinct parallel arcs. A loop arc (from == to) is an arc. Nodes listed in nodes but used by no arc are isolated nodes. Return [V, E, C, F] with V nodes, E distinct arcs, C connected components and F = E - V + C bounded faces.","evaluation_group":"w2-gis-polygon-topology-arc-node-face-count","failed_approach":"Giving every listed arc a fresh key counts arcs listed by both neighbouring polygons twice.","family":"w2-gis-polygon-topology-arc-node-face-count-arc-identity","id":"FA-70726","implementations":{"attempt":{"sha256":"6bb182af6f1a5cbbceac74111c0ba1396030d5c7dddd9cefd532ac1b05a14a54","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    nodes, arcs = x\n    uniq = {}\n    for aid, u, v in arcs:\n        uniq[len(uniq)] = (u, v)\n    parent = {n: n for n in nodes}\n    for u, v in uniq.values():\n        parent.setdefault(u, u)\n        parent.setdefault(v, v)\n    def find(a):\n        while parent[a] != a:\n            a = parent[a]\n        return a\n    for u, v in uniq.values():\n        ru, rv = find(u), find(v)\n        if ru != rv:\n            parent[ru] = rv\n    V = len(parent)\n    E = len(uniq)\n    C = len({find(n) for n in parent})\n    return [V, E, C, E - V + C]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1]]], [4, 4, 1, 1]), ('control #1', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [14, 1, 3]]], [4, 5, 1, 2]), ('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #3', [[1, 2], [[20, 1, 2], [21, 1, 2]]], [2, 2, 1, 1]), ('regression #4', [[1, 2], [[20, 1, 2], [21, 2, 1], [22, 1, 2]]], [2, 3, 1, 2]), ('regression #5', [[1, 2, 3, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [4, 3, 2, 1]), ('regression #6', [[1, 2, 3, 8, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [5, 3, 3, 1]), ('regression #7', [[5], [[30, 5, 5]]], [1, 1, 1, 1])], [('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #4', [[1, 2], [[20, 1, 2], [21, 2, 1], [22, 1, 2]]], [2, 3, 1, 2]), ('regression #5', [[1, 2, 3, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [4, 3, 2, 1]), ('regression #6', [[1, 2, 3, 8, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [5, 3, 3, 1]), ('regression #7', [[5], [[30, 5, 5]]], [1, 1, 1, 1]), ('regression #8', [[5, 6], [[30, 5, 5], [31, 5, 6], [32, 6, 6]]], [2, 3, 1, 2]), ('regression #9', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4]]], [6, 6, 2, 2]), ('regression #10', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4], [7, 3, 4]]], [6, 7, 1, 2])], [('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #7', [[5], [[30, 5, 5]]], [1, 1, 1, 1]), ('regression #8', [[5, 6], [[30, 5, 5], [31, 5, 6], [32, 6, 6]]], [2, 3, 1, 2]), ('regression #9', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4]]], [6, 6, 2, 2]), ('regression #10', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4], [7, 3, 4]]], [6, 7, 1, 2]), ('boundary #11', [[1], []], [1, 0, 1, 0]), ('boundary #12', [[], []], [0, 0, 0, 0]), ('regression #14', [[1, 2, 3, 4], [[1, 1, 2], [2, 3, 4], [3, 2, 1], [4, 4, 3]]], [4, 4, 2, 2])], [('control #0', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1]]], [4, 4, 1, 1]), ('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #3', [[1, 2], [[20, 1, 2], [21, 1, 2]]], [2, 2, 1, 1]), ('boundary #11', [[1], []], [1, 0, 1, 0]), ('boundary #12', [[], []], [0, 0, 0, 0]), ('control #13', [[1, 2, 3], [[1, 1, 2], [2, 2, 3]]], [3, 2, 1, 0]), ('regression #14', [[1, 2, 3, 4], [[1, 1, 2], [2, 3, 4], [3, 2, 1], [4, 4, 3]]], [4, 4, 2, 2]), ('control #15', [[1, 2, 3, 4, 5], [[1, 1, 2], [2, 2, 3], [3, 3, 4], [4, 4, 5], [5, 5, 1], [6, 1, 3], [7, 3, 5]]], [5, 7, 1, 3])], [('control #0', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1]]], [4, 4, 1, 1]), ('control #1', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [14, 1, 3]]], [4, 5, 1, 2]), ('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #3', [[1, 2], [[20, 1, 2], [21, 1, 2]]], [2, 2, 1, 1]), ('regression #4', [[1, 2], [[20, 1, 2], [21, 2, 1], [22, 1, 2]]], [2, 3, 1, 2]), ('regression #5', [[1, 2, 3, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [4, 3, 2, 1]), ('regression #14', [[1, 2, 3, 4], [[1, 1, 2], [2, 3, 4], [3, 2, 1], [4, 4, 3]]], [4, 4, 2, 2]), ('control #15', [[1, 2, 3, 4, 5], [[1, 1, 2], [2, 2, 3], [3, 3, 4], [4, 4, 5], [5, 5, 1], [6, 1, 3], [7, 3, 5]]], [5, 7, 1, 3])]]\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":"6ae5a45da346760c747843b603a58fb0b363c0d7196c776cc8bbb9479549f579","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    nodes, arcs = x\n    uniq = {}\n    for aid, u, v in arcs:\n        uniq[(min(u, v), max(u, v))] = (u, v)\n    parent = {n: n for n in nodes}\n    for u, v in uniq.values():\n        parent.setdefault(u, u)\n        parent.setdefault(v, v)\n    def find(a):\n        while parent[a] != a:\n            a = parent[a]\n        return a\n    for u, v in uniq.values():\n        ru, rv = find(u), find(v)\n        if ru != rv:\n            parent[ru] = rv\n    V = len(parent)\n    E = len(uniq)\n    C = len({find(n) for n in parent})\n    return [V, E, C, E - V + C]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1]]], [4, 4, 1, 1]), ('control #1', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [14, 1, 3]]], [4, 5, 1, 2]), ('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #3', [[1, 2], [[20, 1, 2], [21, 1, 2]]], [2, 2, 1, 1]), ('regression #4', [[1, 2], [[20, 1, 2], [21, 2, 1], [22, 1, 2]]], [2, 3, 1, 2]), ('regression #5', [[1, 2, 3, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [4, 3, 2, 1]), ('regression #6', [[1, 2, 3, 8, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [5, 3, 3, 1]), ('regression #7', [[5], [[30, 5, 5]]], [1, 1, 1, 1])], [('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #4', [[1, 2], [[20, 1, 2], [21, 2, 1], [22, 1, 2]]], [2, 3, 1, 2]), ('regression #5', [[1, 2, 3, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [4, 3, 2, 1]), ('regression #6', [[1, 2, 3, 8, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [5, 3, 3, 1]), ('regression #7', [[5], [[30, 5, 5]]], [1, 1, 1, 1]), ('regression #8', [[5, 6], [[30, 5, 5], [31, 5, 6], [32, 6, 6]]], [2, 3, 1, 2]), ('regression #9', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4]]], [6, 6, 2, 2]), ('regression #10', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4], [7, 3, 4]]], [6, 7, 1, 2])], [('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #7', [[5], [[30, 5, 5]]], [1, 1, 1, 1]), ('regression #8', [[5, 6], [[30, 5, 5], [31, 5, 6], [32, 6, 6]]], [2, 3, 1, 2]), ('regression #9', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4]]], [6, 6, 2, 2]), ('regression #10', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4], [7, 3, 4]]], [6, 7, 1, 2]), ('boundary #11', [[1], []], [1, 0, 1, 0]), ('boundary #12', [[], []], [0, 0, 0, 0]), ('regression #14', [[1, 2, 3, 4], [[1, 1, 2], [2, 3, 4], [3, 2, 1], [4, 4, 3]]], [4, 4, 2, 2])], [('control #0', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1]]], [4, 4, 1, 1]), ('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #3', [[1, 2], [[20, 1, 2], [21, 1, 2]]], [2, 2, 1, 1]), ('boundary #11', [[1], []], [1, 0, 1, 0]), ('boundary #12', [[], []], [0, 0, 0, 0]), ('control #13', [[1, 2, 3], [[1, 1, 2], [2, 2, 3]]], [3, 2, 1, 0]), ('regression #14', [[1, 2, 3, 4], [[1, 1, 2], [2, 3, 4], [3, 2, 1], [4, 4, 3]]], [4, 4, 2, 2]), ('control #15', [[1, 2, 3, 4, 5], [[1, 1, 2], [2, 2, 3], [3, 3, 4], [4, 4, 5], [5, 5, 1], [6, 1, 3], [7, 3, 5]]], [5, 7, 1, 3])], [('control #0', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1]]], [4, 4, 1, 1]), ('control #1', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [14, 1, 3]]], [4, 5, 1, 2]), ('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #3', [[1, 2], [[20, 1, 2], [21, 1, 2]]], [2, 2, 1, 1]), ('regression #4', [[1, 2], [[20, 1, 2], [21, 2, 1], [22, 1, 2]]], [2, 3, 1, 2]), ('regression #5', [[1, 2, 3, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [4, 3, 2, 1]), ('regression #14', [[1, 2, 3, 4], [[1, 1, 2], [2, 3, 4], [3, 2, 1], [4, 4, 3]]], [4, 4, 2, 2]), ('control #15', [[1, 2, 3, 4, 5], [[1, 1, 2], [2, 2, 3], [3, 3, 4], [4, 4, 5], [5, 5, 1], [6, 1, 3], [7, 3, 5]]], [5, 7, 1, 3])]]\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":"c02724a14739b13242a902f5445c61890fb719ee26aa2a2993f982c46eac7b62","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    nodes, arcs = x\n    uniq = {}\n    for aid, u, v in arcs:\n        uniq[aid] = (u, v)\n    parent = {n: n for n in nodes}\n    for u, v in uniq.values():\n        parent.setdefault(u, u)\n        parent.setdefault(v, v)\n    def find(a):\n        while parent[a] != a:\n            a = parent[a]\n        return a\n    for u, v in uniq.values():\n        ru, rv = find(u), find(v)\n        if ru != rv:\n            parent[ru] = rv\n    V = len(parent)\n    E = len(uniq)\n    C = len({find(n) for n in parent})\n    return [V, E, C, E - V + C]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('control #0', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1]]], [4, 4, 1, 1]), ('control #1', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [14, 1, 3]]], [4, 5, 1, 2]), ('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #3', [[1, 2], [[20, 1, 2], [21, 1, 2]]], [2, 2, 1, 1]), ('regression #4', [[1, 2], [[20, 1, 2], [21, 2, 1], [22, 1, 2]]], [2, 3, 1, 2]), ('regression #5', [[1, 2, 3, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [4, 3, 2, 1]), ('regression #6', [[1, 2, 3, 8, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [5, 3, 3, 1]), ('regression #7', [[5], [[30, 5, 5]]], [1, 1, 1, 1])], [('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #4', [[1, 2], [[20, 1, 2], [21, 2, 1], [22, 1, 2]]], [2, 3, 1, 2]), ('regression #5', [[1, 2, 3, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [4, 3, 2, 1]), ('regression #6', [[1, 2, 3, 8, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [5, 3, 3, 1]), ('regression #7', [[5], [[30, 5, 5]]], [1, 1, 1, 1]), ('regression #8', [[5, 6], [[30, 5, 5], [31, 5, 6], [32, 6, 6]]], [2, 3, 1, 2]), ('regression #9', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4]]], [6, 6, 2, 2]), ('regression #10', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4], [7, 3, 4]]], [6, 7, 1, 2])], [('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #7', [[5], [[30, 5, 5]]], [1, 1, 1, 1]), ('regression #8', [[5, 6], [[30, 5, 5], [31, 5, 6], [32, 6, 6]]], [2, 3, 1, 2]), ('regression #9', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4]]], [6, 6, 2, 2]), ('regression #10', [[1, 2, 3, 4, 5, 6], [[1, 1, 2], [2, 2, 3], [3, 3, 1], [4, 4, 5], [5, 5, 6], [6, 6, 4], [7, 3, 4]]], [6, 7, 1, 2]), ('boundary #11', [[1], []], [1, 0, 1, 0]), ('boundary #12', [[], []], [0, 0, 0, 0]), ('regression #14', [[1, 2, 3, 4], [[1, 1, 2], [2, 3, 4], [3, 2, 1], [4, 4, 3]]], [4, 4, 2, 2])], [('control #0', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1]]], [4, 4, 1, 1]), ('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #3', [[1, 2], [[20, 1, 2], [21, 1, 2]]], [2, 2, 1, 1]), ('boundary #11', [[1], []], [1, 0, 1, 0]), ('boundary #12', [[], []], [0, 0, 0, 0]), ('control #13', [[1, 2, 3], [[1, 1, 2], [2, 2, 3]]], [3, 2, 1, 0]), ('regression #14', [[1, 2, 3, 4], [[1, 1, 2], [2, 3, 4], [3, 2, 1], [4, 4, 3]]], [4, 4, 2, 2]), ('control #15', [[1, 2, 3, 4, 5], [[1, 1, 2], [2, 2, 3], [3, 3, 4], [4, 4, 5], [5, 5, 1], [6, 1, 3], [7, 3, 5]]], [5, 7, 1, 3])], [('control #0', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1]]], [4, 4, 1, 1]), ('control #1', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [14, 1, 3]]], [4, 5, 1, 2]), ('regression #2', [[1, 2, 3, 4], [[10, 1, 2], [11, 2, 3], [12, 3, 4], [13, 4, 1], [10, 1, 2], [12, 3, 4]]], [4, 4, 1, 1]), ('regression #3', [[1, 2], [[20, 1, 2], [21, 1, 2]]], [2, 2, 1, 1]), ('regression #4', [[1, 2], [[20, 1, 2], [21, 2, 1], [22, 1, 2]]], [2, 3, 1, 2]), ('regression #5', [[1, 2, 3, 9], [[10, 1, 2], [11, 2, 3], [12, 3, 1]]], [4, 3, 2, 1]), ('regression #14', [[1, 2, 3, 4], [[1, 1, 2], [2, 3, 4], [3, 2, 1], [4, 4, 3]]], [4, 4, 2, 2]), ('control #15', [[1, 2, 3, 4, 5], [[1, 1, 2], [2, 2, 3], [3, 3, 4], [4, 4, 5], [5, 5, 1], [6, 1, 3], [7, 3, 5]]], [5, 7, 1, 3])]]\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":"Stipulated deterministic toy contract on a bounded input domain; results are rounded as stated and no conformance with any published standard or library is claimed. 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-gis-polygon-topology-arc-node-face-count-arc-identity","generated_at":"2026-09-29T14:48:23.323487+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Topology builders check face counts against Euler characteristic to detect missing or doubled arcs after edits.","repair":"At the arc identity step restore `uniq[aid] = (u, v)`, leaving the rest of the model unchanged.","root_cause":"Arcs are de-duplicated by their node pair instead of by arc id, merging distinct parallel arcs.","sha256":"a00033793f9d6280a6ec49aca65eea49cb829b1516eb239ec0dffe862c9de507","title":"Bounded face count of an arc-node topology: arc identity · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.148,"exit_code":1,"observations":[{"actual":[4,4,1,1],"check":"control #0","expected":[4,4,1,1],"passed":true},{"actual":[4,5,1,2],"check":"control #1","expected":[4,5,1,2],"passed":true},{"actual":[4,6,1,3],"check":"regression #2","expected":[4,4,1,1],"passed":false},{"actual":[2,2,1,1],"check":"regression #3","expected":[2,2,1,1],"passed":true},{"actual":[2,3,1,2],"check":"regression #4","expected":[2,3,1,2],"passed":true},{"actual":[4,3,2,1],"check":"regression #5","expected":[4,3,2,1],"passed":true},{"actual":[5,3,3,1],"check":"regression #6","expected":[5,3,3,1],"passed":true},{"actual":[1,1,1,1],"check":"regression #7","expected":[1,1,1,1],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"control #0\", \"actual\": [4, 4, 1, 1], \"expected\": [4, 4, 1, 1], \"passed\": true}, {\"check\": \"control 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