{"abstract":"Repeated members are allowed within a triple.","category":"Combinatorics","checks":4,"contract":"Nonnegative integer counts. Permutation and combination counts are zero when a requested selection exceeds the available objects. Shape sizes satisfy the preconditions stated below. Ordered distinct triples. Exact operational definition: n*(n-1)*(n-2)","contract_signature":"n","evaluation_group":"model-0c80b667aead2343","failed_approach":"Ignoring order collapses six distinct triples into one.","family":"xn-ordered-distinct-triples","id":"FA-5746","implementations":{"attempt":{"sha256":"c94602741d6b04c162fb0844a47d1153824f55c28293252c4b16ed5b0fb10f6c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n):\n    return math.comb(n,3)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 0)\ncheck('fixture 2: (2,)', solve(*(2,)), 0)\ncheck('fixture 3: (3,)', solve(*(3,)), 6)\ncheck('fixture 4: (5,)', solve(*(5,)), 60)\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":"170c439cbd85f4c0a6449f430802a3a006eef28b491ec7d3fc104c21c5d3589a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n):\n    return n**3\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 0)\ncheck('fixture 2: (2,)', solve(*(2,)), 0)\ncheck('fixture 3: (3,)', solve(*(3,)), 6)\ncheck('fixture 4: (5,)', solve(*(5,)), 60)\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":" 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":"xn-ordered-distinct-triples","generated_at":"2026-09-29T14:37:53.182099+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Combinatorics results depend on the stated convention.","root_cause":"Repeated members are allowed within a triple.","sha256":"7e8205f446850775e27e802e7397f2f402eaaa816ebe25cc11906355e47b2cc2","title":"Ordered distinct triples · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":53.464,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":0,"check":"fixture 2: (2,)","expected":0,"passed":true},{"actual":1,"check":"fixture 3: (3,)","expected":6,"passed":false},{"actual":10,"check":"fixture 4: (5,)","expected":60,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (2,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 3: (3,)\", \"actual\": 1, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 4: (5,)\", \"actual\": 10, \"expected\": 60, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":51.035,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":0,"passed":true},{"actual":8,"check":"fixture 2: (2,)","expected":0,"passed":false},{"actual":27,"check":"fixture 3: (3,)","expected":6,"passed":false},{"actual":125,"check":"fixture 4: (5,)","expected":60,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (2,)\", \"actual\": 8, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: (3,)\", \"actual\": 27, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 4: (5,)\", \"actual\": 125, \"expected\": 60, \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}