{"abstract":"Net displacement cancels intermediate variation.","category":"Discrete calculus","checks":4,"contract":"Integer sample values and compatible sample-array lengths. Rational results are reduced Fraction strings; spacing is positive unless explicitly stated otherwise. Discrete total variation. Exact operational definition: sum(abs(b-a) for a,b in zip(values,values[1:]))","contract_signature":"values","evaluation_group":"model-606c20b68109277e","failed_approach":"Squared differences implement a different roughness measure.","family":"xn-discrete-total-variation","id":"FA-6426","implementations":{"attempt":{"sha256":"064f1ab7b45c8598ffef3cf4c212ef27bac1d1c3856e674a6a3e1d05860b9663","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(values):\n    return sum((b-a)**2 for a,b in zip(values,values[1:]))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 2, 0],)', solve(*([0, 2, 0],)), 4)\ncheck('fixture 2: ([1, 4, 9],)', solve(*([1, 4, 9],)), 8)\ncheck('fixture 3: ([5],)', solve(*([5],)), 0)\ncheck('fixture 4: ([],)', solve(*([],)), 0)\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":"546e51c26adf1ab18403dd384b3c49aeebb13027efa2cb13e196751257e1137a","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(values):\n    return abs(values[-1]-values[0]) if values else 0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 2, 0],)', solve(*([0, 2, 0],)), 4)\ncheck('fixture 2: ([1, 4, 9],)', solve(*([1, 4, 9],)), 8)\ncheck('fixture 3: ([5],)', solve(*([5],)), 0)\ncheck('fixture 4: ([],)', solve(*([],)), 0)\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-discrete-total-variation","generated_at":"2026-09-29T14:38:01.616540+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. Discrete calculus results depend on the stated convention.","root_cause":"Net displacement cancels intermediate variation.","sha256":"82d984812b0ca5af3aedf23f3bf13e793e803e407f14e038c0af012eb034e76d","title":"Discrete total variation · 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":53.789,"exit_code":1,"observations":[{"actual":8,"check":"fixture 1: ([0, 2, 0],)","expected":4,"passed":false},{"actual":34,"check":"fixture 2: ([1, 4, 9],)","expected":8,"passed":false},{"actual":0,"check":"fixture 3: ([5],)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 2, 0],)\", \"actual\": 8, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 2: ([1, 4, 9],)\", \"actual\": 34, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 3: ([5],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":53.384,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: ([0, 2, 0],)","expected":4,"passed":false},{"actual":8,"check":"fixture 2: ([1, 4, 9],)","expected":8,"passed":true},{"actual":0,"check":"fixture 3: ([5],)","expected":0,"passed":true},{"actual":0,"check":"fixture 4: ([],)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 2, 0],)\", \"actual\": 0, \"expected\": 4, \"passed\": false}, {\"check\": \"fixture 2: ([1, 4, 9],)\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"fixture 3: ([5],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"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."}}