{"abstract":"The sample spacing is ignored.","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. x and y lengths match and neighboring x values are distinct; return each segment slope. Exact operational definition: [str(Fraction(v-u,b-a)) for a,b,u,v in zip(x,x[1:],y,y[1:])]","evaluation_group":"model-5fd349083319a020","failed_approach":"The reciprocal slope swaps dependent and independent axes.","family":"xn-piecewise-linear-slope-sequence","id":"FA-6431","implementations":{"attempt":{"sha256":"3043004b1134a37a6bf805c744e5b08e01435b3cf04b2d5a46d17dd664e87682","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(x, y):\n    return [str(Fraction(b-a,v-u)) if v!=u else None for a,b,u,v in zip(x,x[1:],y,y[1:])]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 2, 3], [0, 4, 5])', solve(*([0, 2, 3], [0, 4, 5])), ['2', '1'])\ncheck('fixture 2: ([1, 3], [2, 2])', solve(*([1, 3], [2, 2])), ['0'])\ncheck('fixture 3: ([0, 2], [4, 0])', solve(*([0, 2], [4, 0])), ['-2'])\ncheck('fixture 4: ([1], [5])', solve(*([1], [5])), [])\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":"8da810491a1ce76420a7ca3a6178ace2d8b32cfa6e3c70cb8b4714db47263132","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(x, y):\n    return [str(v-u) for u,v in zip(y,y[1:])]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 2, 3], [0, 4, 5])', solve(*([0, 2, 3], [0, 4, 5])), ['2', '1'])\ncheck('fixture 2: ([1, 3], [2, 2])', solve(*([1, 3], [2, 2])), ['0'])\ncheck('fixture 3: ([0, 2], [4, 0])', solve(*([0, 2], [4, 0])), ['-2'])\ncheck('fixture 4: ([1], [5])', solve(*([1], [5])), [])\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":"c2cf8b7518492eab25d2093805b0bc83479fbd7f09c29fad153c8fb7b9428261","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(x, y):\n    return [str(Fraction(v-u,b-a)) for a,b,u,v in zip(x,x[1:],y,y[1:])]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 2, 3], [0, 4, 5])', solve(*([0, 2, 3], [0, 4, 5])), ['2', '1'])\ncheck('fixture 2: ([1, 3], [2, 2])', solve(*([1, 3], [2, 2])), ['0'])\ncheck('fixture 3: ([0, 2], [4, 0])', solve(*([0, 2], [4, 0])), ['-2'])\ncheck('fixture 4: ([1], [5])', solve(*([1], [5])), [])\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-piecewise-linear-slope-sequence","generated_at":"2026-09-29T14:38:01.672532+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.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return [str(Fraction(v-u,b-a)) for a,b,u,v in zip(x,x[1:],y,y[1:])]","root_cause":"The sample spacing is ignored.","sha256":"8367fa25b214cbe8cd1e3d5c503848d17101abe4e20f659c51c953d49d8acaf8","title":"Piecewise linear slope sequence · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":50.027,"exit_code":1,"observations":[{"actual":["1/2","1"],"check":"fixture 1: ([0, 2, 3], [0, 4, 5])","expected":["2","1"],"passed":false},{"actual":[null],"check":"fixture 2: ([1, 3], [2, 2])","expected":["0"],"passed":false},{"actual":["-1/2"],"check":"fixture 3: ([0, 2], [4, 0])","expected":["-2"],"passed":false},{"actual":[],"check":"fixture 4: ([1], [5])","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 2, 3], [0, 4, 5])\", \"actual\": [\"1/2\", \"1\"], \"expected\": [\"2\", \"1\"], \"passed\": false}, {\"check\": \"fixture 2: ([1, 3], [2, 2])\", \"actual\": [null], \"expected\": [\"0\"], \"passed\": false}, {\"check\": \"fixture 3: ([0, 2], [4, 0])\", \"actual\": [\"-1/2\"], \"expected\": [\"-2\"], \"passed\": false}, {\"check\": \"fixture 4: ([1], [5])\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":56.63,"exit_code":1,"observations":[{"actual":["4","1"],"check":"fixture 1: ([0, 2, 3], [0, 4, 5])","expected":["2","1"],"passed":false},{"actual":["0"],"check":"fixture 2: ([1, 3], [2, 2])","expected":["0"],"passed":true},{"actual":["-4"],"check":"fixture 3: ([0, 2], [4, 0])","expected":["-2"],"passed":false},{"actual":[],"check":"fixture 4: ([1], [5])","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 2, 3], [0, 4, 5])\", \"actual\": [\"4\", \"1\"], \"expected\": [\"2\", \"1\"], \"passed\": false}, {\"check\": \"fixture 2: ([1, 3], [2, 2])\", \"actual\": [\"0\"], \"expected\": [\"0\"], \"passed\": true}, {\"check\": \"fixture 3: ([0, 2], [4, 0])\", \"actual\": [\"-4\"], \"expected\": [\"-2\"], \"passed\": false}, {\"check\": \"fixture 4: ([1], [5])\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":48.086,"exit_code":0,"observations":[{"actual":["2","1"],"check":"fixture 1: ([0, 2, 3], [0, 4, 5])","expected":["2","1"],"passed":true},{"actual":["0"],"check":"fixture 2: ([1, 3], [2, 2])","expected":["0"],"passed":true},{"actual":["-2"],"check":"fixture 3: ([0, 2], [4, 0])","expected":["-2"],"passed":true},{"actual":[],"check":"fixture 4: ([1], [5])","expected":[],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 2, 3], [0, 4, 5])\", \"actual\": [\"2\", \"1\"], \"expected\": [\"2\", \"1\"], \"passed\": true}, {\"check\": \"fixture 2: ([1, 3], [2, 2])\", \"actual\": [\"0\"], \"expected\": [\"0\"], \"passed\": true}, {\"check\": \"fixture 3: ([0, 2], [4, 0])\", \"actual\": [\"-2\"], \"expected\": [\"-2\"], \"passed\": true}, {\"check\": \"fixture 4: ([1], [5])\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}