{"abstract":"The start value is scaled rather than retained as the intercept.","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. a,b are integers and t is a rational string; extrapolation outside [0,1] is allowed. Exact operational definition: str(Fraction(a)+(Fraction(b)-Fraction(a))*Fraction(t))","evaluation_group":"model-32b00092911d27ea","failed_approach":"Endpoint weights are reversed.","family":"xn-linear-interpolation-rational","id":"FA-6396","implementations":{"attempt":{"sha256":"37cbc05b938e74864ff25f6c7e247e6782b538967c19e48cc6be6d0b7e86379b","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(a, b, t):\n    return str(Fraction(a)*Fraction(t)+Fraction(b)*(1-Fraction(t)))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck(\"fixture 1: (2, 10, '1/4')\", solve(*(2, 10, '1/4')), '4')\ncheck(\"fixture 2: (3, 7, '0')\", solve(*(3, 7, '0')), '3')\ncheck(\"fixture 3: (3, 7, '1')\", solve(*(3, 7, '1')), '7')\ncheck(\"fixture 4: (2, 2, '1/3')\", solve(*(2, 2, '1/3')), '2')\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":"a252bc5b3a4baf0e5b5925f5ddfd160a498a4475ced2cafa3b49f81c698fa613","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(a, b, t):\n    return str((Fraction(a)+Fraction(b))*Fraction(t))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck(\"fixture 1: (2, 10, '1/4')\", solve(*(2, 10, '1/4')), '4')\ncheck(\"fixture 2: (3, 7, '0')\", solve(*(3, 7, '0')), '3')\ncheck(\"fixture 3: (3, 7, '1')\", solve(*(3, 7, '1')), '7')\ncheck(\"fixture 4: (2, 2, '1/3')\", solve(*(2, 2, '1/3')), '2')\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":"5aaf296c50a486222171f8ba70127d8de9148b72fa06b96f26b1e083595aae76","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(a, b, t):\n    return str(Fraction(a)+(Fraction(b)-Fraction(a))*Fraction(t))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck(\"fixture 1: (2, 10, '1/4')\", solve(*(2, 10, '1/4')), '4')\ncheck(\"fixture 2: (3, 7, '0')\", solve(*(3, 7, '0')), '3')\ncheck(\"fixture 3: (3, 7, '1')\", solve(*(3, 7, '1')), '7')\ncheck(\"fixture 4: (2, 2, '1/3')\", solve(*(2, 2, '1/3')), '2')\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-linear-interpolation-rational","generated_at":"2026-09-29T14:38:01.453112+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(a)+(Fraction(b)-Fraction(a))*Fraction(t))","root_cause":"The start value is scaled rather than retained as the intercept.","sha256":"bcb34ae194d26d45dd4b1112627e4deed7140a3bca2fab5777142e56e6cdecc6","title":"Linear interpolation rational · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":52.558,"exit_code":1,"observations":[{"actual":"8","check":"fixture 1: (2, 10, '1/4')","expected":"4","passed":false},{"actual":"7","check":"fixture 2: (3, 7, '0')","expected":"3","passed":false},{"actual":"3","check":"fixture 3: (3, 7, '1')","expected":"7","passed":false},{"actual":"2","check":"fixture 4: (2, 2, '1/3')","expected":"2","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 10, '1/4')\", \"actual\": \"8\", \"expected\": \"4\", \"passed\": false}, {\"check\": \"fixture 2: (3, 7, '0')\", \"actual\": \"7\", \"expected\": \"3\", \"passed\": false}, {\"check\": \"fixture 3: (3, 7, '1')\", \"actual\": \"3\", \"expected\": \"7\", \"passed\": false}, {\"check\": \"fixture 4: (2, 2, '1/3')\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":59.015,"exit_code":1,"observations":[{"actual":"3","check":"fixture 1: (2, 10, '1/4')","expected":"4","passed":false},{"actual":"0","check":"fixture 2: (3, 7, '0')","expected":"3","passed":false},{"actual":"10","check":"fixture 3: (3, 7, '1')","expected":"7","passed":false},{"actual":"4/3","check":"fixture 4: (2, 2, '1/3')","expected":"2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 10, '1/4')\", \"actual\": \"3\", \"expected\": \"4\", \"passed\": false}, {\"check\": \"fixture 2: (3, 7, '0')\", \"actual\": \"0\", \"expected\": \"3\", \"passed\": false}, {\"check\": \"fixture 3: (3, 7, '1')\", \"actual\": \"10\", \"expected\": \"7\", \"passed\": false}, {\"check\": \"fixture 4: (2, 2, '1/3')\", \"actual\": \"4/3\", \"expected\": \"2\", \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":69.877,"exit_code":0,"observations":[{"actual":"4","check":"fixture 1: (2, 10, '1/4')","expected":"4","passed":true},{"actual":"3","check":"fixture 2: (3, 7, '0')","expected":"3","passed":true},{"actual":"7","check":"fixture 3: (3, 7, '1')","expected":"7","passed":true},{"actual":"2","check":"fixture 4: (2, 2, '1/3')","expected":"2","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (2, 10, '1/4')\", \"actual\": \"4\", \"expected\": \"4\", \"passed\": true}, {\"check\": \"fixture 2: (3, 7, '0')\", \"actual\": \"3\", \"expected\": \"3\", \"passed\": true}, {\"check\": \"fixture 3: (3, 7, '1')\", \"actual\": \"7\", \"expected\": \"7\", \"passed\": true}, {\"check\": \"fixture 4: (2, 2, '1/3')\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}