{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":9,"contract":"Bins [left,right,mass] have positive widths and nonnegative integer masses. Treat each bin as uniform density. Return exact mass in query [a,b] as a Fraction string; reversed/empty queries have zero mass.","contract_signature":"bins, a, b","evaluation_group":"s3-na-histogram-interval-mass","failed_approach":"Absolute overlap turns gaps into positive mass.","family":"s3-numerical-aggregation-histogram-interval-mass-negative-overlap","id":"FA-13026","implementations":{"attempt":{"sha256":"967d99a1baf9aa318eae41321d4223d9ad317a0465d1f65b32172fc8a6cb00db","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom collections import Counter, defaultdict\nimport math\nimport itertools\nN = 1\nobservations = []\ndef solve(bins, a, b):\n    return str(sum((Fraction(m*abs(min(r,b)-max(l,a)),r-l) for l,r,m in bins),Fraction(0))) if a<b else \"0\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[0, 4, 8], [4, 10, 3]], 2, 7)), '11/2')\ncheck('regression 2', solve(*([[0, 4, 8]], 1, 2)), '2')\ncheck('regression 3', solve(*([[0, 4, 8]], -3, 8)), '8')\ncheck('regression 4', solve(*([[0, 4, 8]], 4, 9)), '0')\ncheck('regression 5', solve(*([[0, 4, 8]], 7, 9)), '0')\ncheck('regression 6', solve(*([], 0, 1)), '0')\ncheck('regression 7', solve(*([[0, 4, 8]], 3, 1)), '0')\ncheck('regression 8', solve(*([[2, 7, 10], [10, 12, 8]], 0, 11)), '14')\ncheck(\"variable density mass\",solve([[0,N+2,2*(N+2)]],1,N+1),str(2*N))\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":"32efef394924eb6459c8791afb428f0a726d5e18739a27efe2a8bb2a14862766","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom collections import Counter, defaultdict\nimport math\nimport itertools\nN = 1\nobservations = []\ndef solve(bins, a, b):\n    return str(sum((Fraction(m*(min(r,b)-max(l,a)),r-l) for l,r,m in bins),Fraction(0))) if a<b else \"0\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[0, 4, 8], [4, 10, 3]], 2, 7)), '11/2')\ncheck('regression 2', solve(*([[0, 4, 8]], 1, 2)), '2')\ncheck('regression 3', solve(*([[0, 4, 8]], -3, 8)), '8')\ncheck('regression 4', solve(*([[0, 4, 8]], 4, 9)), '0')\ncheck('regression 5', solve(*([[0, 4, 8]], 7, 9)), '0')\ncheck('regression 6', solve(*([], 0, 1)), '0')\ncheck('regression 7', solve(*([[0, 4, 8]], 3, 1)), '0')\ncheck('regression 8', solve(*([[2, 7, 10], [10, 12, 8]], 0, 11)), '14')\ncheck(\"variable density mass\",solve([[0,N+2,2*(N+2)]],1,N+1),str(2*N))\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":"Small offline integer/rational inputs only; no performance, statistical inference, or production-library conformance claim. 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":"s3-numerical-aggregation-histogram-interval-mass-negative-overlap","generated_at":"2026-09-29T14:39:03.075051+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Exact bounded examples isolate a reduction defect without floating-point or external-service effects.","root_cause":"Disjoint bins contribute negative signed overlap.","sha256":"fe923fc46e5cfa3f71f53b425ceafdd956bc1a4a247f616b209df38899de5531","title":"Histogram interval mass: Disjoint bins contribute negative signed overlap. · 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":51.515,"exit_code":1,"observations":[{"actual":"11/2","check":"regression 1","expected":"11/2","passed":true},{"actual":"2","check":"regression 2","expected":"2","passed":true},{"actual":"8","check":"regression 3","expected":"8","passed":true},{"actual":"0","check":"regression 4","expected":"0","passed":true},{"actual":"6","check":"regression 5","expected":"0","passed":false},{"actual":"0","check":"regression 6","expected":"0","passed":true},{"actual":"0","check":"regression 7","expected":"0","passed":true},{"actual":"14","check":"regression 8","expected":"14","passed":true},{"actual":"2","check":"variable density mass","expected":"2","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"11/2\", \"expected\": \"11/2\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"8\", \"expected\": \"8\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"6\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"14\", \"expected\": \"14\", \"passed\": true}, {\"check\": \"variable density mass\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":54.341,"exit_code":1,"observations":[{"actual":"11/2","check":"regression 1","expected":"11/2","passed":true},{"actual":"2","check":"regression 2","expected":"2","passed":true},{"actual":"8","check":"regression 3","expected":"8","passed":true},{"actual":"0","check":"regression 4","expected":"0","passed":true},{"actual":"-6","check":"regression 5","expected":"0","passed":false},{"actual":"0","check":"regression 6","expected":"0","passed":true},{"actual":"0","check":"regression 7","expected":"0","passed":true},{"actual":"14","check":"regression 8","expected":"14","passed":true},{"actual":"2","check":"variable density mass","expected":"2","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"11/2\", \"expected\": \"11/2\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"8\", \"expected\": \"8\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"-6\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"14\", \"expected\": \"14\", \"passed\": true}, {\"check\": \"variable density mass\", \"actual\": \"2\", \"expected\": \"2\", \"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."}}