{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":8,"contract":"Each [integer timestamp, integer contribution] independently contributes value/2**age at integer query now; exclude future events. Same-time events are independent additive contributions. Return exact Fraction string.","contract_signature":"events, now","evaluation_group":"s3-na-timestamp-half-decayed-mass","failed_approach":"A reciprocal age kernel does not implement half-life decay.","family":"s3-numerical-aggregation-timestamp-half-decayed-mass-decay-sign","id":"FA-13566","implementations":{"attempt":{"sha256":"231ee7a2c0c20888765b498ffe038500e43934cdb281f216e0ed9b63c23d7f87","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(events, now):\n    out=Fraction(0)\n    for t,value in events:\n        if t>now: continue\n        out+=Fraction(value,now-t+1)\n    return str(out)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([(0, 8), (2, 4)], 3)), '3')\ncheck('regression 2', solve(*([], 4)), '0')\ncheck('regression 3', solve(*([(5, 3)], 4)), '0')\ncheck('regression 4', solve(*([(3, -4), (3, 8)], 3)), '4')\ncheck('regression 5', solve(*([(0, 3), (1, 2), (1, 2)], 2)), '11/4')\ncheck('regression 6', solve(*([(-2, 8), (0, -1)], 1)), '1/2')\ncheck('regression 7', solve(*([(4, 9), (0, 16)], 4)), '10')\ncheck(\"variable age\",solve([(0,2**N)],N),\"1\")\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":"a852cf992de572b05f523e704c2fa47ef99c1076c130b0d66ccb01e5b52e3d0c","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(events, now):\n    out=Fraction(0)\n    for t,value in events:\n        if t>now: continue\n        out+=Fraction(value*2**(now-t))\n    return str(out)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([(0, 8), (2, 4)], 3)), '3')\ncheck('regression 2', solve(*([], 4)), '0')\ncheck('regression 3', solve(*([(5, 3)], 4)), '0')\ncheck('regression 4', solve(*([(3, -4), (3, 8)], 3)), '4')\ncheck('regression 5', solve(*([(0, 3), (1, 2), (1, 2)], 2)), '11/4')\ncheck('regression 6', solve(*([(-2, 8), (0, -1)], 1)), '1/2')\ncheck('regression 7', solve(*([(4, 9), (0, 16)], 4)), '10')\ncheck(\"variable age\",solve([(0,2**N)],N),\"1\")\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-timestamp-half-decayed-mass-decay-sign","generated_at":"2026-09-29T14:39:08.845578+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":"The exponential kernel amplifies historical contributions.","sha256":"68783efb1347b975e945412e1cfbc9af1b498fa59b2982d2131102b789b8840f","title":"Timestamp half decayed mass: The exponential kernel amplifies historical contributions. · 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":45.768,"exit_code":1,"observations":[{"actual":"4","check":"regression 1","expected":"3","passed":false},{"actual":"0","check":"regression 2","expected":"0","passed":true},{"actual":"0","check":"regression 3","expected":"0","passed":true},{"actual":"4","check":"regression 4","expected":"4","passed":true},{"actual":"3","check":"regression 5","expected":"11/4","passed":false},{"actual":"3/2","check":"regression 6","expected":"1/2","passed":false},{"actual":"61/5","check":"regression 7","expected":"10","passed":false},{"actual":"1","check":"variable age","expected":"1","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"4\", \"expected\": \"3\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"4\", \"expected\": \"4\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"3\", \"expected\": \"11/4\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": \"3/2\", \"expected\": \"1/2\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"61/5\", \"expected\": \"10\", \"passed\": false}, {\"check\": \"variable age\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.68,"exit_code":1,"observations":[{"actual":"72","check":"regression 1","expected":"3","passed":false},{"actual":"0","check":"regression 2","expected":"0","passed":true},{"actual":"0","check":"regression 3","expected":"0","passed":true},{"actual":"4","check":"regression 4","expected":"4","passed":true},{"actual":"20","check":"regression 5","expected":"11/4","passed":false},{"actual":"62","check":"regression 6","expected":"1/2","passed":false},{"actual":"265","check":"regression 7","expected":"10","passed":false},{"actual":"4","check":"variable age","expected":"1","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"72\", \"expected\": \"3\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"4\", \"expected\": \"4\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"20\", \"expected\": \"11/4\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": \"62\", \"expected\": \"1/2\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"265\", \"expected\": \"10\", \"passed\": false}, {\"check\": \"variable age\", \"actual\": \"4\", \"expected\": \"1\", \"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."}}