{"abstract":"Forecasts for p = 1 sequences are 2.3 times too low.","category":"Seismic magnitude estimation","checks":8,"contract":"Rate K/(t+c)^p aftershocks per day. Expected count on [t1, t2] days: for p == 1 (within 1e-12) K ln((t2+c)/(t1+c)); otherwise K((t1+c)^(1-p) - (t2+c)^(1-p))/(p-1). t1 < 0 or t2 <= t1 returns None. Round to 0.001.","contract_signature":"k, c, p, t1, t2","evaluation_group":"w2-seismic_magnitude_estimation-omori-utsu-count","failed_approach":"ln(t2 - t1) ignores the c offset and the window start.","family":"w2-seismic_magnitude_estimation-omori-utsu-count-p-equals-one-logarithm","id":"FA-71616","implementations":{"attempt":{"sha256":"8edd6f8538155e8de12cbb541ae47bf51ed2169adaed9542862d5113a9118f0f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(k, c, p, t1, t2):\n    if t1 < 0 or t2 <= t1:\n        return None\n    if abs(p - 1.0) < 1e-12:\n        n = k * math.log(t2 - t1)\n    else:\n        n = k * ((t1 + c) ** (1 - p) - (t2 + c) ** (1 - p)) / (p - 1)\n    return round(n, 3)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['K 50.0 c 0.01 p 0.8 window 0.0-1.0 d', [50.0, 0.01, 0.8, 0.0, 1.0], 150.971], ['K 50.0 c 0.01 p 0.8 window 0.5-10.0 d', [50.0, 0.01, 0.8, 0.5, 10.0], 177.801], ['K 50.0 c 0.01 p 0.8 window 1.0-30.0 d', [50.0, 0.01, 0.8, 1.0, 30.0], 243.123], ['K 50.0 c 0.01 p 0.8 window 5.0-5.0 d', [50.0, 0.01, 0.8, 5.0, 5.0], None], ['K 50.0 c 0.01 p 0.8 window 3.0-2.0 d', [50.0, 0.01, 0.8, 3.0, 2.0], None], ['K 50.0 c 0.01 p 0.8 window 0.0-0.0 d', [50.0, 0.01, 0.8, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.0 window 0.0-1.0 d', [50.0, 0.01, 1.0, 0.0, 1.0], 230.756], ['K 50.0 c 0.01 p 1.0 window 0.5-10.0 d', [50.0, 0.01, 1.0, 0.5, 10.0], 148.846]], [['K 50.0 c 0.01 p 1.0 window 0.5-10.0 d', [50.0, 0.01, 1.0, 0.5, 10.0], 148.846], ['K 50.0 c 0.01 p 1.0 window 1.0-30.0 d', [50.0, 0.01, 1.0, 1.0, 30.0], 169.579], ['K 50.0 c 0.01 p 1.0 window 5.0-5.0 d', [50.0, 0.01, 1.0, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.0 window 3.0-2.0 d', [50.0, 0.01, 1.0, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.0 window 0.0-0.0 d', [50.0, 0.01, 1.0, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.1 window 0.0-1.0 d', [50.0, 0.01, 1.1, 0.0, 1.0], 292.944], ['K 50.0 c 0.05 p 1.0 window 0.0-1.0 d', [50.0, 0.05, 1.0, 0.0, 1.0], 152.226], ['K 200.0 c 0.01 p 1.0 window 0.0-1.0 d', [200.0, 0.01, 1.0, 0.0, 1.0], 923.024]], [['K 50.0 c 0.01 p 1.1 window 1.0-30.0 d', [50.0, 0.01, 1.1, 1.0, 30.0], 143.672], ['K 50.0 c 0.01 p 1.1 window 5.0-5.0 d', [50.0, 0.01, 1.1, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.1 window 3.0-2.0 d', [50.0, 0.01, 1.1, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.1 window 0.0-0.0 d', [50.0, 0.01, 1.1, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.3 window 0.0-1.0 d', [50.0, 0.01, 1.3, 0.0, 1.0], 497.342], ['K 50.0 c 0.01 p 1.3 window 0.5-10.0 d', [50.0, 0.01, 1.3, 0.5, 10.0], 120.469], ['K 200.0 c 0.01 p 1.0 window 0.0-1.0 d', [200.0, 0.01, 1.0, 0.0, 1.0], 923.024], ['K 200.0 c 0.05 p 1.0 window 1.0-30.0 d', [200.0, 0.05, 1.0, 1.0, 30.0], 670.814]], [['K 50.0 c 0.01 p 1.3 window 5.0-5.0 d', [50.0, 0.01, 1.3, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.3 window 3.0-2.0 d', [50.0, 0.01, 1.3, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.3 window 0.0-0.0 d', [50.0, 0.01, 1.3, 0.0, 0.0], None], ['K 50.0 c 0.05 p 0.8 window 0.0-1.0 d', [50.0, 0.05, 0.8, 0.0, 1.0], 115.131], ['K 50.0 c 0.05 p 0.8 window 0.5-10.0 d', [50.0, 0.05, 0.8, 0.5, 10.0], 174.793], ['K 50.0 c 0.05 p 0.8 window 1.0-30.0 d', [50.0, 0.05, 0.8, 1.0, 30.0], 241.301], ['K 50.0 c 0.05 p 1.0 window 0.5-10.0 d', [50.0, 0.05, 1.0, 0.5, 10.0], 145.27], ['K 200.0 c 0.05 p 1.0 window 0.0-1.0 d', [200.0, 0.05, 1.0, 0.0, 1.0], 608.904]], [['K 50.0 c 0.01 p 1.0 window 0.0-1.0 d', [50.0, 0.01, 1.0, 0.0, 1.0], 230.756], ['K 50.0 c 0.05 p 0.8 window 3.0-2.0 d', [50.0, 0.05, 0.8, 3.0, 2.0], None], ['K 50.0 c 0.05 p 0.8 window 0.0-0.0 d', [50.0, 0.05, 0.8, 0.0, 0.0], None], ['K 50.0 c 0.05 p 1.0 window 0.0-1.0 d', [50.0, 0.05, 1.0, 0.0, 1.0], 152.226], ['K 50.0 c 0.05 p 1.0 window 0.5-10.0 d', [50.0, 0.05, 1.0, 0.5, 10.0], 145.27], ['K 50.0 c 0.05 p 1.0 window 1.0-30.0 d', [50.0, 0.05, 1.0, 1.0, 30.0], 167.704], ['K 50.0 c 0.05 p 1.0 window 5.0-5.0 d', [50.0, 0.05, 1.0, 5.0, 5.0], None], ['K 200.0 c 0.05 p 1.0 window 0.0-1.0 d', [200.0, 0.05, 1.0, 0.0, 1.0], 608.904]]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\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":"fe595809f23239a6c39374755215296be279c35d135fde024dbc266010622e7d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(k, c, p, t1, t2):\n    if t1 < 0 or t2 <= t1:\n        return None\n    if abs(p - 1.0) < 1e-12:\n        n = k * (math.log10(t2 + c) - math.log10(t1 + c))\n    else:\n        n = k * ((t1 + c) ** (1 - p) - (t2 + c) ** (1 - p)) / (p - 1)\n    return round(n, 3)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['K 50.0 c 0.01 p 0.8 window 0.0-1.0 d', [50.0, 0.01, 0.8, 0.0, 1.0], 150.971], ['K 50.0 c 0.01 p 0.8 window 0.5-10.0 d', [50.0, 0.01, 0.8, 0.5, 10.0], 177.801], ['K 50.0 c 0.01 p 0.8 window 1.0-30.0 d', [50.0, 0.01, 0.8, 1.0, 30.0], 243.123], ['K 50.0 c 0.01 p 0.8 window 5.0-5.0 d', [50.0, 0.01, 0.8, 5.0, 5.0], None], ['K 50.0 c 0.01 p 0.8 window 3.0-2.0 d', [50.0, 0.01, 0.8, 3.0, 2.0], None], ['K 50.0 c 0.01 p 0.8 window 0.0-0.0 d', [50.0, 0.01, 0.8, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.0 window 0.0-1.0 d', [50.0, 0.01, 1.0, 0.0, 1.0], 230.756], ['K 50.0 c 0.01 p 1.0 window 0.5-10.0 d', [50.0, 0.01, 1.0, 0.5, 10.0], 148.846]], [['K 50.0 c 0.01 p 1.0 window 0.5-10.0 d', [50.0, 0.01, 1.0, 0.5, 10.0], 148.846], ['K 50.0 c 0.01 p 1.0 window 1.0-30.0 d', [50.0, 0.01, 1.0, 1.0, 30.0], 169.579], ['K 50.0 c 0.01 p 1.0 window 5.0-5.0 d', [50.0, 0.01, 1.0, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.0 window 3.0-2.0 d', [50.0, 0.01, 1.0, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.0 window 0.0-0.0 d', [50.0, 0.01, 1.0, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.1 window 0.0-1.0 d', [50.0, 0.01, 1.1, 0.0, 1.0], 292.944], ['K 50.0 c 0.05 p 1.0 window 0.0-1.0 d', [50.0, 0.05, 1.0, 0.0, 1.0], 152.226], ['K 200.0 c 0.01 p 1.0 window 0.0-1.0 d', [200.0, 0.01, 1.0, 0.0, 1.0], 923.024]], [['K 50.0 c 0.01 p 1.1 window 1.0-30.0 d', [50.0, 0.01, 1.1, 1.0, 30.0], 143.672], ['K 50.0 c 0.01 p 1.1 window 5.0-5.0 d', [50.0, 0.01, 1.1, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.1 window 3.0-2.0 d', [50.0, 0.01, 1.1, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.1 window 0.0-0.0 d', [50.0, 0.01, 1.1, 0.0, 0.0], None], ['K 50.0 c 0.01 p 1.3 window 0.0-1.0 d', [50.0, 0.01, 1.3, 0.0, 1.0], 497.342], ['K 50.0 c 0.01 p 1.3 window 0.5-10.0 d', [50.0, 0.01, 1.3, 0.5, 10.0], 120.469], ['K 200.0 c 0.01 p 1.0 window 0.0-1.0 d', [200.0, 0.01, 1.0, 0.0, 1.0], 923.024], ['K 200.0 c 0.05 p 1.0 window 1.0-30.0 d', [200.0, 0.05, 1.0, 1.0, 30.0], 670.814]], [['K 50.0 c 0.01 p 1.3 window 5.0-5.0 d', [50.0, 0.01, 1.3, 5.0, 5.0], None], ['K 50.0 c 0.01 p 1.3 window 3.0-2.0 d', [50.0, 0.01, 1.3, 3.0, 2.0], None], ['K 50.0 c 0.01 p 1.3 window 0.0-0.0 d', [50.0, 0.01, 1.3, 0.0, 0.0], None], ['K 50.0 c 0.05 p 0.8 window 0.0-1.0 d', [50.0, 0.05, 0.8, 0.0, 1.0], 115.131], ['K 50.0 c 0.05 p 0.8 window 0.5-10.0 d', [50.0, 0.05, 0.8, 0.5, 10.0], 174.793], ['K 50.0 c 0.05 p 0.8 window 1.0-30.0 d', [50.0, 0.05, 0.8, 1.0, 30.0], 241.301], ['K 50.0 c 0.05 p 1.0 window 0.5-10.0 d', [50.0, 0.05, 1.0, 0.5, 10.0], 145.27], ['K 200.0 c 0.05 p 1.0 window 0.0-1.0 d', [200.0, 0.05, 1.0, 0.0, 1.0], 608.904]], [['K 50.0 c 0.01 p 1.0 window 0.0-1.0 d', [50.0, 0.01, 1.0, 0.0, 1.0], 230.756], ['K 50.0 c 0.05 p 0.8 window 3.0-2.0 d', [50.0, 0.05, 0.8, 3.0, 2.0], None], ['K 50.0 c 0.05 p 0.8 window 0.0-0.0 d', [50.0, 0.05, 0.8, 0.0, 0.0], None], ['K 50.0 c 0.05 p 1.0 window 0.0-1.0 d', [50.0, 0.05, 1.0, 0.0, 1.0], 152.226], ['K 50.0 c 0.05 p 1.0 window 0.5-10.0 d', [50.0, 0.05, 1.0, 0.5, 10.0], 145.27], ['K 50.0 c 0.05 p 1.0 window 1.0-30.0 d', [50.0, 0.05, 1.0, 1.0, 30.0], 167.704], ['K 50.0 c 0.05 p 1.0 window 5.0-5.0 d', [50.0, 0.05, 1.0, 5.0, 5.0], None], ['K 200.0 c 0.05 p 1.0 window 0.0-1.0 d', [200.0, 0.05, 1.0, 0.0, 1.0], 608.904]]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\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":"Stipulated deterministic teaching model of a seismological magnitude procedure; constants and tables are fixed by the contract and no claim of agency or standards conformance is made. 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":"w2-seismic_magnitude_estimation-omori-utsu-count-p-equals-one-logarithm","generated_at":"2026-09-29T14:48:31.176436+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Aftershock forecasts integrate the Omori-Utsu rate over the forecast window.","root_cause":"The p = 1 integral uses log10 instead of the natural log.","sha256":"bc33c74011a7b7473311d508feee9734b2f3bfadfaaa8c11e13c0f59cca43a42","title":"Omori-Utsu expected aftershock count: p equals one logarithm · 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":38.434,"exit_code":1,"observations":[{"actual":150.971,"check":"K 50.0 c 0.01 p 0.8 window 0.0-1.0 d","expected":150.971,"passed":true},{"actual":177.801,"check":"K 50.0 c 0.01 p 0.8 window 0.5-10.0 d","expected":177.801,"passed":true},{"actual":243.123,"check":"K 50.0 c 0.01 p 0.8 window 1.0-30.0 d","expected":243.123,"passed":true},{"actual":null,"check":"K 50.0 c 0.01 p 0.8 window 5.0-5.0 d","expected":null,"passed":true},{"actual":null,"check":"K 50.0 c 0.01 p 0.8 window 3.0-2.0 d","expected":null,"passed":true},{"actual":null,"check":"K 50.0 c 0.01 p 0.8 window 0.0-0.0 d","expected":null,"passed":true},{"actual":0.0,"check":"K 50.0 c 0.01 p 1.0 window 0.0-1.0 d","expected":230.756,"passed":false},{"actual":112.565,"check":"K 50.0 c 0.01 p 1.0 window 0.5-10.0 d","expected":148.846,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"K 50.0 c 0.01 p 0.8 window 0.0-1.0 d\", \"actual\": 150.971, \"expected\": 150.971, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 0.8 window 0.5-10.0 d\", \"actual\": 177.801, \"expected\": 177.801, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 0.8 window 1.0-30.0 d\", \"actual\": 243.123, \"expected\": 243.123, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 0.8 window 5.0-5.0 d\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 0.8 window 3.0-2.0 d\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 0.8 window 0.0-0.0 d\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 1.0 window 0.0-1.0 d\", \"actual\": 0.0, \"expected\": 230.756, \"passed\": false}, {\"check\": \"K 50.0 c 0.01 p 1.0 window 0.5-10.0 d\", \"actual\": 112.565, \"expected\": 148.846, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":36.671,"exit_code":1,"observations":[{"actual":150.971,"check":"K 50.0 c 0.01 p 0.8 window 0.0-1.0 d","expected":150.971,"passed":true},{"actual":177.801,"check":"K 50.0 c 0.01 p 0.8 window 0.5-10.0 d","expected":177.801,"passed":true},{"actual":243.123,"check":"K 50.0 c 0.01 p 0.8 window 1.0-30.0 d","expected":243.123,"passed":true},{"actual":null,"check":"K 50.0 c 0.01 p 0.8 window 5.0-5.0 d","expected":null,"passed":true},{"actual":null,"check":"K 50.0 c 0.01 p 0.8 window 3.0-2.0 d","expected":null,"passed":true},{"actual":null,"check":"K 50.0 c 0.01 p 0.8 window 0.0-0.0 d","expected":null,"passed":true},{"actual":100.216,"check":"K 50.0 c 0.01 p 1.0 window 0.0-1.0 d","expected":230.756,"passed":false},{"actual":64.643,"check":"K 50.0 c 0.01 p 1.0 window 0.5-10.0 d","expected":148.846,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"K 50.0 c 0.01 p 0.8 window 0.0-1.0 d\", \"actual\": 150.971, \"expected\": 150.971, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 0.8 window 0.5-10.0 d\", \"actual\": 177.801, \"expected\": 177.801, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 0.8 window 1.0-30.0 d\", \"actual\": 243.123, \"expected\": 243.123, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 0.8 window 5.0-5.0 d\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 0.8 window 3.0-2.0 d\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 0.8 window 0.0-0.0 d\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"K 50.0 c 0.01 p 1.0 window 0.0-1.0 d\", \"actual\": 100.216, \"expected\": 230.756, \"passed\": false}, {\"check\": \"K 50.0 c 0.01 p 1.0 window 0.5-10.0 d\", \"actual\": 64.643, \"expected\": 148.846, \"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."}}