{"abstract":"A swarm with one large event is reported far smaller than that event alone.","category":"Seismic magnitude estimation","checks":8,"contract":"Surface-wave magnitudes of a swarm; energy per event log10 E = 1.5 Ms + 4.8 (J). Sum energies and invert to the single equivalent magnitude. Return [Meq rounded 0.01, total energy \"%.2e\"] or None for an empty swarm.","evaluation_group":"w2-seismic_magnitude_estimation-swarm-energy-magnitude","failed_approach":"Keeping only the largest event ignores the rest of the swarm.","family":"w2-seismic_magnitude_estimation-swarm-energy-magnitude-energy-summation","id":"FA-71416","implementations":{"attempt":{"sha256":"687a872412c88ba2b69b9f9da288bc9da003b71827be2006c9bc4a6aa9855ee5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(mags):\n    if not mags:\n        return None\n    e = 10 ** (1.5 * max(mags) + 4.8)\n    me = (math.log10(e) - 4.8) / 1.5\n    return [round(me, 2), \"%.2e\" % e]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 1', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 2', [[4.5]], [4.5, '3.55e+11']], ['swarm 3', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 4', [[4.2, 4.2]], [4.4, '2.52e+11']], ['swarm 5', [[4.2, 4.2, 4.2, 4.2, 4.2]], [4.67, '6.29e+11']], ['swarm 6', [[6.2, 6.2, 6.2, 6.2, 6.2]], [6.67, '6.29e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 7', [[3.7, 3.7, 3.7]], [4.02, '6.72e+10']], ['swarm 8', [[3.6, 3.6]], [3.8, '3.17e+10']], ['swarm 9', [[2.2, 2.2, 2.2, 2.2]], [2.6, '5.04e+08']], ['swarm 10', [[5.2, 5.2, 5.2, 5.2, 5.2]], [5.67, '1.99e+13']], ['swarm 11', [[2.4, 2.4, 2.4, 2.4]], [2.8, '1.00e+09']], ['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 13', [[6.0, 6.0, 6.0]], [6.32, '1.89e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 14', [[4.7]], [4.7, '7.08e+11']], ['swarm 15', [[6.0, 6.0]], [6.2, '1.26e+14']], ['swarm 16', [[2.7, 2.7, 2.7]], [3.02, '2.12e+09']], ['swarm 17', [[2.6, 2.6, 2.6, 2.6, 2.6]], [3.07, '2.51e+09']], ['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 19', [[3.6, 3.6, 3.6, 3.6, 3.6, 3.6]], [4.12, '9.51e+10']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 21', [[4.6, 4.6]], [4.8, '1.00e+12']], ['swarm 22', [[6.1, 6.1]], [6.3, '1.78e+14']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 24', [[4.9, 4.9, 4.9, 4.9, 4.9, 4.9]], [5.42, '8.48e+12']], ['swarm 25', [[3.2, 3.2, 3.2, 3.2]], [3.6, '1.59e+10']], ['swarm 26', [[4.5, 4.5, 4.5, 4.5, 4.5, 4.5]], [5.02, '2.13e+12']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 28', [[2.9]], [2.9, '1.41e+09']], ['swarm 29', [[2.9, 2.9, 2.9, 2.9, 2.9]], [3.37, '7.06e+09']], ['single event', [[5.0]], [5.0, '2.00e+12']], ['two equal events', [[4.0, 4.0]], [4.2, '1.26e+11']], ['empty', [[]], None], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]]]\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":"ffede4fc011fdf75e735a3c5449f902777c2f4796138eae0c4e09c83a3e300f8","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(mags):\n    if not mags:\n        return None\n    e = len(mags) * 10 ** (1.5 * (sum(mags) / len(mags)) + 4.8)\n    me = (math.log10(e) - 4.8) / 1.5\n    return [round(me, 2), \"%.2e\" % e]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 1', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 2', [[4.5]], [4.5, '3.55e+11']], ['swarm 3', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 4', [[4.2, 4.2]], [4.4, '2.52e+11']], ['swarm 5', [[4.2, 4.2, 4.2, 4.2, 4.2]], [4.67, '6.29e+11']], ['swarm 6', [[6.2, 6.2, 6.2, 6.2, 6.2]], [6.67, '6.29e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 7', [[3.7, 3.7, 3.7]], [4.02, '6.72e+10']], ['swarm 8', [[3.6, 3.6]], [3.8, '3.17e+10']], ['swarm 9', [[2.2, 2.2, 2.2, 2.2]], [2.6, '5.04e+08']], ['swarm 10', [[5.2, 5.2, 5.2, 5.2, 5.2]], [5.67, '1.99e+13']], ['swarm 11', [[2.4, 2.4, 2.4, 2.4]], [2.8, '1.00e+09']], ['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 13', [[6.0, 6.0, 6.0]], [6.32, '1.89e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 14', [[4.7]], [4.7, '7.08e+11']], ['swarm 15', [[6.0, 6.0]], [6.2, '1.26e+14']], ['swarm 16', [[2.7, 2.7, 2.7]], [3.02, '2.12e+09']], ['swarm 17', [[2.6, 2.6, 2.6, 2.6, 2.6]], [3.07, '2.51e+09']], ['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 19', [[3.6, 3.6, 3.6, 3.6, 3.6, 3.6]], [4.12, '9.51e+10']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 21', [[4.6, 4.6]], [4.8, '1.00e+12']], ['swarm 22', [[6.1, 6.1]], [6.3, '1.78e+14']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 24', [[4.9, 4.9, 4.9, 4.9, 4.9, 4.9]], [5.42, '8.48e+12']], ['swarm 25', [[3.2, 3.2, 3.2, 3.2]], [3.6, '1.59e+10']], ['swarm 26', [[4.5, 4.5, 4.5, 4.5, 4.5, 4.5]], [5.02, '2.13e+12']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 28', [[2.9]], [2.9, '1.41e+09']], ['swarm 29', [[2.9, 2.9, 2.9, 2.9, 2.9]], [3.37, '7.06e+09']], ['single event', [[5.0]], [5.0, '2.00e+12']], ['two equal events', [[4.0, 4.0]], [4.2, '1.26e+11']], ['empty', [[]], None], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]]]\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"},"fixed":{"sha256":"fc2bf381e28075dae1de0b0b6e2b99c171c74b51989c9cfe78f30ff6d98dd6ea","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(mags):\n    if not mags:\n        return None\n    e = sum(10 ** (1.5 * m + 4.8) for m in mags)\n    me = (math.log10(e) - 4.8) / 1.5\n    return [round(me, 2), \"%.2e\" % e]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 1', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 2', [[4.5]], [4.5, '3.55e+11']], ['swarm 3', [[2.5, 2.5]], [2.7, '7.10e+08']], ['swarm 4', [[4.2, 4.2]], [4.4, '2.52e+11']], ['swarm 5', [[4.2, 4.2, 4.2, 4.2, 4.2]], [4.67, '6.29e+11']], ['swarm 6', [[6.2, 6.2, 6.2, 6.2, 6.2]], [6.67, '6.29e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 7', [[3.7, 3.7, 3.7]], [4.02, '6.72e+10']], ['swarm 8', [[3.6, 3.6]], [3.8, '3.17e+10']], ['swarm 9', [[2.2, 2.2, 2.2, 2.2]], [2.6, '5.04e+08']], ['swarm 10', [[5.2, 5.2, 5.2, 5.2, 5.2]], [5.67, '1.99e+13']], ['swarm 11', [[2.4, 2.4, 2.4, 2.4]], [2.8, '1.00e+09']], ['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 13', [[6.0, 6.0, 6.0]], [6.32, '1.89e+14']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 12', [[2.1, 2.1, 2.1, 2.1]], [2.5, '3.57e+08']], ['swarm 14', [[4.7]], [4.7, '7.08e+11']], ['swarm 15', [[6.0, 6.0]], [6.2, '1.26e+14']], ['swarm 16', [[2.7, 2.7, 2.7]], [3.02, '2.12e+09']], ['swarm 17', [[2.6, 2.6, 2.6, 2.6, 2.6]], [3.07, '2.51e+09']], ['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 19', [[3.6, 3.6, 3.6, 3.6, 3.6, 3.6]], [4.12, '9.51e+10']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 18', [[4.1, 4.1]], [4.3, '1.78e+11']], ['swarm 21', [[4.6, 4.6]], [4.8, '1.00e+12']], ['swarm 22', [[6.1, 6.1]], [6.3, '1.78e+14']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 24', [[4.9, 4.9, 4.9, 4.9, 4.9, 4.9]], [5.42, '8.48e+12']], ['swarm 25', [[3.2, 3.2, 3.2, 3.2]], [3.6, '1.59e+10']], ['swarm 26', [[4.5, 4.5, 4.5, 4.5, 4.5, 4.5]], [5.02, '2.13e+12']], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]], [['swarm 0', [[5.0, 5.0, 5.0, 5.0]], [5.4, '7.98e+12']], ['swarm 23', [[3.5, 3.5, 3.5]], [3.82, '3.37e+10']], ['swarm 28', [[2.9]], [2.9, '1.41e+09']], ['swarm 29', [[2.9, 2.9, 2.9, 2.9, 2.9]], [3.37, '7.06e+09']], ['single event', [[5.0]], [5.0, '2.00e+12']], ['two equal events', [[4.0, 4.0]], [4.2, '1.26e+11']], ['empty', [[]], None], ['one big many small', [[6.0, 3.0, 3.0, 3.0]], [6.0, '6.31e+13']]]]\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-swarm-energy-magnitude-energy-summation","generated_at":"2026-09-29T14:48:29.421882+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Swarm summaries compare cumulative energy release with single earthquakes.","repair":"Sum 10^(1.5M+4.8) over events.","root_cause":"Energy is computed from the mean magnitude times the event count instead of summing per-event energies.","sha256":"812a23b123e54af7456cc58ec3449c28aee8b11c02d5328f2380d179227baae0","title":"Equivalent magnitude of a swarm: energy summation · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.258,"exit_code":1,"observations":[{"actual":[5.0,"2.00e+12"],"check":"swarm 0","expected":[5.4,"7.98e+12"],"passed":false},{"actual":[2.5,"3.55e+08"],"check":"swarm 1","expected":[2.7,"7.10e+08"],"passed":false},{"actual":[4.5,"3.55e+11"],"check":"swarm 2","expected":[4.5,"3.55e+11"],"passed":true},{"actual":[2.5,"3.55e+08"],"check":"swarm 3","expected":[2.7,"7.10e+08"],"passed":false},{"actual":[4.2,"1.26e+11"],"check":"swarm 4","expected":[4.4,"2.52e+11"],"passed":false},{"actual":[4.2,"1.26e+11"],"check":"swarm 5","expected":[4.67,"6.29e+11"],"passed":false},{"actual":[6.2,"1.26e+14"],"check":"swarm 6","expected":[6.67,"6.29e+14"],"passed":false},{"actual":[6.0,"6.31e+13"],"check":"one big many small","expected":[6.0,"6.31e+13"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"swarm 0\", \"actual\": [5.0, \"2.00e+12\"], \"expected\": [5.4, \"7.98e+12\"], \"passed\": false}, {\"check\": \"swarm 1\", \"actual\": [2.5, \"3.55e+08\"], \"expected\": [2.7, \"7.10e+08\"], \"passed\": false}, {\"check\": \"swarm 2\", \"actual\": [4.5, \"3.55e+11\"], \"expected\": [4.5, \"3.55e+11\"], \"passed\": true}, {\"check\": \"swarm 3\", \"actual\": [2.5, \"3.55e+08\"], \"expected\": [2.7, \"7.10e+08\"], \"passed\": false}, {\"check\": \"swarm 4\", \"actual\": [4.2, \"1.26e+11\"], \"expected\": [4.4, \"2.52e+11\"], \"passed\": false}, {\"check\": \"swarm 5\", \"actual\": [4.2, \"1.26e+11\"], \"expected\": [4.67, \"6.29e+11\"], \"passed\": false}, {\"check\": \"swarm 6\", \"actual\": [6.2, \"1.26e+14\"], \"expected\": [6.67, \"6.29e+14\"], \"passed\": false}, {\"check\": \"one big many small\", \"actual\": [6.0, \"6.31e+13\"], \"expected\": [6.0, \"6.31e+13\"], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.521,"exit_code":1,"observations":[{"actual":[5.4,"7.98e+12"],"check":"swarm 0","expected":[5.4,"7.98e+12"],"passed":true},{"actual":[2.7,"7.10e+08"],"check":"swarm 1","expected":[2.7,"7.10e+08"],"passed":true},{"actual":[4.5,"3.55e+11"],"check":"swarm 2","expected":[4.5,"3.55e+11"],"passed":true},{"actual":[2.7,"7.10e+08"],"check":"swarm 3","expected":[2.7,"7.10e+08"],"passed":true},{"actual":[4.4,"2.52e+11"],"check":"swarm 4","expected":[4.4,"2.52e+11"],"passed":true},{"actual":[4.67,"6.29e+11"],"check":"swarm 5","expected":[4.67,"6.29e+11"],"passed":true},{"actual":[6.67,"6.29e+14"],"check":"swarm 6","expected":[6.67,"6.29e+14"],"passed":true},{"actual":[4.15,"1.06e+11"],"check":"one big many small","expected":[6.0,"6.31e+13"],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"swarm 0\", \"actual\": [5.4, \"7.98e+12\"], \"expected\": [5.4, \"7.98e+12\"], \"passed\": true}, {\"check\": \"swarm 1\", \"actual\": [2.7, \"7.10e+08\"], \"expected\": [2.7, \"7.10e+08\"], \"passed\": true}, {\"check\": \"swarm 2\", \"actual\": [4.5, \"3.55e+11\"], \"expected\": [4.5, \"3.55e+11\"], \"passed\": true}, {\"check\": \"swarm 3\", \"actual\": [2.7, \"7.10e+08\"], \"expected\": [2.7, \"7.10e+08\"], \"passed\": true}, {\"check\": \"swarm 4\", \"actual\": [4.4, \"2.52e+11\"], \"expected\": [4.4, \"2.52e+11\"], \"passed\": true}, {\"check\": \"swarm 5\", \"actual\": [4.67, \"6.29e+11\"], \"expected\": [4.67, \"6.29e+11\"], \"passed\": true}, {\"check\": \"swarm 6\", \"actual\": [6.67, \"6.29e+14\"], \"expected\": [6.67, \"6.29e+14\"], \"passed\": true}, {\"check\": \"one big many small\", \"actual\": [4.15, \"1.06e+11\"], \"expected\": [6.0, \"6.31e+13\"], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.464,"exit_code":0,"observations":[{"actual":[5.4,"7.98e+12"],"check":"swarm 0","expected":[5.4,"7.98e+12"],"passed":true},{"actual":[2.7,"7.10e+08"],"check":"swarm 1","expected":[2.7,"7.10e+08"],"passed":true},{"actual":[4.5,"3.55e+11"],"check":"swarm 2","expected":[4.5,"3.55e+11"],"passed":true},{"actual":[2.7,"7.10e+08"],"check":"swarm 3","expected":[2.7,"7.10e+08"],"passed":true},{"actual":[4.4,"2.52e+11"],"check":"swarm 4","expected":[4.4,"2.52e+11"],"passed":true},{"actual":[4.67,"6.29e+11"],"check":"swarm 5","expected":[4.67,"6.29e+11"],"passed":true},{"actual":[6.67,"6.29e+14"],"check":"swarm 6","expected":[6.67,"6.29e+14"],"passed":true},{"actual":[6.0,"6.31e+13"],"check":"one big many small","expected":[6.0,"6.31e+13"],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"swarm 0\", \"actual\": [5.4, \"7.98e+12\"], \"expected\": [5.4, \"7.98e+12\"], \"passed\": true}, {\"check\": \"swarm 1\", \"actual\": [2.7, \"7.10e+08\"], \"expected\": [2.7, \"7.10e+08\"], \"passed\": true}, {\"check\": \"swarm 2\", \"actual\": [4.5, \"3.55e+11\"], \"expected\": [4.5, \"3.55e+11\"], \"passed\": true}, {\"check\": \"swarm 3\", \"actual\": [2.7, \"7.10e+08\"], \"expected\": [2.7, \"7.10e+08\"], \"passed\": true}, {\"check\": \"swarm 4\", \"actual\": [4.4, \"2.52e+11\"], \"expected\": [4.4, \"2.52e+11\"], \"passed\": true}, {\"check\": \"swarm 5\", \"actual\": [4.67, \"6.29e+11\"], \"expected\": [4.67, \"6.29e+11\"], \"passed\": true}, {\"check\": \"swarm 6\", \"actual\": [6.67, \"6.29e+14\"], \"expected\": [6.67, \"6.29e+14\"], \"passed\": true}, {\"check\": \"one big many small\", \"actual\": [6.0, \"6.31e+13\"], \"expected\": [6.0, \"6.31e+13\"], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}