{"abstract":"Earlier long cues are skipped once a short cue follows them.","category":"Subtitle cue timing","checks":8,"contract":"cues [start,end] are sorted by start. Return the ascending indices of cues active at t (start <= t < end). The search bisects the starts and walks backwards while the running maximum end of the prefix exceeds t.","evaluation_group":"w2-subtitle-cue-timing-active-cue-lookup","failed_approach":"Tracking the maximum start never covers long earlier cues.","family":"w2-subtitle-cue-timing-active-cue-lookup-prefix-maximum","id":"FA-78306","implementations":{"attempt":{"sha256":"b71c59f5772da1342af812d8d5ae9bf43507a347319c41c4978edfdc063fe9f4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport bisect\nN = 1\nobservations = []\ndef solve(cues, t):\n    starts=[c[0] for c in cues]\n    hi=bisect.bisect_right(starts,t)\n    maxend=[]\n    run=0\n    for c in cues:\n        run=max(run,c[0])\n        maxend.append(run)\n    res=[]\n    i=hi-1\n    while i>=0 and maxend[i]>t:\n        if cues[i][1]>t:\n            res.append(i)\n        i-=1\n    return sorted(res)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: prefix maximum', [[[0, 1000], [100, 200], [300, 400]], 350], [0, 2]), ('regression variant: prefix maximum', [[[300, 600], [300, 350], [400, 700], [400, 500]], 600], [2]), ('partial repair probe: prefix maximum', [[[0, 50], [0, 500], [200, 250]], 300], [1]), ('partial repair variant: prefix maximum', [[[0, 50], [100, 400], [200, 500], [400, 450], [500, 1500]], 1200], [4]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[100, 400], [300, 400], [400, 450], [400, 700], [400, 1400]], 0], []), ('normal control', [[[0, 50], [0, 50], [300, 400]], 1200], []), ('normal control', [[[400, 1400]], 300], [])], [('regression: prefix maximum', [[[0, 50], [0, 500], [200, 250]], 300], [1]), ('regression variant: prefix maximum', [[[100, 1100], [100, 1100], [400, 500], [400, 700], [400, 450], [500, 550]], 500], [0, 1, 3, 5]), ('partial repair probe: prefix maximum', [[[0, 100], [100, 1100], [200, 300], [200, 500]], 50], [0]), ('partial repair variant: prefix maximum', [[[100, 400], [300, 350], [500, 550]], 300], [0, 1]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[0, 100], [0, 100], [100, 150]], 200], []), ('normal control', [[[200, 500]], 500], []), ('normal control', [[[500, 550]], 50], [])], [('regression: prefix maximum', [[[0, 100], [0, 1000], [400, 500], [500, 600], [500, 1500], [500, 550]], 600], [1, 4]), ('regression variant: prefix maximum', [[[0, 300], [0, 100], [200, 1200], [200, 300], [300, 600], [300, 1300]], 400], [2, 4, 5]), ('partial repair probe: prefix maximum', [[[100, 400], [300, 400], [300, 400], [300, 350], [400, 500], [500, 800]], 300], [0, 1, 2, 3]), ('partial repair variant: prefix maximum', [[[0, 1000], [100, 1100], [200, 500], [200, 500]], 200], [0, 1, 2, 3]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[100, 1100], [100, 400], [100, 1100], [400, 700], [500, 550]], 1499], []), ('normal control', [[[200, 300]], 150], []), ('normal control', [[[300, 600]], 600], [])], [('regression: prefix maximum', [[[0, 100], [200, 1200], [300, 400], [500, 800]], 600], [1, 3]), ('regression variant: prefix maximum', [[[0, 300], [0, 50], [100, 200], [200, 500], [400, 500]], 100], [0, 2]), ('partial repair probe: prefix maximum', [[[100, 400], [400, 500], [500, 550], [500, 600]], 100], [0]), ('partial repair variant: prefix maximum', [[[0, 100], [0, 1000], [400, 500], [500, 600], [500, 1500], [500, 550]], 600], [1, 4]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[200, 250], [200, 300], [300, 350], [400, 1400], [500, 550]], 1499], []), ('normal control', [[[200, 300], [200, 250], [300, 1300], [300, 1300], [300, 1300]], 0], []), ('normal control', [[[200, 300]], 1200], [])], [('regression: prefix maximum', [[[0, 1000], [100, 150], [100, 400], [200, 1200]], 300], [0, 2, 3]), ('regression variant: prefix maximum', [[[200, 250], [200, 1200], [300, 350], [300, 350], [400, 700]], 600], [1, 4]), ('partial repair probe: prefix maximum', [[[0, 1000], [200, 300], [400, 450]], 200], [0, 1]), ('partial repair variant: prefix maximum', [[[0, 300], [500, 550]], 50], [0]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[200, 300], [500, 1500], [500, 1500]], 150], []), ('normal control', [[[0, 50]], 500], []), ('normal control', [[[0, 50], [200, 250]], 500], [])]]\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":"7ba286b85d7924388465c70eb588c2fb7740f91dcd4cc1a6ce6f34b39f1ff4aa","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport bisect\nN = 1\nobservations = []\ndef solve(cues, t):\n    starts=[c[0] for c in cues]\n    hi=bisect.bisect_right(starts,t)\n    maxend=[]\n    run=0\n    for c in cues:\n        run=c[1]\n        maxend.append(run)\n    res=[]\n    i=hi-1\n    while i>=0 and maxend[i]>t:\n        if cues[i][1]>t:\n            res.append(i)\n        i-=1\n    return sorted(res)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: prefix maximum', [[[0, 1000], [100, 200], [300, 400]], 350], [0, 2]), ('regression variant: prefix maximum', [[[300, 600], [300, 350], [400, 700], [400, 500]], 600], [2]), ('partial repair probe: prefix maximum', [[[0, 50], [0, 500], [200, 250]], 300], [1]), ('partial repair variant: prefix maximum', [[[0, 50], [100, 400], [200, 500], [400, 450], [500, 1500]], 1200], [4]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[100, 400], [300, 400], [400, 450], [400, 700], [400, 1400]], 0], []), ('normal control', [[[0, 50], [0, 50], [300, 400]], 1200], []), ('normal control', [[[400, 1400]], 300], [])], [('regression: prefix maximum', [[[0, 50], [0, 500], [200, 250]], 300], [1]), ('regression variant: prefix maximum', [[[100, 1100], [100, 1100], [400, 500], [400, 700], [400, 450], [500, 550]], 500], [0, 1, 3, 5]), ('partial repair probe: prefix maximum', [[[0, 100], [100, 1100], [200, 300], [200, 500]], 50], [0]), ('partial repair variant: prefix maximum', [[[100, 400], [300, 350], [500, 550]], 300], [0, 1]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[0, 100], [0, 100], [100, 150]], 200], []), ('normal control', [[[200, 500]], 500], []), ('normal control', [[[500, 550]], 50], [])], [('regression: prefix maximum', [[[0, 100], [0, 1000], [400, 500], [500, 600], [500, 1500], [500, 550]], 600], [1, 4]), ('regression variant: prefix maximum', [[[0, 300], [0, 100], [200, 1200], [200, 300], [300, 600], [300, 1300]], 400], [2, 4, 5]), ('partial repair probe: prefix maximum', [[[100, 400], [300, 400], [300, 400], [300, 350], [400, 500], [500, 800]], 300], [0, 1, 2, 3]), ('partial repair variant: prefix maximum', [[[0, 1000], [100, 1100], [200, 500], [200, 500]], 200], [0, 1, 2, 3]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[100, 1100], [100, 400], [100, 1100], [400, 700], [500, 550]], 1499], []), ('normal control', [[[200, 300]], 150], []), ('normal control', [[[300, 600]], 600], [])], [('regression: prefix maximum', [[[0, 100], [200, 1200], [300, 400], [500, 800]], 600], [1, 3]), ('regression variant: prefix maximum', [[[0, 300], [0, 50], [100, 200], [200, 500], [400, 500]], 100], [0, 2]), ('partial repair probe: prefix maximum', [[[100, 400], [400, 500], [500, 550], [500, 600]], 100], [0]), ('partial repair variant: prefix maximum', [[[0, 100], [0, 1000], [400, 500], [500, 600], [500, 1500], [500, 550]], 600], [1, 4]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[200, 250], [200, 300], [300, 350], [400, 1400], [500, 550]], 1499], []), ('normal control', [[[200, 300], [200, 250], [300, 1300], [300, 1300], [300, 1300]], 0], []), ('normal control', [[[200, 300]], 1200], [])], [('regression: prefix maximum', [[[0, 1000], [100, 150], [100, 400], [200, 1200]], 300], [0, 2, 3]), ('regression variant: prefix maximum', [[[200, 250], [200, 1200], [300, 350], [300, 350], [400, 700]], 600], [1, 4]), ('partial repair probe: prefix maximum', [[[0, 1000], [200, 300], [400, 450]], 200], [0, 1]), ('partial repair variant: prefix maximum', [[[0, 300], [500, 550]], 50], [0]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[200, 300], [500, 1500], [500, 1500]], 150], []), ('normal control', [[[0, 50]], 500], []), ('normal control', [[[0, 50], [200, 250]], 500], [])]]\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":"1e861d8e6ce48499cf0dc354daf33fa6607dcd33ca593abb9d08243e9fd0fb9e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport bisect\nN = 1\nobservations = []\ndef solve(cues, t):\n    starts=[c[0] for c in cues]\n    hi=bisect.bisect_right(starts,t)\n    maxend=[]\n    run=0\n    for c in cues:\n        run=max(run,c[1])\n        maxend.append(run)\n    res=[]\n    i=hi-1\n    while i>=0 and maxend[i]>t:\n        if cues[i][1]>t:\n            res.append(i)\n        i-=1\n    return sorted(res)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: prefix maximum', [[[0, 1000], [100, 200], [300, 400]], 350], [0, 2]), ('regression variant: prefix maximum', [[[300, 600], [300, 350], [400, 700], [400, 500]], 600], [2]), ('partial repair probe: prefix maximum', [[[0, 50], [0, 500], [200, 250]], 300], [1]), ('partial repair variant: prefix maximum', [[[0, 50], [100, 400], [200, 500], [400, 450], [500, 1500]], 1200], [4]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[100, 400], [300, 400], [400, 450], [400, 700], [400, 1400]], 0], []), ('normal control', [[[0, 50], [0, 50], [300, 400]], 1200], []), ('normal control', [[[400, 1400]], 300], [])], [('regression: prefix maximum', [[[0, 50], [0, 500], [200, 250]], 300], [1]), ('regression variant: prefix maximum', [[[100, 1100], [100, 1100], [400, 500], [400, 700], [400, 450], [500, 550]], 500], [0, 1, 3, 5]), ('partial repair probe: prefix maximum', [[[0, 100], [100, 1100], [200, 300], [200, 500]], 50], [0]), ('partial repair variant: prefix maximum', [[[100, 400], [300, 350], [500, 550]], 300], [0, 1]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[0, 100], [0, 100], [100, 150]], 200], []), ('normal control', [[[200, 500]], 500], []), ('normal control', [[[500, 550]], 50], [])], [('regression: prefix maximum', [[[0, 100], [0, 1000], [400, 500], [500, 600], [500, 1500], [500, 550]], 600], [1, 4]), ('regression variant: prefix maximum', [[[0, 300], [0, 100], [200, 1200], [200, 300], [300, 600], [300, 1300]], 400], [2, 4, 5]), ('partial repair probe: prefix maximum', [[[100, 400], [300, 400], [300, 400], [300, 350], [400, 500], [500, 800]], 300], [0, 1, 2, 3]), ('partial repair variant: prefix maximum', [[[0, 1000], [100, 1100], [200, 500], [200, 500]], 200], [0, 1, 2, 3]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[100, 1100], [100, 400], [100, 1100], [400, 700], [500, 550]], 1499], []), ('normal control', [[[200, 300]], 150], []), ('normal control', [[[300, 600]], 600], [])], [('regression: prefix maximum', [[[0, 100], [200, 1200], [300, 400], [500, 800]], 600], [1, 3]), ('regression variant: prefix maximum', [[[0, 300], [0, 50], [100, 200], [200, 500], [400, 500]], 100], [0, 2]), ('partial repair probe: prefix maximum', [[[100, 400], [400, 500], [500, 550], [500, 600]], 100], [0]), ('partial repair variant: prefix maximum', [[[0, 100], [0, 1000], [400, 500], [500, 600], [500, 1500], [500, 550]], 600], [1, 4]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[200, 250], [200, 300], [300, 350], [400, 1400], [500, 550]], 1499], []), ('normal control', [[[200, 300], [200, 250], [300, 1300], [300, 1300], [300, 1300]], 0], []), ('normal control', [[[200, 300]], 1200], [])], [('regression: prefix maximum', [[[0, 1000], [100, 150], [100, 400], [200, 1200]], 300], [0, 2, 3]), ('regression variant: prefix maximum', [[[200, 250], [200, 1200], [300, 350], [300, 350], [400, 700]], 600], [1, 4]), ('partial repair probe: prefix maximum', [[[0, 1000], [200, 300], [400, 450]], 200], [0, 1]), ('partial repair variant: prefix maximum', [[[0, 300], [500, 550]], 50], [0]), ('boundary control', [[[0, 100]], 100], []), ('normal control', [[[200, 300], [500, 1500], [500, 1500]], 150], []), ('normal control', [[[0, 50]], 500], []), ('normal control', [[[0, 50], [200, 250]], 500], [])]]\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":"A deterministic bounded teaching model with a stipulated toy contract; it does not claim conformance to any subtitle standard. 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-subtitle-cue-timing-active-cue-lookup-prefix-maximum","generated_at":"2026-09-29T14:49:34.033044+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Subtitle timing defects shift, hide or overlap captions that viewers depend on for comprehension and accessibility.","repair":"Track the maximum end over the prefix.","root_cause":"The running value records each cue end instead of the maximum so far.","sha256":"adb8bffd70a73b6b366a799ded1a607afc3cf39e18b961b3d3fa83869a7e82d0","title":"Active cue lookup with prefix maximum ends: prefix maximum · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.752,"exit_code":1,"observations":[{"actual":[],"check":"regression: prefix maximum","expected":[0,2],"passed":false},{"actual":[],"check":"regression variant: prefix maximum","expected":[2],"passed":false},{"actual":[],"check":"partial repair probe: prefix maximum","expected":[1],"passed":false},{"actual":[],"check":"partial repair variant: prefix maximum","expected":[4],"passed":false},{"actual":[],"check":"boundary control","expected":[],"passed":true},{"actual":[],"check":"normal control","expected":[],"passed":true},{"actual":[],"check":"normal control","expected":[],"passed":true},{"actual":[],"check":"normal control","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: prefix maximum\", \"actual\": [], \"expected\": [0, 2], \"passed\": false}, {\"check\": \"regression variant: prefix maximum\", \"actual\": [], \"expected\": [2], \"passed\": false}, {\"check\": \"partial repair probe: prefix maximum\", \"actual\": [], \"expected\": [1], \"passed\": false}, {\"check\": \"partial repair variant: prefix maximum\", \"actual\": [], \"expected\": [4], \"passed\": false}, {\"check\": \"boundary control\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.71,"exit_code":1,"observations":[{"actual":[2],"check":"regression: prefix maximum","expected":[0,2],"passed":false},{"actual":[],"check":"regression variant: prefix maximum","expected":[2],"passed":false},{"actual":[],"check":"partial repair probe: prefix maximum","expected":[1],"passed":false},{"actual":[4],"check":"partial repair variant: prefix maximum","expected":[4],"passed":true},{"actual":[],"check":"boundary control","expected":[],"passed":true},{"actual":[],"check":"normal control","expected":[],"passed":true},{"actual":[],"check":"normal control","expected":[],"passed":true},{"actual":[],"check":"normal control","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: prefix maximum\", \"actual\": [2], \"expected\": [0, 2], \"passed\": false}, {\"check\": \"regression variant: prefix maximum\", \"actual\": [], \"expected\": [2], \"passed\": false}, {\"check\": \"partial repair probe: prefix maximum\", \"actual\": [], \"expected\": [1], \"passed\": false}, {\"check\": \"partial repair variant: prefix maximum\", \"actual\": [4], \"expected\": [4], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":40.845,"exit_code":0,"observations":[{"actual":[0,2],"check":"regression: prefix maximum","expected":[0,2],"passed":true},{"actual":[2],"check":"regression variant: prefix maximum","expected":[2],"passed":true},{"actual":[1],"check":"partial repair probe: prefix maximum","expected":[1],"passed":true},{"actual":[4],"check":"partial repair variant: prefix maximum","expected":[4],"passed":true},{"actual":[],"check":"boundary control","expected":[],"passed":true},{"actual":[],"check":"normal control","expected":[],"passed":true},{"actual":[],"check":"normal control","expected":[],"passed":true},{"actual":[],"check":"normal control","expected":[],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: prefix maximum\", \"actual\": [0, 2], \"expected\": [0, 2], \"passed\": true}, {\"check\": \"regression variant: prefix maximum\", \"actual\": [2], \"expected\": [2], \"passed\": true}, {\"check\": \"partial repair probe: prefix maximum\", \"actual\": [1], \"expected\": [1], \"passed\": true}, {\"check\": \"partial repair variant: prefix maximum\", \"actual\": [4], \"expected\": [4], \"passed\": true}, {\"check\": \"boundary control\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"normal control\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}