{"abstract":"The programme start itself is labelled -00:00:00:00.","category":"Broadcast timecode arithmetic","checks":9,"contract":"Express label tc relative to programme start as \"+HH:MM:SS:FF\" or \"-HH:MM:SS:FF\" along the shorter way round the 24-hour clock (an offset of exactly 12 hours is negative). Zero is \"+\".","evaluation_group":"w2-broadcast-timecode-arithmetic-programme-relative","failed_approach":"Omitting the plus sign breaks the fixed signed format.","family":"w2-broadcast-timecode-arithmetic-programme-relative-zero-sign","id":"FA-78651","implementations":{"attempt":{"sha256":"5834e4d3e68c873b1fdd891cea27634b647b51106a07fca27e58241b079c1329","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(tc, start, fps):\n    def fr(t):\n        h,m,s,f=map(int,t.split(':'))\n        return ((h*60+m)*60+s)*fps+f\n    day=86400*fps\n    d=(fr(tc)-fr(start))%day\n    if d>=day//2:\n        d-=day\n    sign='' if d>=0 else '-'\n    a=abs(d)\n    return '%s%02d:%02d:%02d:%02d'%(sign,a//(3600*fps),a//(60*fps)%60,a//fps%60,a%fps)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('partial repair variant: zero sign', ['12:59:59:24', '01:00:00:00', 30], '+11:59:59:24'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('normal control', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('normal control', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15')], [('regression: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['23:59:00:00', '23:59:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('partial repair variant: zero sign', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('normal control', ['23:59:59:15', '01:00:00:00', 30], '-01:00:00:15'), ('normal control', ['00:00:00:00', '00:00:10:00', 30], '-00:00:10:00')], [('regression: zero sign', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['10:00:00:00', '10:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('partial repair variant: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '23:59:00:00', 25], '-01:59:00:00'), ('normal control', ['23:01:59:12', '10:00:00:00', 25], '-10:58:00:13'), ('normal control', ['00:01:00:00', '01:00:00:00', 30], '-00:59:00:00')], [('regression: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01'), ('partial repair variant: zero sign', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:59:01:00', '10:00:00:00', 25], '-09:00:59:00'), ('normal control', ['13:00:00:00', '23:59:00:00', 30], '-10:59:00:00'), ('normal control', ['00:01:00:01', '10:00:00:00', 25], '-09:58:59:24')], [('regression: zero sign', ['23:59:00:00', '23:59:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('partial repair variant: zero sign', ['01:01:30:01', '01:00:00:00', 30], '+00:01:30:01'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['23:59:50:00', '01:00:00:00', 30], '-01:00:10:00'), ('normal control', ['23:01:01:12', '00:00:10:00', 25], '-00:59:08:13'), ('normal control', ['23:29:30:15', '00:00:10:00', 30], '-00:30:39:15')]]\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":"8c70cff6b8bc685428494d472c5b84bd99454c233ce906c6556f84ec825c3945","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(tc, start, fps):\n    def fr(t):\n        h,m,s,f=map(int,t.split(':'))\n        return ((h*60+m)*60+s)*fps+f\n    day=86400*fps\n    d=(fr(tc)-fr(start))%day\n    if d>=day//2:\n        d-=day\n    sign='-' if d<=0 else '+'\n    a=abs(d)\n    return '%s%02d:%02d:%02d:%02d'%(sign,a//(3600*fps),a//(60*fps)%60,a//fps%60,a%fps)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('partial repair variant: zero sign', ['12:59:59:24', '01:00:00:00', 30], '+11:59:59:24'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('normal control', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('normal control', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15')], [('regression: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['23:59:00:00', '23:59:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('partial repair variant: zero sign', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('normal control', ['23:59:59:15', '01:00:00:00', 30], '-01:00:00:15'), ('normal control', ['00:00:00:00', '00:00:10:00', 30], '-00:00:10:00')], [('regression: zero sign', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['10:00:00:00', '10:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('partial repair variant: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '23:59:00:00', 25], '-01:59:00:00'), ('normal control', ['23:01:59:12', '10:00:00:00', 25], '-10:58:00:13'), ('normal control', ['00:01:00:00', '01:00:00:00', 30], '-00:59:00:00')], [('regression: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01'), ('partial repair variant: zero sign', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:59:01:00', '10:00:00:00', 25], '-09:00:59:00'), ('normal control', ['13:00:00:00', '23:59:00:00', 30], '-10:59:00:00'), ('normal control', ['00:01:00:01', '10:00:00:00', 25], '-09:58:59:24')], [('regression: zero sign', ['23:59:00:00', '23:59:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('partial repair variant: zero sign', ['01:01:30:01', '01:00:00:00', 30], '+00:01:30:01'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['23:59:50:00', '01:00:00:00', 30], '-01:00:10:00'), ('normal control', ['23:01:01:12', '00:00:10:00', 25], '-00:59:08:13'), ('normal control', ['23:29:30:15', '00:00:10:00', 30], '-00:30:39:15')]]\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":"9fe1520a791c85c6be68c94f236ec49485050a99b89b90e49f8309d9f059bb83","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(tc, start, fps):\n    def fr(t):\n        h,m,s,f=map(int,t.split(':'))\n        return ((h*60+m)*60+s)*fps+f\n    day=86400*fps\n    d=(fr(tc)-fr(start))%day\n    if d>=day//2:\n        d-=day\n    sign='-' if d<0 else '+'\n    a=abs(d)\n    return '%s%02d:%02d:%02d:%02d'%(sign,a//(3600*fps),a//(60*fps)%60,a//fps%60,a%fps)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('regression: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['00:00:10:00', '00:00:10:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:59:59:29', '23:59:00:00', 30], '+02:00:59:29'), ('partial repair variant: zero sign', ['12:59:59:24', '01:00:00:00', 30], '+11:59:59:24'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '10:00:00:00', 30], '-12:00:00:00'), ('normal control', ['12:59:59:24', '23:59:00:00', 25], '-10:59:00:01'), ('normal control', ['23:00:59:15', '00:00:10:00', 30], '-00:59:10:15')], [('regression: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['23:59:00:00', '23:59:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 25], '+00:59:20:00'), ('partial repair variant: zero sign', ['10:59:59:15', '01:00:00:00', 30], '+09:59:59:15'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:01:59:15', '01:00:00:00', 30], '-00:58:00:15'), ('normal control', ['23:59:59:15', '01:00:00:00', 30], '-01:00:00:15'), ('normal control', ['00:00:00:00', '00:00:10:00', 30], '-00:00:10:00')], [('regression: zero sign', ['10:00:00:00', '10:00:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['10:00:00:00', '10:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['11:59:59:00', '01:00:00:00', 25], '+10:59:59:00'), ('partial repair variant: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['22:00:00:00', '23:59:00:00', 25], '-01:59:00:00'), ('normal control', ['23:01:59:12', '10:00:00:00', 25], '-10:58:00:13'), ('normal control', ['00:01:00:00', '01:00:00:00', 30], '-00:59:00:00')], [('regression: zero sign', ['00:00:10:00', '00:00:10:00', 30], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 30], '+00:00:00:00'), ('partial repair probe: zero sign', ['01:01:01:01', '01:00:00:00', 25], '+00:01:01:01'), ('partial repair variant: zero sign', ['01:01:01:00', '23:59:00:00', 25], '+01:02:01:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('normal control', ['00:59:01:00', '10:00:00:00', 25], '-09:00:59:00'), ('normal control', ['13:00:00:00', '23:59:00:00', 30], '-10:59:00:00'), ('normal control', ['00:01:00:01', '10:00:00:00', 25], '-09:58:59:24')], [('regression: zero sign', ['23:59:00:00', '23:59:00:00', 25], '+00:00:00:00'), ('regression variant: zero sign', ['01:00:00:00', '01:00:00:00', 25], '+00:00:00:00'), ('partial repair probe: zero sign', ['00:59:30:00', '00:00:10:00', 30], '+00:59:20:00'), ('partial repair variant: zero sign', ['01:01:30:01', '01:00:00:00', 30], '+00:01:30:01'), ('boundary control', ['00:59:30:00', '01:00:00:00', 25], '-00:00:30:00'), ('boundary control', ['23:59:50:00', '00:00:10:00', 25], '-00:00:20:00'), ('normal control', ['23:59:50:00', '01:00:00:00', 30], '-01:00:10:00'), ('normal control', ['23:01:01:12', '00:00:10:00', 25], '-00:59:08:13'), ('normal control', ['23:29:30:15', '00:00:10:00', 30], '-00:30:39:15')]]\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 SMPTE or any broadcast 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-broadcast-timecode-arithmetic-programme-relative-zero-sign","generated_at":"2026-09-29T14:49:37.333165+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Timecode arithmetic errors misplace edits, commercial breaks and captions against the broadcast clock.","repair":"Use \"+\" for zero and positive offsets.","root_cause":"Zero is treated as negative.","sha256":"b52497885cd447faf77b3182013f1d24a1f8a32d16eda10c35bfac2b8f5d1510","title":"Programme-relative signed timecode: zero sign · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.56,"exit_code":1,"observations":[{"actual":"00:00:00:00","check":"regression: zero sign","expected":"+00:00:00:00","passed":false},{"actual":"00:00:00:00","check":"regression variant: zero sign","expected":"+00:00:00:00","passed":false},{"actual":"02:00:59:29","check":"partial repair probe: zero sign","expected":"+02:00:59:29","passed":false},{"actual":"11:59:59:24","check":"partial repair variant: zero sign","expected":"+11:59:59:24","passed":false},{"actual":"-00:00:30:00","check":"boundary control","expected":"-00:00:30:00","passed":true},{"actual":"-00:00:20:00","check":"boundary control","expected":"-00:00:20:00","passed":true},{"actual":"-12:00:00:00","check":"normal control","expected":"-12:00:00:00","passed":true},{"actual":"-10:59:00:01","check":"normal control","expected":"-10:59:00:01","passed":true},{"actual":"-00:59:10:15","check":"normal control","expected":"-00:59:10:15","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: zero sign\", \"actual\": \"00:00:00:00\", \"expected\": \"+00:00:00:00\", \"passed\": false}, {\"check\": \"regression variant: zero sign\", \"actual\": \"00:00:00:00\", \"expected\": \"+00:00:00:00\", \"passed\": false}, {\"check\": \"partial repair probe: zero sign\", \"actual\": \"02:00:59:29\", \"expected\": \"+02:00:59:29\", \"passed\": false}, {\"check\": \"partial repair variant: zero sign\", \"actual\": \"11:59:59:24\", \"expected\": \"+11:59:59:24\", \"passed\": false}, {\"check\": \"boundary control\", \"actual\": \"-00:00:30:00\", \"expected\": \"-00:00:30:00\", \"passed\": true}, {\"check\": \"boundary control\", \"actual\": \"-00:00:20:00\", \"expected\": \"-00:00:20:00\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"-12:00:00:00\", \"expected\": \"-12:00:00:00\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"-10:59:00:01\", \"expected\": \"-10:59:00:01\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"-00:59:10:15\", \"expected\": \"-00:59:10:15\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.603,"exit_code":1,"observations":[{"actual":"-00:00:00:00","check":"regression: zero sign","expected":"+00:00:00:00","passed":false},{"actual":"-00:00:00:00","check":"regression variant: zero sign","expected":"+00:00:00:00","passed":false},{"actual":"+02:00:59:29","check":"partial repair probe: zero sign","expected":"+02:00:59:29","passed":true},{"actual":"+11:59:59:24","check":"partial repair variant: zero sign","expected":"+11:59:59:24","passed":true},{"actual":"-00:00:30:00","check":"boundary control","expected":"-00:00:30:00","passed":true},{"actual":"-00:00:20:00","check":"boundary control","expected":"-00:00:20:00","passed":true},{"actual":"-12:00:00:00","check":"normal control","expected":"-12:00:00:00","passed":true},{"actual":"-10:59:00:01","check":"normal control","expected":"-10:59:00:01","passed":true},{"actual":"-00:59:10:15","check":"normal control","expected":"-00:59:10:15","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: zero sign\", \"actual\": \"-00:00:00:00\", \"expected\": \"+00:00:00:00\", \"passed\": false}, {\"check\": \"regression variant: zero sign\", \"actual\": \"-00:00:00:00\", \"expected\": \"+00:00:00:00\", \"passed\": false}, {\"check\": \"partial repair probe: zero sign\", \"actual\": \"+02:00:59:29\", \"expected\": \"+02:00:59:29\", \"passed\": true}, {\"check\": \"partial repair variant: zero sign\", \"actual\": \"+11:59:59:24\", \"expected\": \"+11:59:59:24\", \"passed\": true}, {\"check\": \"boundary control\", \"actual\": \"-00:00:30:00\", \"expected\": \"-00:00:30:00\", \"passed\": true}, {\"check\": \"boundary control\", \"actual\": \"-00:00:20:00\", \"expected\": \"-00:00:20:00\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"-12:00:00:00\", \"expected\": \"-12:00:00:00\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"-10:59:00:01\", \"expected\": \"-10:59:00:01\", \"passed\": true}, {\"check\": \"normal control\", \"actual\": \"-00:59:10:15\", \"expected\": \"-00:59:10:15\", \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":39.914,"exit_code":0,"observations":[{"actual":"+00:00:00:00","check":"regression: zero sign","expected":"+00:00:00:00","passed":true},{"actual":"+00:00:00:00","check":"regression variant: zero sign","expected":"+00:00:00:00","passed":true},{"actual":"+02:00:59:29","check":"partial repair probe: zero sign","expected":"+02:00:59:29","passed":true},{"actual":"+11:59:59:24","check":"partial repair variant: zero sign","expected":"+11:59:59:24","passed":true},{"actual":"-00:00:30:00","check":"boundary 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