FAILURE MAP
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FA-78581 / Broadcast timecode arithmetic / Open access

Reverse telecine field attribution: cadence base offset · case 01

With a non-zero phase, fields are attributed as if the cadence started at A.

Verified by executionVariant 1 · 9 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The field offset of the starting phase is not added.

VERIFIED REPAIR

Offset fields by the phase field position before the table lookup.

Unsuccessful approach: Offsetting by the phase index instead of its field position misreads the table.

Case contract

Fields carry film frames in A2 B3 C2 D3 cadence; film frame 0 has cadence position phase and starts at field 0. Video frame v consists of fields 2v and 2v+1. For order "upper" field 2v is the top field; for "lower" field 2v is the bottom field. Return [film frame in top field, film frame in bottom field, "clean" or "mixed"]; a negative v returns None.

Why this case matters

Timecode arithmetic errors misplace edits, commercial breaks and captions against the broadcast clock.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(v, phase, order):
    if v<0:
        return None
    base=[0,2,5,7][phase]
    def film(f):
        g,w=divmod(f,10)
        return 4*g+[0,0,1,1,1,2,2,3,3,3][w]-phase
    top,bottom=film(2*v),film(2*v+1)
    if order=='lower':
        top,bottom=bottom,top
    return [top,bottom,'clean' if top==bottom else 'mixed']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: cadence base offset', [0, 1, 'upper'], [0, 0, 'clean']), ('regression variant: cadence base offset', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair probe: cadence base offset', [16, 3, 'upper'], [12, 13, 'mixed']), ('partial repair variant: cadence base offset', [15, 1, 'upper'], [12, 12, 'clean']), ('boundary control', [0, 0, 'upper'], [0, 0, 'clean']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('normal control', [2, 0, 'lower'], [2, 1, 'mixed']), ('normal control', [24, 0, 'upper'], [19, 19, 'clean']), ('normal control', [23, 0, 'lower'], [19, 18, 'mixed'])], [('regression: cadence base offset', [4, 3, 'lower'], [3, 3, 'clean']), ('regression variant: cadence base offset', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair probe: cadence base offset', [10, 2, 'upper'], [8, 8, 'clean']), ('partial repair variant: cadence base offset', [17, 1, 'upper'], [13, 14, 'mixed']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('boundary control', [2, 0, 'lower'], [2, 1, 'mixed']), ('normal control', [1, 0, 'upper'], [1, 1, 'clean']), ('normal control', [-4, 0, 'upper'], None), ('normal control', [-5, 0, 'lower'], None)], [('regression: cadence base offset', [16, 3, 'upper'], [12, 13, 'mixed']), ('regression variant: cadence base offset', [20, 2, 'upper'], [16, 16, 'clean']), ('partial repair probe: cadence base offset', [30, 3, 'lower'], [24, 24, 'clean']), ('partial repair variant: cadence base offset', [28, 2, 'lower'], [23, 22, 'mixed']), ('boundary control', [2, 0, 'lower'], [2, 1, 'mixed']), ('boundary control', [0, 0, 'upper'], [0, 0, 'clean']), ('normal control', [4, 0, 'upper'], [3, 3, 'clean']), ('normal control', [6, 0, 'upper'], [5, 5, 'clean']), ('normal control', [25, 0, 'lower'], [20, 20, 'clean'])], [('regression: cadence base offset', [10, 2, 'upper'], [8, 8, 'clean']), ('regression variant: cadence base offset', [29, 1, 'lower'], [23, 23, 'clean']), ('partial repair probe: cadence base offset', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair variant: cadence base offset', [12, 1, 'upper'], [9, 10, 'mixed']), ('boundary control', [0, 0, 'upper'], [0, 0, 'clean']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('normal control', [-5, 3, 'lower'], None), ('normal control', [28, 0, 'upper'], [22, 23, 'mixed']), ('normal control', [8, 0, 'upper'], [6, 7, 'mixed'])], [('regression: cadence base offset', [30, 3, 'lower'], [24, 24, 'clean']), ('regression variant: cadence base offset', [15, 1, 'upper'], [12, 12, 'clean']), ('partial repair probe: cadence base offset', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair variant: cadence base offset', [22, 3, 'upper'], [17, 18, 'mixed']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('boundary control', [2, 0, 'lower'], [2, 1, 'mixed']), ('normal control', [-2, 1, 'upper'], None), ('normal control', [19, 0, 'lower'], [15, 15, 'clean']), ('normal control', [22, 0, 'upper'], [17, 18, 'mixed'])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: cadence base offset[-1, -1, 'clean'][0, 0, 'clean']Failed
regression variant: cadence base offset[7, 6, 'mixed'][10, 9, 'mixed']Failed
partial repair probe: cadence base offset[10, 10, 'clean'][12, 13, 'mixed']Failed
partial repair variant: cadence base offset[11, 11, 'clean'][12, 12, 'clean']Failed
boundary control[0, 0, 'clean'][0, 0, 'clean']Passed
boundary control[1, 2, 'mixed'][1, 2, 'mixed']Passed
normal control[2, 1, 'mixed'][2, 1, 'mixed']Passed
normal control[19, 19, 'clean'][19, 19, 'clean']Passed
normal control[19, 18, 'mixed'][19, 18, 'mixed']Passed

SHA-256 / c49d15d903aef848e9ad099153055cf318203180db399eafcf42964546c25d75

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(v, phase, order):
    if v<0:
        return None
    base=[0,2,5,7][phase]
    def film(f):
        g,w=divmod(f+phase,10)
        return 4*g+[0,0,1,1,1,2,2,3,3,3][w]-phase
    top,bottom=film(2*v),film(2*v+1)
    if order=='lower':
        top,bottom=bottom,top
    return [top,bottom,'clean' if top==bottom else 'mixed']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: cadence base offset', [0, 1, 'upper'], [0, 0, 'clean']), ('regression variant: cadence base offset', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair probe: cadence base offset', [16, 3, 'upper'], [12, 13, 'mixed']), ('partial repair variant: cadence base offset', [15, 1, 'upper'], [12, 12, 'clean']), ('boundary control', [0, 0, 'upper'], [0, 0, 'clean']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('normal control', [2, 0, 'lower'], [2, 1, 'mixed']), ('normal control', [24, 0, 'upper'], [19, 19, 'clean']), ('normal control', [23, 0, 'lower'], [19, 18, 'mixed'])], [('regression: cadence base offset', [4, 3, 'lower'], [3, 3, 'clean']), ('regression variant: cadence base offset', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair probe: cadence base offset', [10, 2, 'upper'], [8, 8, 'clean']), ('partial repair variant: cadence base offset', [17, 1, 'upper'], [13, 14, 'mixed']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('boundary control', [2, 0, 'lower'], [2, 1, 'mixed']), ('normal control', [1, 0, 'upper'], [1, 1, 'clean']), ('normal control', [-4, 0, 'upper'], None), ('normal control', [-5, 0, 'lower'], None)], [('regression: cadence base offset', [16, 3, 'upper'], [12, 13, 'mixed']), ('regression variant: cadence base offset', [20, 2, 'upper'], [16, 16, 'clean']), ('partial repair probe: cadence base offset', [30, 3, 'lower'], [24, 24, 'clean']), ('partial repair variant: cadence base offset', [28, 2, 'lower'], [23, 22, 'mixed']), ('boundary control', [2, 0, 'lower'], [2, 1, 'mixed']), ('boundary control', [0, 0, 'upper'], [0, 0, 'clean']), ('normal control', [4, 0, 'upper'], [3, 3, 'clean']), ('normal control', [6, 0, 'upper'], [5, 5, 'clean']), ('normal control', [25, 0, 'lower'], [20, 20, 'clean'])], [('regression: cadence base offset', [10, 2, 'upper'], [8, 8, 'clean']), ('regression variant: cadence base offset', [29, 1, 'lower'], [23, 23, 'clean']), ('partial repair probe: cadence base offset', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair variant: cadence base offset', [12, 1, 'upper'], [9, 10, 'mixed']), ('boundary control', [0, 0, 'upper'], [0, 0, 'clean']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('normal control', [-5, 3, 'lower'], None), ('normal control', [28, 0, 'upper'], [22, 23, 'mixed']), ('normal control', [8, 0, 'upper'], [6, 7, 'mixed'])], [('regression: cadence base offset', [30, 3, 'lower'], [24, 24, 'clean']), ('regression variant: cadence base offset', [15, 1, 'upper'], [12, 12, 'clean']), ('partial repair probe: cadence base offset', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair variant: cadence base offset', [22, 3, 'upper'], [17, 18, 'mixed']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('boundary control', [2, 0, 'lower'], [2, 1, 'mixed']), ('normal control', [-2, 1, 'upper'], None), ('normal control', [19, 0, 'lower'], [15, 15, 'clean']), ('normal control', [22, 0, 'upper'], [17, 18, 'mixed'])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: cadence base offset[-1, 0, 'mixed'][0, 0, 'clean']Failed
regression variant: cadence base offset[8, 8, 'clean'][10, 9, 'mixed']Failed
partial repair probe: cadence base offset[11, 11, 'clean'][12, 13, 'mixed']Failed
partial repair variant: cadence base offset[11, 12, 'mixed'][12, 12, 'clean']Failed
boundary control[0, 0, 'clean'][0, 0, 'clean']Passed
boundary control[1, 2, 'mixed'][1, 2, 'mixed']Passed
normal control[2, 1, 'mixed'][2, 1, 'mixed']Passed
normal control[19, 19, 'clean'][19, 19, 'clean']Passed
normal control[19, 18, 'mixed'][19, 18, 'mixed']Passed

SHA-256 / 5957a790fd4d05543d0a17cc1453d2da0dd6c2d6751db10f54c2492cc72fae99

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(v, phase, order):
    if v<0:
        return None
    base=[0,2,5,7][phase]
    def film(f):
        g,w=divmod(f+base,10)
        return 4*g+[0,0,1,1,1,2,2,3,3,3][w]-phase
    top,bottom=film(2*v),film(2*v+1)
    if order=='lower':
        top,bottom=bottom,top
    return [top,bottom,'clean' if top==bottom else 'mixed']
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: cadence base offset', [0, 1, 'upper'], [0, 0, 'clean']), ('regression variant: cadence base offset', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair probe: cadence base offset', [16, 3, 'upper'], [12, 13, 'mixed']), ('partial repair variant: cadence base offset', [15, 1, 'upper'], [12, 12, 'clean']), ('boundary control', [0, 0, 'upper'], [0, 0, 'clean']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('normal control', [2, 0, 'lower'], [2, 1, 'mixed']), ('normal control', [24, 0, 'upper'], [19, 19, 'clean']), ('normal control', [23, 0, 'lower'], [19, 18, 'mixed'])], [('regression: cadence base offset', [4, 3, 'lower'], [3, 3, 'clean']), ('regression variant: cadence base offset', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair probe: cadence base offset', [10, 2, 'upper'], [8, 8, 'clean']), ('partial repair variant: cadence base offset', [17, 1, 'upper'], [13, 14, 'mixed']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('boundary control', [2, 0, 'lower'], [2, 1, 'mixed']), ('normal control', [1, 0, 'upper'], [1, 1, 'clean']), ('normal control', [-4, 0, 'upper'], None), ('normal control', [-5, 0, 'lower'], None)], [('regression: cadence base offset', [16, 3, 'upper'], [12, 13, 'mixed']), ('regression variant: cadence base offset', [20, 2, 'upper'], [16, 16, 'clean']), ('partial repair probe: cadence base offset', [30, 3, 'lower'], [24, 24, 'clean']), ('partial repair variant: cadence base offset', [28, 2, 'lower'], [23, 22, 'mixed']), ('boundary control', [2, 0, 'lower'], [2, 1, 'mixed']), ('boundary control', [0, 0, 'upper'], [0, 0, 'clean']), ('normal control', [4, 0, 'upper'], [3, 3, 'clean']), ('normal control', [6, 0, 'upper'], [5, 5, 'clean']), ('normal control', [25, 0, 'lower'], [20, 20, 'clean'])], [('regression: cadence base offset', [10, 2, 'upper'], [8, 8, 'clean']), ('regression variant: cadence base offset', [29, 1, 'lower'], [23, 23, 'clean']), ('partial repair probe: cadence base offset', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair variant: cadence base offset', [12, 1, 'upper'], [9, 10, 'mixed']), ('boundary control', [0, 0, 'upper'], [0, 0, 'clean']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('normal control', [-5, 3, 'lower'], None), ('normal control', [28, 0, 'upper'], [22, 23, 'mixed']), ('normal control', [8, 0, 'upper'], [6, 7, 'mixed'])], [('regression: cadence base offset', [30, 3, 'lower'], [24, 24, 'clean']), ('regression variant: cadence base offset', [15, 1, 'upper'], [12, 12, 'clean']), ('partial repair probe: cadence base offset', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair variant: cadence base offset', [22, 3, 'upper'], [17, 18, 'mixed']), ('boundary control', [2, 0, 'upper'], [1, 2, 'mixed']), ('boundary control', [2, 0, 'lower'], [2, 1, 'mixed']), ('normal control', [-2, 1, 'upper'], None), ('normal control', [19, 0, 'lower'], [15, 15, 'clean']), ('normal control', [22, 0, 'upper'], [17, 18, 'mixed'])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: cadence base offset[0, 0, 'clean'][0, 0, 'clean']Passed
regression variant: cadence base offset[10, 9, 'mixed'][10, 9, 'mixed']Passed
partial repair probe: cadence base offset[12, 13, 'mixed'][12, 13, 'mixed']Passed
partial repair variant: cadence base offset[12, 12, 'clean'][12, 12, 'clean']Passed
boundary control[0, 0, 'clean'][0, 0, 'clean']Passed
boundary control[1, 2, 'mixed'][1, 2, 'mixed']Passed
normal control[2, 1, 'mixed'][2, 1, 'mixed']Passed
normal control[19, 19, 'clean'][19, 19, 'clean']Passed
normal control[19, 18, 'mixed'][19, 18, 'mixed']Passed

SHA-256 / 717508c1327311356cebb18158e849b30eb6c25670a178e670e60ec740e8e272

Verification & scope

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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:49:36.642935+00:00.

Case digest / 12e14c974b092e21c25757e3acb2ff21efcd1818cd4bb44cdc3bb1f24f15fe55