FAILURE MAP
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FA-78556 / Broadcast timecode arithmetic / Open access

2:3 pulldown film frame placement: field count lookup · case 01

Field counts are wrong whenever the cadence phase is not zero.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The count is looked up from the film index without the phase.

VERIFIED REPAIR

Look up the count at the phased cadence position.

Unsuccessful approach: The inverted count table swaps two- and three-field frames.

Case contract

Film frames follow the A2 B3 C2 D3 field cadence (10 fields per 4 film frames). phase is the cadence position (0=A..3=D) of film frame 0, which starts at video field 0. Negative n returns None. For film frame n return [video frame of its first field, "upper" for an even field index else "lower", number of fields].

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(n, phase):
    if n<0:
        return None
    def sf(a):
        return 10*(a//4)+[0,2,5,7][a%4]
    a=n+phase
    start=sf(a)-sf(phase)
    count=[2,3,2,3][n%4]
    return [start//2,'upper' if start%2==0 else 'lower',count]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: field count lookup', [0, 1], [0, 'upper', 3]), ('regression variant: field count lookup', [10, 1], [12, 'lower', 3]), ('partial repair probe: field count lookup', [3, 0], [3, 'lower', 3]), ('partial repair variant: field count lookup', [34, 2], [42, 'lower', 2]), ('normal control', [-3, 2], None), ('normal control', [-2, 3], None), ('normal control', [-2, 1], None)], [('regression: field count lookup', [2, 3], [2, 'lower', 3]), ('regression variant: field count lookup', [36, 1], [45, 'upper', 3]), ('partial repair probe: field count lookup', [4, 0], [5, 'upper', 2]), ('partial repair variant: field count lookup', [9, 3], [11, 'lower', 2]), ('normal control', [-5, 1], None), ('normal control', [-1, 1], None), ('normal control', [-4, 1], None)], [('regression: field count lookup', [9, 1], [11, 'lower', 2]), ('regression variant: field count lookup', [38, 3], [47, 'lower', 3]), ('partial repair probe: field count lookup', [0, 1], [0, 'upper', 3]), ('partial repair variant: field count lookup', [10, 1], [12, 'lower', 3]), ('normal control', [-2, 2], None), ('normal control', [-1, 0], None), ('normal control', [-2, 0], None)], [('regression: field count lookup', [35, 1], [44, 'upper', 2]), ('regression variant: field count lookup', [1, 3], [1, 'lower', 2]), ('partial repair probe: field count lookup', [2, 3], [2, 'lower', 3]), ('partial repair variant: field count lookup', [22, 2], [27, 'lower', 2]), ('normal control', [-1, 2], None), ('normal control', [-4, 2], None), ('normal control', [-2, 3], None)], [('regression: field count lookup', [9, 3], [11, 'lower', 2]), ('regression variant: field count lookup', [30, 3], [37, 'lower', 3]), ('partial repair probe: field count lookup', [8, 0], [10, 'upper', 2]), ('partial repair variant: field count lookup', [26, 2], [32, 'lower', 2]), ('normal control', [-2, 1], None), ('normal control', [-3, 0], None), ('normal control', [-1, 1], None)]]
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: field count lookup[0, 'upper', 2][0, 'upper', 3]Failed
regression variant: field count lookup[12, 'lower', 2][12, 'lower', 3]Failed
partial repair probe: field count lookup[3, 'lower', 3][3, 'lower', 3]Passed
partial repair variant: field count lookup[42, 'lower', 2][42, 'lower', 2]Passed
normal controlNoneNonePassed
normal controlNoneNonePassed
normal controlNoneNonePassed

SHA-256 / ad5cc010f830d75f047ecbae9bc60163cbafd67b20a6802907e83ce0d463f699

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(n, phase):
    if n<0:
        return None
    def sf(a):
        return 10*(a//4)+[0,2,5,7][a%4]
    a=n+phase
    start=sf(a)-sf(phase)
    count=[3,2,3,2][a%4]
    return [start//2,'upper' if start%2==0 else 'lower',count]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: field count lookup', [0, 1], [0, 'upper', 3]), ('regression variant: field count lookup', [10, 1], [12, 'lower', 3]), ('partial repair probe: field count lookup', [3, 0], [3, 'lower', 3]), ('partial repair variant: field count lookup', [34, 2], [42, 'lower', 2]), ('normal control', [-3, 2], None), ('normal control', [-2, 3], None), ('normal control', [-2, 1], None)], [('regression: field count lookup', [2, 3], [2, 'lower', 3]), ('regression variant: field count lookup', [36, 1], [45, 'upper', 3]), ('partial repair probe: field count lookup', [4, 0], [5, 'upper', 2]), ('partial repair variant: field count lookup', [9, 3], [11, 'lower', 2]), ('normal control', [-5, 1], None), ('normal control', [-1, 1], None), ('normal control', [-4, 1], None)], [('regression: field count lookup', [9, 1], [11, 'lower', 2]), ('regression variant: field count lookup', [38, 3], [47, 'lower', 3]), ('partial repair probe: field count lookup', [0, 1], [0, 'upper', 3]), ('partial repair variant: field count lookup', [10, 1], [12, 'lower', 3]), ('normal control', [-2, 2], None), ('normal control', [-1, 0], None), ('normal control', [-2, 0], None)], [('regression: field count lookup', [35, 1], [44, 'upper', 2]), ('regression variant: field count lookup', [1, 3], [1, 'lower', 2]), ('partial repair probe: field count lookup', [2, 3], [2, 'lower', 3]), ('partial repair variant: field count lookup', [22, 2], [27, 'lower', 2]), ('normal control', [-1, 2], None), ('normal control', [-4, 2], None), ('normal control', [-2, 3], None)], [('regression: field count lookup', [9, 3], [11, 'lower', 2]), ('regression variant: field count lookup', [30, 3], [37, 'lower', 3]), ('partial repair probe: field count lookup', [8, 0], [10, 'upper', 2]), ('partial repair variant: field count lookup', [26, 2], [32, 'lower', 2]), ('normal control', [-2, 1], None), ('normal control', [-3, 0], None), ('normal control', [-1, 1], None)]]
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: field count lookup[0, 'upper', 2][0, 'upper', 3]Failed
regression variant: field count lookup[12, 'lower', 2][12, 'lower', 3]Failed
partial repair probe: field count lookup[3, 'lower', 2][3, 'lower', 3]Failed
partial repair variant: field count lookup[42, 'lower', 3][42, 'lower', 2]Failed
normal controlNoneNonePassed
normal controlNoneNonePassed
normal controlNoneNonePassed

SHA-256 / fcfc7592ae4cf9ad53d83533d39988e7d35b5717eed7305922cfb9197f934dc2

3 / The verified repair

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

N = 1
observations = []
def solve(n, phase):
    if n<0:
        return None
    def sf(a):
        return 10*(a//4)+[0,2,5,7][a%4]
    a=n+phase
    start=sf(a)-sf(phase)
    count=[2,3,2,3][a%4]
    return [start//2,'upper' if start%2==0 else 'lower',count]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: field count lookup', [0, 1], [0, 'upper', 3]), ('regression variant: field count lookup', [10, 1], [12, 'lower', 3]), ('partial repair probe: field count lookup', [3, 0], [3, 'lower', 3]), ('partial repair variant: field count lookup', [34, 2], [42, 'lower', 2]), ('normal control', [-3, 2], None), ('normal control', [-2, 3], None), ('normal control', [-2, 1], None)], [('regression: field count lookup', [2, 3], [2, 'lower', 3]), ('regression variant: field count lookup', [36, 1], [45, 'upper', 3]), ('partial repair probe: field count lookup', [4, 0], [5, 'upper', 2]), ('partial repair variant: field count lookup', [9, 3], [11, 'lower', 2]), ('normal control', [-5, 1], None), ('normal control', [-1, 1], None), ('normal control', [-4, 1], None)], [('regression: field count lookup', [9, 1], [11, 'lower', 2]), ('regression variant: field count lookup', [38, 3], [47, 'lower', 3]), ('partial repair probe: field count lookup', [0, 1], [0, 'upper', 3]), ('partial repair variant: field count lookup', [10, 1], [12, 'lower', 3]), ('normal control', [-2, 2], None), ('normal control', [-1, 0], None), ('normal control', [-2, 0], None)], [('regression: field count lookup', [35, 1], [44, 'upper', 2]), ('regression variant: field count lookup', [1, 3], [1, 'lower', 2]), ('partial repair probe: field count lookup', [2, 3], [2, 'lower', 3]), ('partial repair variant: field count lookup', [22, 2], [27, 'lower', 2]), ('normal control', [-1, 2], None), ('normal control', [-4, 2], None), ('normal control', [-2, 3], None)], [('regression: field count lookup', [9, 3], [11, 'lower', 2]), ('regression variant: field count lookup', [30, 3], [37, 'lower', 3]), ('partial repair probe: field count lookup', [8, 0], [10, 'upper', 2]), ('partial repair variant: field count lookup', [26, 2], [32, 'lower', 2]), ('normal control', [-2, 1], None), ('normal control', [-3, 0], None), ('normal control', [-1, 1], None)]]
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: field count lookup[0, 'upper', 3][0, 'upper', 3]Passed
regression variant: field count lookup[12, 'lower', 3][12, 'lower', 3]Passed
partial repair probe: field count lookup[3, 'lower', 3][3, 'lower', 3]Passed
partial repair variant: field count lookup[42, 'lower', 2][42, 'lower', 2]Passed
normal controlNoneNonePassed
normal controlNoneNonePassed
normal controlNoneNonePassed

SHA-256 / fc430c535bbbf7bafc122a35fb4fd7e9b1c96773334c5c4ad695fc298557d320

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 2026-09-29T14:49:36.593849+00:00.

Case digest / 504e97ba28ea904cfebcc767c78f20b21bf43863ec828b091e1ff2cb2271f7c3