FAILURE MAP
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FA-78551 / Broadcast timecode arithmetic / Open access

2:3 pulldown film frame placement: phase alignment · case 01

With a non-zero cadence phase the first film frame does not start at field 0.

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

ROOT CAUSE

The field position of the starting cadence phase is not subtracted.

VERIFIED REPAIR

Subtract the field offset of the phase.

Unsuccessful approach: Subtracting the phase index instead of its field offset misaligns the cadence.

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)
    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: phase alignment', [0, 1], [0, 'upper', 3]), ('regression variant: phase alignment', [9, 3], [11, 'lower', 2]), ('partial repair probe: phase alignment', [9, 1], [11, 'lower', 2]), ('partial repair variant: phase alignment', [36, 1], [45, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [1, 0], [1, 'upper', 3]), ('normal control', [8, 0], [10, 'upper', 2]), ('normal control', [-3, 2], None)], [('regression: phase alignment', [2, 3], [2, 'lower', 3]), ('regression variant: phase alignment', [10, 1], [12, 'lower', 3]), ('partial repair probe: phase alignment', [35, 1], [44, 'upper', 2]), ('partial repair variant: phase alignment', [38, 3], [47, 'lower', 3]), ('boundary control', [1, 0], [1, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('normal control', [-6, 0], None), ('normal control', [-3, 1], None), ('normal control', [-6, 1], None)], [('regression: phase alignment', [9, 1], [11, 'lower', 2]), ('regression variant: phase alignment', [22, 2], [27, 'lower', 2]), ('partial repair probe: phase alignment', [34, 2], [42, 'lower', 2]), ('partial repair variant: phase alignment', [1, 3], [1, 'lower', 2]), ('boundary control', [3, 0], [3, 'lower', 3]), ('boundary control', [1, 0], [1, 'upper', 3]), ('normal control', [-3, 0], None), ('normal control', [-1, 1], None), ('normal control', [-5, 2], None)], [('regression: phase alignment', [35, 1], [44, 'upper', 2]), ('regression variant: phase alignment', [26, 2], [32, 'lower', 2]), ('partial repair probe: phase alignment', [9, 3], [11, 'lower', 2]), ('partial repair variant: phase alignment', [3, 2], [3, 'lower', 3]), ('boundary control', [4, 0], [5, 'upper', 2]), ('boundary control', [3, 0], [3, 'lower', 3]), ('normal control', [33, 0], [41, 'upper', 3]), ('normal control', [24, 0], [30, 'upper', 2]), ('normal control', [-4, 1], None)], [('regression: phase alignment', [34, 2], [42, 'lower', 2]), ('regression variant: phase alignment', [36, 1], [45, 'upper', 3]), ('partial repair probe: phase alignment', [10, 1], [12, 'lower', 3]), ('partial repair variant: phase alignment', [39, 2], [48, 'lower', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [31, 0], [38, 'lower', 3]), ('normal control', [37, 0], [46, 'upper', 3]), ('normal control', [11, 0], [13, 'lower', 3])]]
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: phase alignment[1, 'upper', 3][0, 'upper', 3]Failed
regression variant: phase alignment[15, 'upper', 2][11, 'lower', 2]Failed
partial repair probe: phase alignment[12, 'lower', 2][11, 'lower', 2]Failed
partial repair variant: phase alignment[46, 'upper', 3][45, 'upper', 3]Failed
boundary control[0, 'upper', 2][0, 'upper', 2]Passed
boundary control[5, 'upper', 2][5, 'upper', 2]Passed
normal control[1, 'upper', 3][1, 'upper', 3]Passed
normal control[10, 'upper', 2][10, 'upper', 2]Passed
normal controlNoneNonePassed

SHA-256 / 3c60d2824fe073522a0cb9c889786a0bcf72f4ee2b9de72b13b10d766669106f

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)-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: phase alignment', [0, 1], [0, 'upper', 3]), ('regression variant: phase alignment', [9, 3], [11, 'lower', 2]), ('partial repair probe: phase alignment', [9, 1], [11, 'lower', 2]), ('partial repair variant: phase alignment', [36, 1], [45, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [1, 0], [1, 'upper', 3]), ('normal control', [8, 0], [10, 'upper', 2]), ('normal control', [-3, 2], None)], [('regression: phase alignment', [2, 3], [2, 'lower', 3]), ('regression variant: phase alignment', [10, 1], [12, 'lower', 3]), ('partial repair probe: phase alignment', [35, 1], [44, 'upper', 2]), ('partial repair variant: phase alignment', [38, 3], [47, 'lower', 3]), ('boundary control', [1, 0], [1, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('normal control', [-6, 0], None), ('normal control', [-3, 1], None), ('normal control', [-6, 1], None)], [('regression: phase alignment', [9, 1], [11, 'lower', 2]), ('regression variant: phase alignment', [22, 2], [27, 'lower', 2]), ('partial repair probe: phase alignment', [34, 2], [42, 'lower', 2]), ('partial repair variant: phase alignment', [1, 3], [1, 'lower', 2]), ('boundary control', [3, 0], [3, 'lower', 3]), ('boundary control', [1, 0], [1, 'upper', 3]), ('normal control', [-3, 0], None), ('normal control', [-1, 1], None), ('normal control', [-5, 2], None)], [('regression: phase alignment', [35, 1], [44, 'upper', 2]), ('regression variant: phase alignment', [26, 2], [32, 'lower', 2]), ('partial repair probe: phase alignment', [9, 3], [11, 'lower', 2]), ('partial repair variant: phase alignment', [3, 2], [3, 'lower', 3]), ('boundary control', [4, 0], [5, 'upper', 2]), ('boundary control', [3, 0], [3, 'lower', 3]), ('normal control', [33, 0], [41, 'upper', 3]), ('normal control', [24, 0], [30, 'upper', 2]), ('normal control', [-4, 1], None)], [('regression: phase alignment', [34, 2], [42, 'lower', 2]), ('regression variant: phase alignment', [36, 1], [45, 'upper', 3]), ('partial repair probe: phase alignment', [10, 1], [12, 'lower', 3]), ('partial repair variant: phase alignment', [39, 2], [48, 'lower', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [31, 0], [38, 'lower', 3]), ('normal control', [37, 0], [46, 'upper', 3]), ('normal control', [11, 0], [13, 'lower', 3])]]
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: phase alignment[0, 'lower', 3][0, 'upper', 3]Failed
regression variant: phase alignment[13, 'lower', 2][11, 'lower', 2]Failed
partial repair probe: phase alignment[12, 'upper', 2][11, 'lower', 2]Failed
partial repair variant: phase alignment[45, 'lower', 3][45, 'upper', 3]Failed
boundary control[0, 'upper', 2][0, 'upper', 2]Passed
boundary control[5, 'upper', 2][5, 'upper', 2]Passed
normal control[1, 'upper', 3][1, 'upper', 3]Passed
normal control[10, 'upper', 2][10, 'upper', 2]Passed
normal controlNoneNonePassed

SHA-256 / 3863f3eb5d864157ed8ef4c1f636040bae789212d1f634bf8b9400bb8752f811

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: phase alignment', [0, 1], [0, 'upper', 3]), ('regression variant: phase alignment', [9, 3], [11, 'lower', 2]), ('partial repair probe: phase alignment', [9, 1], [11, 'lower', 2]), ('partial repair variant: phase alignment', [36, 1], [45, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [1, 0], [1, 'upper', 3]), ('normal control', [8, 0], [10, 'upper', 2]), ('normal control', [-3, 2], None)], [('regression: phase alignment', [2, 3], [2, 'lower', 3]), ('regression variant: phase alignment', [10, 1], [12, 'lower', 3]), ('partial repair probe: phase alignment', [35, 1], [44, 'upper', 2]), ('partial repair variant: phase alignment', [38, 3], [47, 'lower', 3]), ('boundary control', [1, 0], [1, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('normal control', [-6, 0], None), ('normal control', [-3, 1], None), ('normal control', [-6, 1], None)], [('regression: phase alignment', [9, 1], [11, 'lower', 2]), ('regression variant: phase alignment', [22, 2], [27, 'lower', 2]), ('partial repair probe: phase alignment', [34, 2], [42, 'lower', 2]), ('partial repair variant: phase alignment', [1, 3], [1, 'lower', 2]), ('boundary control', [3, 0], [3, 'lower', 3]), ('boundary control', [1, 0], [1, 'upper', 3]), ('normal control', [-3, 0], None), ('normal control', [-1, 1], None), ('normal control', [-5, 2], None)], [('regression: phase alignment', [35, 1], [44, 'upper', 2]), ('regression variant: phase alignment', [26, 2], [32, 'lower', 2]), ('partial repair probe: phase alignment', [9, 3], [11, 'lower', 2]), ('partial repair variant: phase alignment', [3, 2], [3, 'lower', 3]), ('boundary control', [4, 0], [5, 'upper', 2]), ('boundary control', [3, 0], [3, 'lower', 3]), ('normal control', [33, 0], [41, 'upper', 3]), ('normal control', [24, 0], [30, 'upper', 2]), ('normal control', [-4, 1], None)], [('regression: phase alignment', [34, 2], [42, 'lower', 2]), ('regression variant: phase alignment', [36, 1], [45, 'upper', 3]), ('partial repair probe: phase alignment', [10, 1], [12, 'lower', 3]), ('partial repair variant: phase alignment', [39, 2], [48, 'lower', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [31, 0], [38, 'lower', 3]), ('normal control', [37, 0], [46, 'upper', 3]), ('normal control', [11, 0], [13, 'lower', 3])]]
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: phase alignment[0, 'upper', 3][0, 'upper', 3]Passed
regression variant: phase alignment[11, 'lower', 2][11, 'lower', 2]Passed
partial repair probe: phase alignment[11, 'lower', 2][11, 'lower', 2]Passed
partial repair variant: phase alignment[45, 'upper', 3][45, 'upper', 3]Passed
boundary control[0, 'upper', 2][0, 'upper', 2]Passed
boundary control[5, 'upper', 2][5, 'upper', 2]Passed
normal control[1, 'upper', 3][1, 'upper', 3]Passed
normal control[10, 'upper', 2][10, 'upper', 2]Passed
normal controlNoneNonePassed

SHA-256 / 78a5911724e6160396aa1a796f331908e70bb5b80eaf16d87aaf61cfc0928df3

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 2026-09-29T14:49:36.377368+00:00.

Case digest / d38038bfad556cff318fdb01572b3118615d40656ba6da52cbbc75ed372e0a54