FAILURE MAP
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FA-78586 / Broadcast timecode arithmetic / Open access

Reverse telecine field attribution: phase frame rebasing · case 01

Film frame numbers are too high by the cadence phase.

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

ROOT CAUSE

The absolute cadence frame is not rebased to film frame 0.

VERIFIED REPAIR

Subtract the phase from the cadence frame number.

Unsuccessful approach: Subtracting the field offset instead of the frame offset over-corrects.

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+base,10)
        return 4*g+[0,0,1,1,1,2,2,3,3,3][w]
    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: phase frame rebasing', [0, 1, 'upper'], [0, 0, 'clean']), ('regression variant: phase frame rebasing', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair probe: phase frame rebasing', [16, 3, 'upper'], [12, 13, 'mixed']), ('partial repair variant: phase frame rebasing', [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: phase frame rebasing', [4, 3, 'lower'], [3, 3, 'clean']), ('regression variant: phase frame rebasing', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair probe: phase frame rebasing', [10, 2, 'upper'], [8, 8, 'clean']), ('partial repair variant: phase frame rebasing', [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: phase frame rebasing', [16, 3, 'upper'], [12, 13, 'mixed']), ('regression variant: phase frame rebasing', [20, 2, 'upper'], [16, 16, 'clean']), ('partial repair probe: phase frame rebasing', [30, 3, 'lower'], [24, 24, 'clean']), ('partial repair variant: phase frame rebasing', [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: phase frame rebasing', [10, 2, 'upper'], [8, 8, 'clean']), ('regression variant: phase frame rebasing', [29, 1, 'lower'], [23, 23, 'clean']), ('partial repair probe: phase frame rebasing', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair variant: phase frame rebasing', [28, 1, 'upper'], [22, 22, 'clean']), ('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: phase frame rebasing', [30, 3, 'lower'], [24, 24, 'clean']), ('regression variant: phase frame rebasing', [15, 1, 'upper'], [12, 12, 'clean']), ('partial repair probe: phase frame rebasing', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair variant: phase frame rebasing', [12, 1, 'upper'], [9, 10, '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: phase frame rebasing[1, 1, 'clean'][0, 0, 'clean']Failed
regression variant: phase frame rebasing[13, 12, 'mixed'][10, 9, 'mixed']Failed
partial repair probe: phase frame rebasing[15, 16, 'mixed'][12, 13, 'mixed']Failed
partial repair variant: phase frame rebasing[13, 13, '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 / 03b1ae9797bd3476611f3a8d4e9dabc834cc9f78276601dc0d312da8ae1349a9

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+base,10)
        return 4*g+[0,0,1,1,1,2,2,3,3,3][w]-base
    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: phase frame rebasing', [0, 1, 'upper'], [0, 0, 'clean']), ('regression variant: phase frame rebasing', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair probe: phase frame rebasing', [16, 3, 'upper'], [12, 13, 'mixed']), ('partial repair variant: phase frame rebasing', [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: phase frame rebasing', [4, 3, 'lower'], [3, 3, 'clean']), ('regression variant: phase frame rebasing', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair probe: phase frame rebasing', [10, 2, 'upper'], [8, 8, 'clean']), ('partial repair variant: phase frame rebasing', [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: phase frame rebasing', [16, 3, 'upper'], [12, 13, 'mixed']), ('regression variant: phase frame rebasing', [20, 2, 'upper'], [16, 16, 'clean']), ('partial repair probe: phase frame rebasing', [30, 3, 'lower'], [24, 24, 'clean']), ('partial repair variant: phase frame rebasing', [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: phase frame rebasing', [10, 2, 'upper'], [8, 8, 'clean']), ('regression variant: phase frame rebasing', [29, 1, 'lower'], [23, 23, 'clean']), ('partial repair probe: phase frame rebasing', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair variant: phase frame rebasing', [28, 1, 'upper'], [22, 22, 'clean']), ('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: phase frame rebasing', [30, 3, 'lower'], [24, 24, 'clean']), ('regression variant: phase frame rebasing', [15, 1, 'upper'], [12, 12, 'clean']), ('partial repair probe: phase frame rebasing', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair variant: phase frame rebasing', [12, 1, 'upper'], [9, 10, '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: phase frame rebasing[-1, -1, 'clean'][0, 0, 'clean']Failed
regression variant: phase frame rebasing[6, 5, 'mixed'][10, 9, 'mixed']Failed
partial repair probe: phase frame rebasing[8, 9, 'mixed'][12, 13, 'mixed']Failed
partial repair variant: phase frame rebasing[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 / 006d5e0c3449d54a834e1c518c47b558de31cdc4298736d1d18ca5e474286e15

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: phase frame rebasing', [0, 1, 'upper'], [0, 0, 'clean']), ('regression variant: phase frame rebasing', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair probe: phase frame rebasing', [16, 3, 'upper'], [12, 13, 'mixed']), ('partial repair variant: phase frame rebasing', [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: phase frame rebasing', [4, 3, 'lower'], [3, 3, 'clean']), ('regression variant: phase frame rebasing', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair probe: phase frame rebasing', [10, 2, 'upper'], [8, 8, 'clean']), ('partial repair variant: phase frame rebasing', [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: phase frame rebasing', [16, 3, 'upper'], [12, 13, 'mixed']), ('regression variant: phase frame rebasing', [20, 2, 'upper'], [16, 16, 'clean']), ('partial repair probe: phase frame rebasing', [30, 3, 'lower'], [24, 24, 'clean']), ('partial repair variant: phase frame rebasing', [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: phase frame rebasing', [10, 2, 'upper'], [8, 8, 'clean']), ('regression variant: phase frame rebasing', [29, 1, 'lower'], [23, 23, 'clean']), ('partial repair probe: phase frame rebasing', [12, 3, 'lower'], [10, 9, 'mixed']), ('partial repair variant: phase frame rebasing', [28, 1, 'upper'], [22, 22, 'clean']), ('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: phase frame rebasing', [30, 3, 'lower'], [24, 24, 'clean']), ('regression variant: phase frame rebasing', [15, 1, 'upper'], [12, 12, 'clean']), ('partial repair probe: phase frame rebasing', [26, 3, 'upper'], [20, 21, 'mixed']), ('partial repair variant: phase frame rebasing', [12, 1, 'upper'], [9, 10, '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: phase frame rebasing[0, 0, 'clean'][0, 0, 'clean']Passed
regression variant: phase frame rebasing[10, 9, 'mixed'][10, 9, 'mixed']Passed
partial repair probe: phase frame rebasing[12, 13, 'mixed'][12, 13, 'mixed']Passed
partial repair variant: phase frame rebasing[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 / 93309547b493242f62756cad8a8aed6bbb58599a20aa6fd03a40dac12b9334d4

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 2026-09-29T14:49:36.645915+00:00.

Case digest / e7318e9c1811f09d351c0ec709dc62568183188d7ac4aa2fb82bf35b63218821