FA-78546 / Broadcast timecode arithmetic / Open access
2:3 pulldown film frame placement: field offset table · case 01
B-frames are placed as if every film frame had two fields.
ROOT CAUSE
The in-group field offsets ignore the three-field frames.
VERIFIED REPAIR
Use offsets 0, 2, 5, 7 for A, B, C, D.
Unsuccessful approach: The 3:2 offsets describe a different cadence starting with a three-field frame.
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)+[0,2,4,6][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 offset table', [3, 0], [3, 'lower', 3]), ('regression variant: field offset table', [10, 1], [12, 'lower', 3]), ('partial repair probe: field offset table', [9, 1], [11, 'lower', 2]), ('partial repair variant: field offset table', [21, 2], [26, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [0, 1], [0, 'upper', 3]), ('normal control', [8, 0], [10, 'upper', 2]), ('normal control', [36, 1], [45, 'upper', 3])], [('regression: field offset table', [2, 3], [2, 'lower', 3]), ('regression variant: field offset table', [22, 2], [27, 'lower', 2]), ('partial repair probe: field offset table', [35, 1], [44, 'upper', 2]), ('partial repair variant: field offset table', [19, 2], [23, 'lower', 3]), ('boundary control', [4, 0], [5, 'upper', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('normal control', [-6, 0], None), ('normal control', [-2, 3], None), ('normal control', [-3, 1], None)], [('regression: field offset table', [9, 1], [11, 'lower', 2]), ('regression variant: field offset table', [26, 2], [32, 'lower', 2]), ('partial repair probe: field offset table', [9, 3], [11, 'lower', 2]), ('partial repair variant: field offset table', [17, 1], [21, 'lower', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('normal control', [-6, 1], None), ('normal control', [-3, 0], None), ('normal control', [8, 3], [10, 'upper', 3])], [('regression: field offset table', [34, 2], [42, 'lower', 2]), ('regression variant: field offset table', [38, 3], [47, 'lower', 3]), ('partial repair probe: field offset table', [1, 3], [1, 'lower', 2]), ('partial repair variant: field offset table', [5, 2], [6, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [-1, 1], None), ('normal control', [36, 0], [45, 'upper', 2]), ('normal control', [-3, 3], None)], [('regression: field offset table', [9, 3], [11, 'lower', 2]), ('regression variant: field offset table', [1, 3], [1, 'lower', 2]), ('partial repair probe: field offset table', [3, 2], [3, 'lower', 3]), ('partial repair variant: field offset table', [7, 2], [8, 'lower', 3]), ('boundary control', [4, 0], [5, 'upper', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('normal control', [28, 0], [35, 'upper', 2]), ('normal control', [28, 3], [35, 'upper', 3]), ('normal control', [24, 1], [30, 'upper', 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: field offset table | [3, 'upper', 3] | [3, 'lower', 3] | Failed |
| regression variant: field offset table | [12, 'upper', 3] | [12, 'lower', 3] | Failed |
| partial repair probe: field offset table | [11, 'upper', 2] | [11, 'lower', 2] | Failed |
| partial repair variant: field offset table | [26, 'upper', 3] | [26, 'upper', 3] | Passed |
| boundary control | [0, 'upper', 2] | [0, 'upper', 2] | Passed |
| boundary control | [5, 'upper', 2] | [5, 'upper', 2] | Passed |
| normal control | [0, 'upper', 3] | [0, 'upper', 3] | Passed |
| normal control | [10, 'upper', 2] | [10, 'upper', 2] | Passed |
| normal control | [45, 'upper', 3] | [45, 'upper', 3] | Passed |
SHA-256 / 435b2d14844165f514ec96f9cfdbf010d60d6d68de40e6f551d7305ab41a09a3
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)+[0,3,5,8][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 offset table', [3, 0], [3, 'lower', 3]), ('regression variant: field offset table', [10, 1], [12, 'lower', 3]), ('partial repair probe: field offset table', [9, 1], [11, 'lower', 2]), ('partial repair variant: field offset table', [21, 2], [26, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [0, 1], [0, 'upper', 3]), ('normal control', [8, 0], [10, 'upper', 2]), ('normal control', [36, 1], [45, 'upper', 3])], [('regression: field offset table', [2, 3], [2, 'lower', 3]), ('regression variant: field offset table', [22, 2], [27, 'lower', 2]), ('partial repair probe: field offset table', [35, 1], [44, 'upper', 2]), ('partial repair variant: field offset table', [19, 2], [23, 'lower', 3]), ('boundary control', [4, 0], [5, 'upper', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('normal control', [-6, 0], None), ('normal control', [-2, 3], None), ('normal control', [-3, 1], None)], [('regression: field offset table', [9, 1], [11, 'lower', 2]), ('regression variant: field offset table', [26, 2], [32, 'lower', 2]), ('partial repair probe: field offset table', [9, 3], [11, 'lower', 2]), ('partial repair variant: field offset table', [17, 1], [21, 'lower', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('normal control', [-6, 1], None), ('normal control', [-3, 0], None), ('normal control', [8, 3], [10, 'upper', 3])], [('regression: field offset table', [34, 2], [42, 'lower', 2]), ('regression variant: field offset table', [38, 3], [47, 'lower', 3]), ('partial repair probe: field offset table', [1, 3], [1, 'lower', 2]), ('partial repair variant: field offset table', [5, 2], [6, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [-1, 1], None), ('normal control', [36, 0], [45, 'upper', 2]), ('normal control', [-3, 3], None)], [('regression: field offset table', [9, 3], [11, 'lower', 2]), ('regression variant: field offset table', [1, 3], [1, 'lower', 2]), ('partial repair probe: field offset table', [3, 2], [3, 'lower', 3]), ('partial repair variant: field offset table', [7, 2], [8, 'lower', 3]), ('boundary control', [4, 0], [5, 'upper', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('normal control', [28, 0], [35, 'upper', 2]), ('normal control', [28, 3], [35, 'upper', 3]), ('normal control', [24, 1], [30, 'upper', 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: field offset table | [4, 'upper', 3] | [3, 'lower', 3] | Failed |
| regression variant: field offset table | [12, 'lower', 3] | [12, 'lower', 3] | Passed |
| partial repair probe: field offset table | [11, 'upper', 2] | [11, 'lower', 2] | Failed |
| partial repair variant: field offset table | [26, 'lower', 3] | [26, 'upper', 3] | Failed |
| boundary control | [0, 'upper', 2] | [0, 'upper', 2] | Passed |
| boundary control | [5, 'upper', 2] | [5, 'upper', 2] | Passed |
| normal control | [0, 'upper', 3] | [0, 'upper', 3] | Passed |
| normal control | [10, 'upper', 2] | [10, 'upper', 2] | Passed |
| normal control | [45, 'upper', 3] | [45, 'upper', 3] | Passed |
SHA-256 / a470d1e066533a0d9000f1fdc99b544db00a2b226bb1b92b97de2deaf980cd08
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 offset table', [3, 0], [3, 'lower', 3]), ('regression variant: field offset table', [10, 1], [12, 'lower', 3]), ('partial repair probe: field offset table', [9, 1], [11, 'lower', 2]), ('partial repair variant: field offset table', [21, 2], [26, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [0, 1], [0, 'upper', 3]), ('normal control', [8, 0], [10, 'upper', 2]), ('normal control', [36, 1], [45, 'upper', 3])], [('regression: field offset table', [2, 3], [2, 'lower', 3]), ('regression variant: field offset table', [22, 2], [27, 'lower', 2]), ('partial repair probe: field offset table', [35, 1], [44, 'upper', 2]), ('partial repair variant: field offset table', [19, 2], [23, 'lower', 3]), ('boundary control', [4, 0], [5, 'upper', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('normal control', [-6, 0], None), ('normal control', [-2, 3], None), ('normal control', [-3, 1], None)], [('regression: field offset table', [9, 1], [11, 'lower', 2]), ('regression variant: field offset table', [26, 2], [32, 'lower', 2]), ('partial repair probe: field offset table', [9, 3], [11, 'lower', 2]), ('partial repair variant: field offset table', [17, 1], [21, 'lower', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('normal control', [-6, 1], None), ('normal control', [-3, 0], None), ('normal control', [8, 3], [10, 'upper', 3])], [('regression: field offset table', [34, 2], [42, 'lower', 2]), ('regression variant: field offset table', [38, 3], [47, 'lower', 3]), ('partial repair probe: field offset table', [1, 3], [1, 'lower', 2]), ('partial repair variant: field offset table', [5, 2], [6, 'upper', 3]), ('boundary control', [0, 0], [0, 'upper', 2]), ('boundary control', [4, 0], [5, 'upper', 2]), ('normal control', [-1, 1], None), ('normal control', [36, 0], [45, 'upper', 2]), ('normal control', [-3, 3], None)], [('regression: field offset table', [9, 3], [11, 'lower', 2]), ('regression variant: field offset table', [1, 3], [1, 'lower', 2]), ('partial repair probe: field offset table', [3, 2], [3, 'lower', 3]), ('partial repair variant: field offset table', [7, 2], [8, 'lower', 3]), ('boundary control', [4, 0], [5, 'upper', 2]), ('boundary control', [0, 1], [0, 'upper', 3]), ('normal control', [28, 0], [35, 'upper', 2]), ('normal control', [28, 3], [35, 'upper', 3]), ('normal control', [24, 1], [30, 'upper', 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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: field offset table | [3, 'lower', 3] | [3, 'lower', 3] | Passed |
| regression variant: field offset table | [12, 'lower', 3] | [12, 'lower', 3] | Passed |
| partial repair probe: field offset table | [11, 'lower', 2] | [11, 'lower', 2] | Passed |
| partial repair variant: field offset table | [26, 'upper', 3] | [26, 'upper', 3] | Passed |
| boundary control | [0, 'upper', 2] | [0, 'upper', 2] | Passed |
| boundary control | [5, 'upper', 2] | [5, 'upper', 2] | Passed |
| normal control | [0, 'upper', 3] | [0, 'upper', 3] | Passed |
| normal control | [10, 'upper', 2] | [10, 'upper', 2] | Passed |
| normal control | [45, 'upper', 3] | [45, 'upper', 3] | Passed |
SHA-256 / 59899212c5868cf98dadd108886fc5b438ba36c0701ef21601e21e3e15b9efda
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 2026-09-29T14:49:36.300938+00:00.
Case digest / f85ad74fceaba439839347cc3a95e09e20db1c08478b073c96d963b945f998b6