FA-78621 / Broadcast timecode arithmetic / Open access
Linear timecode BCD field packing: drop-frame flag bit · case 01
Drop-frame timecode corrupts the frame units digit.
ROOT CAUSE
The drop-frame flag is written into bit 2, inside the units nibble.
VERIFIED REPAIR
Set bit 6 of the frames byte for drop frame.
Unsuccessful approach: Bit 5 belongs to the frames tens digit.
Case contract
Pack HH:MM:SS:FF into four bytes [frames, seconds, minutes, hours] in transmission order. Each byte holds units in bits 0-3 and tens from bit 4 upward. The frames byte carries the drop-frame flag (bit 6, set when the last separator is ";") and the color-frame flag (bit 7).
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
import re
N = 1
observations = []
def solve(tc, color):
h,m,s,f=map(int,re.split('[:;]',tc))
drop=';' in tc
def bcd(v,flags):
return (v//10)<<4|v%10|flags
b0=bcd(f,(0x04 if drop else 0)|(0x80 if color else 0))
b1=bcd(s,0)
b2=bcd(m,0)
b3=bcd(h,0)
return [b0,b1,b2,b3]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: drop-frame flag bit', ['23:59:59;29', True], [233, 89, 89, 35]), ('regression variant: drop-frame flag bit', ['10:00:10;19', True], [217, 16, 0, 16]), ('partial repair probe: drop-frame flag bit', ['10:10:09;24', False], [100, 9, 16, 16]), ('partial repair variant: drop-frame flag bit', ['10:00:10;09', False], [73, 16, 0, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('normal control', ['01:07:10:29', True], [169, 16, 7, 1]), ('normal control', ['00:00:00:00', True], [128, 0, 0, 0]), ('normal control', ['00:07:09:29', True], [169, 9, 7, 0])], [('regression: drop-frame flag bit', ['01:02:03;04', False], [68, 3, 2, 1]), ('regression variant: drop-frame flag bit', ['10:59:10;24', True], [228, 16, 89, 16]), ('partial repair probe: drop-frame flag bit', ['00:00:00;00', False], [64, 0, 0, 0]), ('partial repair variant: drop-frame flag bit', ['01:07:00;19', False], [89, 0, 7, 1]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('normal control', ['10:07:59:01', False], [1, 89, 7, 16]), ('normal control', ['23:10:09:01', False], [1, 9, 16, 35]), ('normal control', ['01:10:00:24', False], [36, 0, 16, 1])], [('regression: drop-frame flag bit', ['10:10:09;24', False], [100, 9, 16, 16]), ('regression variant: drop-frame flag bit', ['01:00:59;19', True], [217, 89, 0, 1]), ('partial repair probe: drop-frame flag bit', ['19:00:09;19', True], [217, 9, 0, 25]), ('partial repair variant: drop-frame flag bit', ['19:07:09;19', True], [217, 9, 7, 25]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('normal control', ['23:07:10:00', True], [128, 16, 7, 35]), ('normal control', ['00:00:09:24', True], [164, 9, 0, 0]), ('normal control', ['23:10:45:09', False], [9, 69, 16, 35])], [('regression: drop-frame flag bit', ['00:00:00;00', False], [64, 0, 0, 0]), ('regression variant: drop-frame flag bit', ['23:59:59;01', True], [193, 89, 89, 35]), ('partial repair probe: drop-frame flag bit', ['10:00:10;19', True], [217, 16, 0, 16]), ('partial repair variant: drop-frame flag bit', ['23:07:00;00', False], [64, 0, 7, 35]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('normal control', ['23:10:00:29', False], [41, 0, 16, 35]), ('normal control', ['19:59:09:00', True], [128, 9, 89, 25]), ('normal control', ['19:59:45:29', True], [169, 69, 89, 25])], [('regression: drop-frame flag bit', ['19:00:09;19', True], [217, 9, 0, 25]), ('regression variant: drop-frame flag bit', ['10:00:10;09', False], [73, 16, 0, 16]), ('partial repair probe: drop-frame flag bit', ['10:59:10;24', True], [228, 16, 89, 16]), ('partial repair variant: drop-frame flag bit', ['10:10:00;29', False], [105, 0, 16, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('normal control', ['10:00:59:29', False], [41, 89, 0, 16]), ('normal control', ['19:00:09:29', False], [41, 9, 0, 25]), ('normal control', ['01:59:10:01', True], [129, 16, 89, 1])]]
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: drop-frame flag bit | [173, 89, 89, 35] | [233, 89, 89, 35] | Failed |
| regression variant: drop-frame flag bit | [157, 16, 0, 16] | [217, 16, 0, 16] | Failed |
| partial repair probe: drop-frame flag bit | [36, 9, 16, 16] | [100, 9, 16, 16] | Failed |
| partial repair variant: drop-frame flag bit | [13, 16, 0, 16] | [73, 16, 0, 16] | Failed |
| boundary control | [0, 0, 0, 0] | [0, 0, 0, 0] | Passed |
| boundary control | [16, 16, 16, 16] | [16, 16, 16, 16] | Passed |
| normal control | [169, 16, 7, 1] | [169, 16, 7, 1] | Passed |
| normal control | [128, 0, 0, 0] | [128, 0, 0, 0] | Passed |
| normal control | [169, 9, 7, 0] | [169, 9, 7, 0] | Passed |
SHA-256 / a576566ab8d7bb72174ad6c3aba49af65d4e006189f0a5f8a2c1b82e81342ccd
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import re
N = 1
observations = []
def solve(tc, color):
h,m,s,f=map(int,re.split('[:;]',tc))
drop=';' in tc
def bcd(v,flags):
return (v//10)<<4|v%10|flags
b0=bcd(f,(0x20 if drop else 0)|(0x80 if color else 0))
b1=bcd(s,0)
b2=bcd(m,0)
b3=bcd(h,0)
return [b0,b1,b2,b3]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: drop-frame flag bit', ['23:59:59;29', True], [233, 89, 89, 35]), ('regression variant: drop-frame flag bit', ['10:00:10;19', True], [217, 16, 0, 16]), ('partial repair probe: drop-frame flag bit', ['10:10:09;24', False], [100, 9, 16, 16]), ('partial repair variant: drop-frame flag bit', ['10:00:10;09', False], [73, 16, 0, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('normal control', ['01:07:10:29', True], [169, 16, 7, 1]), ('normal control', ['00:00:00:00', True], [128, 0, 0, 0]), ('normal control', ['00:07:09:29', True], [169, 9, 7, 0])], [('regression: drop-frame flag bit', ['01:02:03;04', False], [68, 3, 2, 1]), ('regression variant: drop-frame flag bit', ['10:59:10;24', True], [228, 16, 89, 16]), ('partial repair probe: drop-frame flag bit', ['00:00:00;00', False], [64, 0, 0, 0]), ('partial repair variant: drop-frame flag bit', ['01:07:00;19', False], [89, 0, 7, 1]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('normal control', ['10:07:59:01', False], [1, 89, 7, 16]), ('normal control', ['23:10:09:01', False], [1, 9, 16, 35]), ('normal control', ['01:10:00:24', False], [36, 0, 16, 1])], [('regression: drop-frame flag bit', ['10:10:09;24', False], [100, 9, 16, 16]), ('regression variant: drop-frame flag bit', ['01:00:59;19', True], [217, 89, 0, 1]), ('partial repair probe: drop-frame flag bit', ['19:00:09;19', True], [217, 9, 0, 25]), ('partial repair variant: drop-frame flag bit', ['19:07:09;19', True], [217, 9, 7, 25]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('normal control', ['23:07:10:00', True], [128, 16, 7, 35]), ('normal control', ['00:00:09:24', True], [164, 9, 0, 0]), ('normal control', ['23:10:45:09', False], [9, 69, 16, 35])], [('regression: drop-frame flag bit', ['00:00:00;00', False], [64, 0, 0, 0]), ('regression variant: drop-frame flag bit', ['23:59:59;01', True], [193, 89, 89, 35]), ('partial repair probe: drop-frame flag bit', ['10:00:10;19', True], [217, 16, 0, 16]), ('partial repair variant: drop-frame flag bit', ['23:07:00;00', False], [64, 0, 7, 35]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('normal control', ['23:10:00:29', False], [41, 0, 16, 35]), ('normal control', ['19:59:09:00', True], [128, 9, 89, 25]), ('normal control', ['19:59:45:29', True], [169, 69, 89, 25])], [('regression: drop-frame flag bit', ['19:00:09;19', True], [217, 9, 0, 25]), ('regression variant: drop-frame flag bit', ['10:00:10;09', False], [73, 16, 0, 16]), ('partial repair probe: drop-frame flag bit', ['10:59:10;24', True], [228, 16, 89, 16]), ('partial repair variant: drop-frame flag bit', ['10:10:00;29', False], [105, 0, 16, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('normal control', ['10:00:59:29', False], [41, 89, 0, 16]), ('normal control', ['19:00:09:29', False], [41, 9, 0, 25]), ('normal control', ['01:59:10:01', True], [129, 16, 89, 1])]]
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: drop-frame flag bit | [169, 89, 89, 35] | [233, 89, 89, 35] | Failed |
| regression variant: drop-frame flag bit | [185, 16, 0, 16] | [217, 16, 0, 16] | Failed |
| partial repair probe: drop-frame flag bit | [36, 9, 16, 16] | [100, 9, 16, 16] | Failed |
| partial repair variant: drop-frame flag bit | [41, 16, 0, 16] | [73, 16, 0, 16] | Failed |
| boundary control | [0, 0, 0, 0] | [0, 0, 0, 0] | Passed |
| boundary control | [16, 16, 16, 16] | [16, 16, 16, 16] | Passed |
| normal control | [169, 16, 7, 1] | [169, 16, 7, 1] | Passed |
| normal control | [128, 0, 0, 0] | [128, 0, 0, 0] | Passed |
| normal control | [169, 9, 7, 0] | [169, 9, 7, 0] | Passed |
SHA-256 / 4ab32a5db888ab5940d87a0fa981165dd710e30a9f0fb9e62ef81820ecf8fff4
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import re
N = 1
observations = []
def solve(tc, color):
h,m,s,f=map(int,re.split('[:;]',tc))
drop=';' in tc
def bcd(v,flags):
return (v//10)<<4|v%10|flags
b0=bcd(f,(0x40 if drop else 0)|(0x80 if color else 0))
b1=bcd(s,0)
b2=bcd(m,0)
b3=bcd(h,0)
return [b0,b1,b2,b3]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: drop-frame flag bit', ['23:59:59;29', True], [233, 89, 89, 35]), ('regression variant: drop-frame flag bit', ['10:00:10;19', True], [217, 16, 0, 16]), ('partial repair probe: drop-frame flag bit', ['10:10:09;24', False], [100, 9, 16, 16]), ('partial repair variant: drop-frame flag bit', ['10:00:10;09', False], [73, 16, 0, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('normal control', ['01:07:10:29', True], [169, 16, 7, 1]), ('normal control', ['00:00:00:00', True], [128, 0, 0, 0]), ('normal control', ['00:07:09:29', True], [169, 9, 7, 0])], [('regression: drop-frame flag bit', ['01:02:03;04', False], [68, 3, 2, 1]), ('regression variant: drop-frame flag bit', ['10:59:10;24', True], [228, 16, 89, 16]), ('partial repair probe: drop-frame flag bit', ['00:00:00;00', False], [64, 0, 0, 0]), ('partial repair variant: drop-frame flag bit', ['01:07:00;19', False], [89, 0, 7, 1]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('normal control', ['10:07:59:01', False], [1, 89, 7, 16]), ('normal control', ['23:10:09:01', False], [1, 9, 16, 35]), ('normal control', ['01:10:00:24', False], [36, 0, 16, 1])], [('regression: drop-frame flag bit', ['10:10:09;24', False], [100, 9, 16, 16]), ('regression variant: drop-frame flag bit', ['01:00:59;19', True], [217, 89, 0, 1]), ('partial repair probe: drop-frame flag bit', ['19:00:09;19', True], [217, 9, 0, 25]), ('partial repair variant: drop-frame flag bit', ['19:07:09;19', True], [217, 9, 7, 25]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('normal control', ['23:07:10:00', True], [128, 16, 7, 35]), ('normal control', ['00:00:09:24', True], [164, 9, 0, 0]), ('normal control', ['23:10:45:09', False], [9, 69, 16, 35])], [('regression: drop-frame flag bit', ['00:00:00;00', False], [64, 0, 0, 0]), ('regression variant: drop-frame flag bit', ['23:59:59;01', True], [193, 89, 89, 35]), ('partial repair probe: drop-frame flag bit', ['10:00:10;19', True], [217, 16, 0, 16]), ('partial repair variant: drop-frame flag bit', ['23:07:00;00', False], [64, 0, 7, 35]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('normal control', ['23:10:00:29', False], [41, 0, 16, 35]), ('normal control', ['19:59:09:00', True], [128, 9, 89, 25]), ('normal control', ['19:59:45:29', True], [169, 69, 89, 25])], [('regression: drop-frame flag bit', ['19:00:09;19', True], [217, 9, 0, 25]), ('regression variant: drop-frame flag bit', ['10:00:10;09', False], [73, 16, 0, 16]), ('partial repair probe: drop-frame flag bit', ['10:59:10;24', True], [228, 16, 89, 16]), ('partial repair variant: drop-frame flag bit', ['10:10:00;29', False], [105, 0, 16, 16]), ('boundary control', ['00:00:00:00', False], [0, 0, 0, 0]), ('boundary control', ['10:10:10:10', False], [16, 16, 16, 16]), ('normal control', ['10:00:59:29', False], [41, 89, 0, 16]), ('normal control', ['19:00:09:29', False], [41, 9, 0, 25]), ('normal control', ['01:59:10:01', True], [129, 16, 89, 1])]]
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: drop-frame flag bit | [233, 89, 89, 35] | [233, 89, 89, 35] | Passed |
| regression variant: drop-frame flag bit | [217, 16, 0, 16] | [217, 16, 0, 16] | Passed |
| partial repair probe: drop-frame flag bit | [100, 9, 16, 16] | [100, 9, 16, 16] | Passed |
| partial repair variant: drop-frame flag bit | [73, 16, 0, 16] | [73, 16, 0, 16] | Passed |
| boundary control | [0, 0, 0, 0] | [0, 0, 0, 0] | Passed |
| boundary control | [16, 16, 16, 16] | [16, 16, 16, 16] | Passed |
| normal control | [169, 16, 7, 1] | [169, 16, 7, 1] | Passed |
| normal control | [128, 0, 0, 0] | [128, 0, 0, 0] | Passed |
| normal control | [169, 9, 7, 0] | [169, 9, 7, 0] | Passed |
SHA-256 / 4e114f96a35bc6a3066ce997eb85111ce8196268168a4cfcc7a5163c27bba727
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 2026-09-29T14:49:37.082072+00:00.
Case digest / 8db9e5ec56a411ed03e0abd97949d58b9c2bfd7acf76da60c83b205a94fa9245