FA-79666 / Barcode symbology encoding / Open access
Byte mode count indicator follows the numeric progression · case 01
Byte segments at versions 10-26 are written with a 12-bit count and misparse.
ROOT CAUSE
The byte-mode widths are recorded as 8/12/16 instead of 8/16/16.
VERIFIED REPAIR
Byte mode uses 8 bits for versions 1-9 and 16 bits above.
Unsuccessful approach: Keeping 8 bits for the middle band cannot count more than 255 bytes.
Case contract
Compute the length in bits of one QR segment: 4-bit mode indicator, a character count indicator whose width depends on mode and version band (1-9, 10-26, 27-40): numeric 10/12/14, alphanumeric 9/11/13, byte 8/16/16, and the data bits: numeric 10 bits per 3 digits plus 4 or 7 for a remainder of 1 or 2, alphanumeric 11 bits per pair plus 6 for a single, byte 8 bits per UTF-8 byte. Alphanumeric allows 0-9 A-Z space $ % * + - . / :. A count that does not fit the indicator is too-long. Errors: version, charset, mode, too-long.
Why this case matters
Retail, logistics, pharmacy and document workflows depend on encoders that produce exactly the module pattern, code-set switches, separators and quiet zones scanners expect; one misplaced module or separator makes a label unreadable or, worse, scan as different data.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(mode, data, version):
if not 1 <= version <= 40:
return {'error': 'version'}
band = 0 if version <= 9 else (1 if version <= 26 else 2)
ALNUM = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:'
if mode == 'numeric':
if not all(c in '0123456789' for c in data):
return {'error': 'charset'}
count = len(data)
bits = 10 * (count // 3) + [0, 4, 7][count % 3]
cci = [10, 12, 14][band]
elif mode == 'alnum':
if not all(c in ALNUM for c in data):
return {'error': 'charset'}
count = len(data)
bits = 11 * (count // 2) + 6 * (count % 2)
cci = [9, 11, 13][band]
elif mode == 'byte':
count = len(data.encode('utf-8'))
bits = 8 * count
cci = [8, 12, 16][band]
else:
return {'error': 'mode'}
if count >= 1 << cci:
return {'error': 'too-long'}
return 4 + cci + bits
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('byte', '1', 26), 28], [('byte', '11 ', 15), 44], [('alnum', '-/$é+/%é+', 0), {'error': 'version'}], [('alnum', '-', 1), 19], [('alnum', '%', 1), 19], [('byte', '1€11€é', 40), 108], [('alnum', 'ééA- q', 9), {'error': 'charset'}], [('byte', 'b1', 26), 36]], [[('byte', 'éé1 ébé1', 15), 116], [('byte', '€éaéaa', 15), 100], [('numeric', '053142', 0), {'error': 'version'}], [('numeric', '089405', 10), 36], [('kanji', 'b1ab11', 5), {'error': 'mode'}], [('alnum', 'q+$ ', 40), {'error': 'charset'}], [('alnum', '++$:é1*.+', 10), {'error': 'charset'}], [('byte', ' aa1', 10), 52]], [[('byte', '', 26), 20], [('numeric', '00575', 9), 31], [('numeric', '37219', 5), 31], [('numeric', '', 40), 18], [('numeric', '716925614701', 5), 54], [('kanji', 'é b€b', 10), {'error': 'mode'}], [('numeric', '53', 26), 23], [('byte', '€a€', 10), 76]], [[('byte', '', 15), 20], [('byte', 'éb1€ ', 26), 84], [('byte', '€', 41), {'error': 'version'}], [('numeric', '', 0), {'error': 'version'}], [('numeric', '2', 1), 18], [('alnum', '%1.qZ-', 5), {'error': 'charset'}], [('alnum', 'A:*éZA', 40), {'error': 'charset'}], [('byte', 'éb aa€a', 10), 100]], [[('byte', '1é', 26), 44], [('byte', ' éa ', 15), 68], [('kanji', 'é ba', 40), {'error': 'mode'}], [('kanji', 'éb', 1), {'error': 'mode'}], [('alnum', '.', 5), 19], [('byte', '€é1', 27), 68], [('numeric', '4813206244', 15), 50], [('byte', 'a1a', 15), 44]]]
labels = ["regression: byte mode indicator widths", "repair trap", "combined fault", "control", "control", "boundary", "boundary", "control"]
for i, (args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (labels[i % len(labels)], i), 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: byte mode indicator widths 0 | 24 | 28 | Failed |
| repair trap 1 | 40 | 44 | Failed |
| combined fault 2 | {'error': 'version'} | {'error': 'version'} | Passed |
| control 3 | 19 | 19 | Passed |
| control 4 | 19 | 19 | Passed |
| boundary 5 | 108 | 108 | Passed |
| boundary 6 | {'error': 'charset'} | {'error': 'charset'} | Passed |
| control 7 | 32 | 36 | Failed |
SHA-256 / e8dc5f0a6705c487ed158348bd1d64bae5fe30df0b0bcd0d6b9ee33fdfd93ed8
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(mode, data, version):
if not 1 <= version <= 40:
return {'error': 'version'}
band = 0 if version <= 9 else (1 if version <= 26 else 2)
ALNUM = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:'
if mode == 'numeric':
if not all(c in '0123456789' for c in data):
return {'error': 'charset'}
count = len(data)
bits = 10 * (count // 3) + [0, 4, 7][count % 3]
cci = [10, 12, 14][band]
elif mode == 'alnum':
if not all(c in ALNUM for c in data):
return {'error': 'charset'}
count = len(data)
bits = 11 * (count // 2) + 6 * (count % 2)
cci = [9, 11, 13][band]
elif mode == 'byte':
count = len(data.encode('utf-8'))
bits = 8 * count
cci = [8, 8, 16][band]
else:
return {'error': 'mode'}
if count >= 1 << cci:
return {'error': 'too-long'}
return 4 + cci + bits
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('byte', '1', 26), 28], [('byte', '11 ', 15), 44], [('alnum', '-/$é+/%é+', 0), {'error': 'version'}], [('alnum', '-', 1), 19], [('alnum', '%', 1), 19], [('byte', '1€11€é', 40), 108], [('alnum', 'ééA- q', 9), {'error': 'charset'}], [('byte', 'b1', 26), 36]], [[('byte', 'éé1 ébé1', 15), 116], [('byte', '€éaéaa', 15), 100], [('numeric', '053142', 0), {'error': 'version'}], [('numeric', '089405', 10), 36], [('kanji', 'b1ab11', 5), {'error': 'mode'}], [('alnum', 'q+$ ', 40), {'error': 'charset'}], [('alnum', '++$:é1*.+', 10), {'error': 'charset'}], [('byte', ' aa1', 10), 52]], [[('byte', '', 26), 20], [('numeric', '00575', 9), 31], [('numeric', '37219', 5), 31], [('numeric', '', 40), 18], [('numeric', '716925614701', 5), 54], [('kanji', 'é b€b', 10), {'error': 'mode'}], [('numeric', '53', 26), 23], [('byte', '€a€', 10), 76]], [[('byte', '', 15), 20], [('byte', 'éb1€ ', 26), 84], [('byte', '€', 41), {'error': 'version'}], [('numeric', '', 0), {'error': 'version'}], [('numeric', '2', 1), 18], [('alnum', '%1.qZ-', 5), {'error': 'charset'}], [('alnum', 'A:*éZA', 40), {'error': 'charset'}], [('byte', 'éb aa€a', 10), 100]], [[('byte', '1é', 26), 44], [('byte', ' éa ', 15), 68], [('kanji', 'é ba', 40), {'error': 'mode'}], [('kanji', 'éb', 1), {'error': 'mode'}], [('alnum', '.', 5), 19], [('byte', '€é1', 27), 68], [('numeric', '4813206244', 15), 50], [('byte', 'a1a', 15), 44]]]
labels = ["regression: byte mode indicator widths", "repair trap", "combined fault", "control", "control", "boundary", "boundary", "control"]
for i, (args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (labels[i % len(labels)], i), 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: byte mode indicator widths 0 | 20 | 28 | Failed |
| repair trap 1 | 36 | 44 | Failed |
| combined fault 2 | {'error': 'version'} | {'error': 'version'} | Passed |
| control 3 | 19 | 19 | Passed |
| control 4 | 19 | 19 | Passed |
| boundary 5 | 108 | 108 | Passed |
| boundary 6 | {'error': 'charset'} | {'error': 'charset'} | Passed |
| control 7 | 28 | 36 | Failed |
SHA-256 / 4086d87b5b2b487615128a0fd67f4421647a5083b228dc1cfddc6d08496fd266
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(mode, data, version):
if not 1 <= version <= 40:
return {'error': 'version'}
band = 0 if version <= 9 else (1 if version <= 26 else 2)
ALNUM = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./:'
if mode == 'numeric':
if not all(c in '0123456789' for c in data):
return {'error': 'charset'}
count = len(data)
bits = 10 * (count // 3) + [0, 4, 7][count % 3]
cci = [10, 12, 14][band]
elif mode == 'alnum':
if not all(c in ALNUM for c in data):
return {'error': 'charset'}
count = len(data)
bits = 11 * (count // 2) + 6 * (count % 2)
cci = [9, 11, 13][band]
elif mode == 'byte':
count = len(data.encode('utf-8'))
bits = 8 * count
cci = [8, 16, 16][band]
else:
return {'error': 'mode'}
if count >= 1 << cci:
return {'error': 'too-long'}
return 4 + cci + bits
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('byte', '1', 26), 28], [('byte', '11 ', 15), 44], [('alnum', '-/$é+/%é+', 0), {'error': 'version'}], [('alnum', '-', 1), 19], [('alnum', '%', 1), 19], [('byte', '1€11€é', 40), 108], [('alnum', 'ééA- q', 9), {'error': 'charset'}], [('byte', 'b1', 26), 36]], [[('byte', 'éé1 ébé1', 15), 116], [('byte', '€éaéaa', 15), 100], [('numeric', '053142', 0), {'error': 'version'}], [('numeric', '089405', 10), 36], [('kanji', 'b1ab11', 5), {'error': 'mode'}], [('alnum', 'q+$ ', 40), {'error': 'charset'}], [('alnum', '++$:é1*.+', 10), {'error': 'charset'}], [('byte', ' aa1', 10), 52]], [[('byte', '', 26), 20], [('numeric', '00575', 9), 31], [('numeric', '37219', 5), 31], [('numeric', '', 40), 18], [('numeric', '716925614701', 5), 54], [('kanji', 'é b€b', 10), {'error': 'mode'}], [('numeric', '53', 26), 23], [('byte', '€a€', 10), 76]], [[('byte', '', 15), 20], [('byte', 'éb1€ ', 26), 84], [('byte', '€', 41), {'error': 'version'}], [('numeric', '', 0), {'error': 'version'}], [('numeric', '2', 1), 18], [('alnum', '%1.qZ-', 5), {'error': 'charset'}], [('alnum', 'A:*éZA', 40), {'error': 'charset'}], [('byte', 'éb aa€a', 10), 100]], [[('byte', '1é', 26), 44], [('byte', ' éa ', 15), 68], [('kanji', 'é ba', 40), {'error': 'mode'}], [('kanji', 'éb', 1), {'error': 'mode'}], [('alnum', '.', 5), 19], [('byte', '€é1', 27), 68], [('numeric', '4813206244', 15), 50], [('byte', 'a1a', 15), 44]]]
labels = ["regression: byte mode indicator widths", "repair trap", "combined fault", "control", "control", "boundary", "boundary", "control"]
for i, (args, expected) in enumerate(fixtures[N-1]):
check("%s %d" % (labels[i % len(labels)], i), 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: byte mode indicator widths 0 | 28 | 28 | Passed |
| repair trap 1 | 44 | 44 | Passed |
| combined fault 2 | {'error': 'version'} | {'error': 'version'} | Passed |
| control 3 | 19 | 19 | Passed |
| control 4 | 19 | 19 | Passed |
| boundary 5 | 108 | 108 | Passed |
| boundary 6 | {'error': 'charset'} | {'error': 'charset'} | Passed |
| control 7 | 36 | 36 | Passed |
SHA-256 / 929e34a52aef06d672b42dcce3197d5bb0a7553f77ab99adcc42bbd38f4d5520
Verification & scope
A deterministic bounded teaching model with a stipulated contract; it makes no claim of conformance to any published specification. 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 2026-09-29T14:49:46.656267+00:00.
Case digest / e76398f51f59caad971ee74e34332802a1ce668e6afde4c4f63be9ab272b7f9d