FA-79646 / Barcode symbology encoding / Open access
Odd alphanumeric character is sized as a full pair · case 01
Odd-length alphanumeric payloads are overestimated by five bits and may bump the version.
ROOT CAUSE
A trailing single character is counted with the 11-bit pair width.
VERIFIED REPAIR
A single trailing alphanumeric character takes 6 bits.
Unsuccessful approach: Eight bits is the byte-mode width, not the alphanumeric single width.
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 $%*+-./:'
if mode == 'numeric':
if not all(c in '0123456789' for c in data):
return {'error': 'charset'}
count = len(data)
bits = 10 * (count // 3) + [0, 4, 7][count % 3]
cci = [10, 12, 14][band]
elif mode == 'alnum':
if not all(c in ALNUM for c in data):
return {'error': 'charset'}
count = len(data)
bits = 11 * (count // 2) + 11 * (count % 2)
cci = [9, 11, 13][band]
elif mode == 'byte':
count = len(data.encode('utf-8'))
bits = 8 * count
cci = [8, 16, 16][band]
else:
return {'error': 'mode'}
if count >= 1 << cci:
return {'error': 'too-long'}
return 4 + cci + bits
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('alnum', '-', 1), 19], [('alnum', '$', 15), 21], [('alnum', '-/$é+/%é+', 0), {'error': 'version'}], [('byte', '1€11€é', 40), 108], [('alnum', 'ééA- q', 9), {'error': 'charset'}], [('byte', '', 1), 12], [('numeric', '548976', 15), 36], [('alnum', '%', 1), 19]], [[('alnum', ':', 9), 19], [('alnum', 'A', 10), 21], [('numeric', '053142', 0), {'error': 'version'}], [('numeric', '089405', 10), 36], [('kanji', 'b1ab11', 5), {'error': 'mode'}], [('alnum', 'q+$ ', 40), {'error': 'charset'}], [('alnum', '++$:é1*.+', 10), {'error': 'charset'}], [('alnum', ' -/', 26), 32]], [[('alnum', 'A. ', 27), 34], [('alnum', 'A*%/ :Z', 15), 54], [('numeric', '00575', 9), 31], [('numeric', '37219', 5), 31], [('numeric', '', 40), 18], [('numeric', '716925614701', 5), 54], [('kanji', 'é b€b', 10), {'error': 'mode'}], [('alnum', '+:.:Z', 10), 43]], [[('alnum', '$A.', 9), 30], [('alnum', '.1A', 15), 32], [('byte', 'abbbaaa', 26), 76], [('byte', '€', 41), {'error': 'version'}], [('numeric', '', 0), {'error': 'version'}], [('numeric', '2', 1), 18], [('alnum', '%1.qZ-', 5), {'error': 'charset'}], [('alnum', ' ', 40), 23]], [[('alnum', '*:B', 10), 32], [('alnum', '/ -', 40), 34], [('kanji', 'é ba', 40), {'error': 'mode'}], [('kanji', 'éb', 1), {'error': 'mode'}], [('byte', 'a€', 26), 52], [('byte', '€é1', 27), 68], [('numeric', '4813206244', 15), 50], [('alnum', '+', 10), 21]]]
labels = ["regression: alphanumeric trailing character", "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: alphanumeric trailing character 0 | 24 | 19 | Failed |
| repair trap 1 | 26 | 21 | Failed |
| combined fault 2 | {'error': 'version'} | {'error': 'version'} | Passed |
| control 3 | 108 | 108 | Passed |
| control 4 | {'error': 'charset'} | {'error': 'charset'} | Passed |
| boundary 5 | 12 | 12 | Passed |
| boundary 6 | 36 | 36 | Passed |
| control 7 | 24 | 19 | Failed |
SHA-256 / 2d51ed23e12501ae6cd2f41f02967a82cd9b6c2724f1b88e04b906f0cf91a9d2
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 $%*+-./:'
if mode == 'numeric':
if not all(c in '0123456789' for c in data):
return {'error': 'charset'}
count = len(data)
bits = 10 * (count // 3) + [0, 4, 7][count % 3]
cci = [10, 12, 14][band]
elif mode == 'alnum':
if not all(c in ALNUM for c in data):
return {'error': 'charset'}
count = len(data)
bits = 11 * (count // 2) + 8 * (count % 2)
cci = [9, 11, 13][band]
elif mode == 'byte':
count = len(data.encode('utf-8'))
bits = 8 * count
cci = [8, 16, 16][band]
else:
return {'error': 'mode'}
if count >= 1 << cci:
return {'error': 'too-long'}
return 4 + cci + bits
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('alnum', '-', 1), 19], [('alnum', '$', 15), 21], [('alnum', '-/$é+/%é+', 0), {'error': 'version'}], [('byte', '1€11€é', 40), 108], [('alnum', 'ééA- q', 9), {'error': 'charset'}], [('byte', '', 1), 12], [('numeric', '548976', 15), 36], [('alnum', '%', 1), 19]], [[('alnum', ':', 9), 19], [('alnum', 'A', 10), 21], [('numeric', '053142', 0), {'error': 'version'}], [('numeric', '089405', 10), 36], [('kanji', 'b1ab11', 5), {'error': 'mode'}], [('alnum', 'q+$ ', 40), {'error': 'charset'}], [('alnum', '++$:é1*.+', 10), {'error': 'charset'}], [('alnum', ' -/', 26), 32]], [[('alnum', 'A. ', 27), 34], [('alnum', 'A*%/ :Z', 15), 54], [('numeric', '00575', 9), 31], [('numeric', '37219', 5), 31], [('numeric', '', 40), 18], [('numeric', '716925614701', 5), 54], [('kanji', 'é b€b', 10), {'error': 'mode'}], [('alnum', '+:.:Z', 10), 43]], [[('alnum', '$A.', 9), 30], [('alnum', '.1A', 15), 32], [('byte', 'abbbaaa', 26), 76], [('byte', '€', 41), {'error': 'version'}], [('numeric', '', 0), {'error': 'version'}], [('numeric', '2', 1), 18], [('alnum', '%1.qZ-', 5), {'error': 'charset'}], [('alnum', ' ', 40), 23]], [[('alnum', '*:B', 10), 32], [('alnum', '/ -', 40), 34], [('kanji', 'é ba', 40), {'error': 'mode'}], [('kanji', 'éb', 1), {'error': 'mode'}], [('byte', 'a€', 26), 52], [('byte', '€é1', 27), 68], [('numeric', '4813206244', 15), 50], [('alnum', '+', 10), 21]]]
labels = ["regression: alphanumeric trailing character", "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: alphanumeric trailing character 0 | 21 | 19 | Failed |
| repair trap 1 | 23 | 21 | Failed |
| combined fault 2 | {'error': 'version'} | {'error': 'version'} | Passed |
| control 3 | 108 | 108 | Passed |
| control 4 | {'error': 'charset'} | {'error': 'charset'} | Passed |
| boundary 5 | 12 | 12 | Passed |
| boundary 6 | 36 | 36 | Passed |
| control 7 | 21 | 19 | Failed |
SHA-256 / bc7814ae7610efcc0235cfa0843d71eda791a0c7911310f595e7702540721127
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 $%*+-./:'
if mode == 'numeric':
if not all(c in '0123456789' for c in data):
return {'error': 'charset'}
count = len(data)
bits = 10 * (count // 3) + [0, 4, 7][count % 3]
cci = [10, 12, 14][band]
elif mode == 'alnum':
if not all(c in ALNUM for c in data):
return {'error': 'charset'}
count = len(data)
bits = 11 * (count // 2) + 6 * (count % 2)
cci = [9, 11, 13][band]
elif mode == 'byte':
count = len(data.encode('utf-8'))
bits = 8 * count
cci = [8, 16, 16][band]
else:
return {'error': 'mode'}
if count >= 1 << cci:
return {'error': 'too-long'}
return 4 + cci + bits
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('alnum', '-', 1), 19], [('alnum', '$', 15), 21], [('alnum', '-/$é+/%é+', 0), {'error': 'version'}], [('byte', '1€11€é', 40), 108], [('alnum', 'ééA- q', 9), {'error': 'charset'}], [('byte', '', 1), 12], [('numeric', '548976', 15), 36], [('alnum', '%', 1), 19]], [[('alnum', ':', 9), 19], [('alnum', 'A', 10), 21], [('numeric', '053142', 0), {'error': 'version'}], [('numeric', '089405', 10), 36], [('kanji', 'b1ab11', 5), {'error': 'mode'}], [('alnum', 'q+$ ', 40), {'error': 'charset'}], [('alnum', '++$:é1*.+', 10), {'error': 'charset'}], [('alnum', ' -/', 26), 32]], [[('alnum', 'A. ', 27), 34], [('alnum', 'A*%/ :Z', 15), 54], [('numeric', '00575', 9), 31], [('numeric', '37219', 5), 31], [('numeric', '', 40), 18], [('numeric', '716925614701', 5), 54], [('kanji', 'é b€b', 10), {'error': 'mode'}], [('alnum', '+:.:Z', 10), 43]], [[('alnum', '$A.', 9), 30], [('alnum', '.1A', 15), 32], [('byte', 'abbbaaa', 26), 76], [('byte', '€', 41), {'error': 'version'}], [('numeric', '', 0), {'error': 'version'}], [('numeric', '2', 1), 18], [('alnum', '%1.qZ-', 5), {'error': 'charset'}], [('alnum', ' ', 40), 23]], [[('alnum', '*:B', 10), 32], [('alnum', '/ -', 40), 34], [('kanji', 'é ba', 40), {'error': 'mode'}], [('kanji', 'éb', 1), {'error': 'mode'}], [('byte', 'a€', 26), 52], [('byte', '€é1', 27), 68], [('numeric', '4813206244', 15), 50], [('alnum', '+', 10), 21]]]
labels = ["regression: alphanumeric trailing character", "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: alphanumeric trailing character 0 | 19 | 19 | Passed |
| repair trap 1 | 21 | 21 | Passed |
| combined fault 2 | {'error': 'version'} | {'error': 'version'} | Passed |
| control 3 | 108 | 108 | Passed |
| control 4 | {'error': 'charset'} | {'error': 'charset'} | Passed |
| boundary 5 | 12 | 12 | Passed |
| boundary 6 | 36 | 36 | Passed |
| control 7 | 19 | 19 | Passed |
SHA-256 / 0dc708728014e6f17b084205737fd8316abc0a81e0a59e3e759cbb05c22f7799
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 2026-09-29T14:49:46.384300+00:00.
Case digest / 4cbd8130b8324c4f2ab9d0bdb24e0db25d67427ebac091dcefc85715fa297363