FA-79821 / Barcode symbology encoding / Open access

Pharmacode accepts a seventeen-bar value · case 01

Value 131071 produces 17 narrow bars that exceed the symbol definition.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The upper bound allows 131071.

VERIFIED REPAIR

Accept values up to 131070.

Unsuccessful approach: A 16-bit bound rejects valid values between 65536 and 131070.

Case contract

Encode an integer 3..131070 as a one-track Pharmacode: repeatedly, an even value adds a wide bar and becomes (n - 2) / 2, an odd value adds a narrow bar and becomes (n - 1) / 2, until zero; bars are read in the reverse order of generation (left to right). Width: narrow 1, wide 3, spaces 2 between bars. Return [pattern, width] or None outside the range.

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(n):
    if not isinstance(n, int) or n < 3 or n > 131071:
        return None
    bars = []
    while n > 0:
        if n % 2 == 0:
            bars.append('w')
            n = (n - 2) // 2
        else:
            bars.append('n')
            n = (n - 1) // 2
    bars.reverse()
    width = sum(3 if b == 'w' else 1 for b in bars) + 2 * (len(bars) - 1)
    return [''.join(bars), width]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[131071, None], [88037, ['nwnwnwwwwwwnnwwn', 66]], [34, ['nnnww', 17]], [306, ['nnwwnnww', 30]], [371, ['nwwwnwnn', 30]], [120, ['wwwnnw', 24]], [98, ['wnnnww', 22]], [124778, ['wwwnnwwwnwwnwnww', 68]]], [[131071, None], [96385, ['nwwwwnnnwnnnnnwn', 58]], [6, ['ww', 8]], [85, ['nwnwwn', 22]], [155, ['nnwwwnn', 25]], [306, ['nnwwnnww', 30]], [201, ['wnnwnwn', 25]], [106660, ['wnwnnnnnwnwnnwnw', 58]]], [[131071, None], [93303, ['nwwnwwnnnwwwwnnn', 62]], [142, ['nnnwwww', 27]], [335, ['nwnwnnnn', 26]], [232, ['wwnwnnw', 27]], [397, ['wnnnwwwn', 30]], [147, ['nnwnwnn', 23]], [130692, ['wwwwwwwnwnnnnwnw', 66]]], [[131071, None], [80722, ['nnwwwnwwnwnwnnww', 64]], [229, ['wwnnwwn', 27]], [157, ['nnwwwwn', 27]], [19, ['nwnn', 12]], [27, ['wwnn', 14]], [36, ['nnwnw', 17]], [72515, ['nnnwwnwwnwnnnwnn', 58]]], [[131071, None], [98004, ['nwwwwwwnwwnwnwnw', 68]], [157, ['nnwwwwn', 27]], [228, ['wwnnwnw', 27]], [361, ['nwwnwnwn', 30]], [153, ['nnwwnwn', 25]], [326, ['nwnnnwww', 30]], [84211, ['nwnnwnnnwwwwnwnn', 60]]]]
labels = ["regression: maximum encodable value", "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: maximum encodable value 0	`['nnnnnnnnnnnnnnnnn', 49]`	`None`	Failed
repair trap 1	`['nwnwnwwwwwwnnwwn', 66]`	`['nwnwnwwwwwwnnwwn', 66]`	Passed
combined fault 2	`['nnnww', 17]`	`['nnnww', 17]`	Passed
control 3	`['nnwwnnww', 30]`	`['nnwwnnww', 30]`	Passed
control 4	`['nwwwnwnn', 30]`	`['nwwwnwnn', 30]`	Passed
boundary 5	`['wwwnnw', 24]`	`['wwwnnw', 24]`	Passed
boundary 6	`['wnnnww', 22]`	`['wnnnww', 22]`	Passed
control 7	`['wwwnnwwwnwwnwnww', 68]`	`['wwwnnwwwnwwnwnww', 68]`	Passed

SHA-256 / 7f7795525e68ac935e084db8cd62c93fffad4ebcbcc4c4c72caccd271d38e55c

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(n):
    if not isinstance(n, int) or n < 3 or n > 65535:
        return None
    bars = []
    while n > 0:
        if n % 2 == 0:
            bars.append('w')
            n = (n - 2) // 2
        else:
            bars.append('n')
            n = (n - 1) // 2
    bars.reverse()
    width = sum(3 if b == 'w' else 1 for b in bars) + 2 * (len(bars) - 1)
    return [''.join(bars), width]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[131071, None], [88037, ['nwnwnwwwwwwnnwwn', 66]], [34, ['nnnww', 17]], [306, ['nnwwnnww', 30]], [371, ['nwwwnwnn', 30]], [120, ['wwwnnw', 24]], [98, ['wnnnww', 22]], [124778, ['wwwnnwwwnwwnwnww', 68]]], [[131071, None], [96385, ['nwwwwnnnwnnnnnwn', 58]], [6, ['ww', 8]], [85, ['nwnwwn', 22]], [155, ['nnwwwnn', 25]], [306, ['nnwwnnww', 30]], [201, ['wnnwnwn', 25]], [106660, ['wnwnnnnnwnwnnwnw', 58]]], [[131071, None], [93303, ['nwwnwwnnnwwwwnnn', 62]], [142, ['nnnwwww', 27]], [335, ['nwnwnnnn', 26]], [232, ['wwnwnnw', 27]], [397, ['wnnnwwwn', 30]], [147, ['nnwnwnn', 23]], [130692, ['wwwwwwwnwnnnnwnw', 66]]], [[131071, None], [80722, ['nnwwwnwwnwnwnnww', 64]], [229, ['wwnnwwn', 27]], [157, ['nnwwwwn', 27]], [19, ['nwnn', 12]], [27, ['wwnn', 14]], [36, ['nnwnw', 17]], [72515, ['nnnwwnwwnwnnnwnn', 58]]], [[131071, None], [98004, ['nwwwwwwnwwnwnwnw', 68]], [157, ['nnwwwwn', 27]], [228, ['wwnnwnw', 27]], [361, ['nwwnwnwn', 30]], [153, ['nnwwnwn', 25]], [326, ['nwnnnwww', 30]], [84211, ['nwnnwnnnwwwwnwnn', 60]]]]
labels = ["regression: maximum encodable value", "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: maximum encodable value 0	`None`	`None`	Passed
repair trap 1	`None`	`['nwnwnwwwwwwnnwwn', 66]`	Failed
combined fault 2	`['nnnww', 17]`	`['nnnww', 17]`	Passed
control 3	`['nnwwnnww', 30]`	`['nnwwnnww', 30]`	Passed
control 4	`['nwwwnwnn', 30]`	`['nwwwnwnn', 30]`	Passed
boundary 5	`['wwwnnw', 24]`	`['wwwnnw', 24]`	Passed
boundary 6	`['wnnnww', 22]`	`['wnnnww', 22]`	Passed
control 7	`None`	`['wwwnnwwwnwwnwnww', 68]`	Failed

SHA-256 / 44266b55b1dd990874c64f5e1425e3b0740ed49d89e99dfbf808d832b0f5a6fd

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(n):
    if not isinstance(n, int) or n < 3 or n > 131070:
        return None
    bars = []
    while n > 0:
        if n % 2 == 0:
            bars.append('w')
            n = (n - 2) // 2
        else:
            bars.append('n')
            n = (n - 1) // 2
    bars.reverse()
    width = sum(3 if b == 'w' else 1 for b in bars) + 2 * (len(bars) - 1)
    return [''.join(bars), width]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[131071, None], [88037, ['nwnwnwwwwwwnnwwn', 66]], [34, ['nnnww', 17]], [306, ['nnwwnnww', 30]], [371, ['nwwwnwnn', 30]], [120, ['wwwnnw', 24]], [98, ['wnnnww', 22]], [124778, ['wwwnnwwwnwwnwnww', 68]]], [[131071, None], [96385, ['nwwwwnnnwnnnnnwn', 58]], [6, ['ww', 8]], [85, ['nwnwwn', 22]], [155, ['nnwwwnn', 25]], [306, ['nnwwnnww', 30]], [201, ['wnnwnwn', 25]], [106660, ['wnwnnnnnwnwnnwnw', 58]]], [[131071, None], [93303, ['nwwnwwnnnwwwwnnn', 62]], [142, ['nnnwwww', 27]], [335, ['nwnwnnnn', 26]], [232, ['wwnwnnw', 27]], [397, ['wnnnwwwn', 30]], [147, ['nnwnwnn', 23]], [130692, ['wwwwwwwnwnnnnwnw', 66]]], [[131071, None], [80722, ['nnwwwnwwnwnwnnww', 64]], [229, ['wwnnwwn', 27]], [157, ['nnwwwwn', 27]], [19, ['nwnn', 12]], [27, ['wwnn', 14]], [36, ['nnwnw', 17]], [72515, ['nnnwwnwwnwnnnwnn', 58]]], [[131071, None], [98004, ['nwwwwwwnwwnwnwnw', 68]], [157, ['nnwwwwn', 27]], [228, ['wwnnwnw', 27]], [361, ['nwwnwnwn', 30]], [153, ['nnwwnwn', 25]], [326, ['nwnnnwww', 30]], [84211, ['nwnnwnnnwwwwnwnn', 60]]]]
labels = ["regression: maximum encodable value", "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: maximum encodable value 0	`None`	`None`	Passed
repair trap 1	`['nwnwnwwwwwwnnwwn', 66]`	`['nwnwnwwwwwwnnwwn', 66]`	Passed
combined fault 2	`['nnnww', 17]`	`['nnnww', 17]`	Passed
control 3	`['nnwwnnww', 30]`	`['nnwwnnww', 30]`	Passed
control 4	`['nwwwnwnn', 30]`	`['nwwwnwnn', 30]`	Passed
boundary 5	`['wwwnnw', 24]`	`['wwwnnw', 24]`	Passed
boundary 6	`['wnnnww', 22]`	`['wnnnww', 22]`	Passed
control 7	`['wwwnnwwwnwwnwnww', 68]`	`['wwwnnwwwnwwnwnww', 68]`	Passed

SHA-256 / c2845ba3caffaff739487b331b065a3b160b8087c0475cadef5d260a4e0e115f

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 2026-09-29T14:49:48.202191+00:00.

Case digest / 8e55dcaec4a12f71d9ff62b7f7e1bd6d85191fae675304ca78a633229d7c957f