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FA-79816 / Barcode symbology encoding / Open access

Pharmacode encodes values 1 and 2 · case 01

Single-bar codes are printed although scanners require at least two bars.

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

ROOT CAUSE

The lower bound is 1 instead of 3.

VERIFIED REPAIR

Accept values from 3.

Unsuccessful approach: A lower bound of 2 still allows a single wide bar.

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 < 1 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 = [[[1, None], [2, None], [34, ['nnnww', 17]], [306, ['nnwwnnww', 30]], [371, ['nwwwnwnn', 30]], [120, ['wwwnnw', 24]], [98, ['wnnnww', 22]], [297, ['nnwnwnwn', 28]]], [[2, None], [6, ['ww', 8]], [85, ['nwnwwn', 22]], [155, ['nnwwwnn', 25]], [306, ['nnwwnnww', 30]], [201, ['wnnwnwn', 25]], [146, ['nnwnnww', 25]], [240, ['wwwnnnw', 27]]], [[1, None], [2, None], [142, ['nnnwwww', 27]], [335, ['nwnwnnnn', 26]], [232, ['wwnwnnw', 27]], [397, ['wnnnwwwn', 30]], [147, ['nnwnwnn', 23]], [225, ['wwnnnwn', 25]]], [[2, None], [229, ['wwnnwwn', 27]], [157, ['nnwwwwn', 27]], [19, ['nwnn', 12]], [27, ['wwnn', 14]], [36, ['nnwnw', 17]], [75, ['nnwwnn', 20]], [228, ['wwnnwnw', 27]]], [[1, None], [2, None], [157, ['nnwwwwn', 27]], [228, ['wwnnwnw', 27]], [361, ['nwwnwnwn', 30]], [153, ['nnwwnwn', 25]], [326, ['nwnnnwww', 30]], [188, ['nwwwwnw', 29]]]]
labels = ["regression: minimum 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 fixtureActualExpectedOutcome
regression: minimum encodable value 0['n', 1]NoneFailed
repair trap 1['w', 3]NoneFailed
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['nnwnwnwn', 28]['nnwnwnwn', 28]Passed

SHA-256 / 7c4d6dbb9dc225d6d12142777641cd230f10fce90f7e5ab85d0d62b5b061bb8a

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 < 2 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 = [[[1, None], [2, None], [34, ['nnnww', 17]], [306, ['nnwwnnww', 30]], [371, ['nwwwnwnn', 30]], [120, ['wwwnnw', 24]], [98, ['wnnnww', 22]], [297, ['nnwnwnwn', 28]]], [[2, None], [6, ['ww', 8]], [85, ['nwnwwn', 22]], [155, ['nnwwwnn', 25]], [306, ['nnwwnnww', 30]], [201, ['wnnwnwn', 25]], [146, ['nnwnnww', 25]], [240, ['wwwnnnw', 27]]], [[1, None], [2, None], [142, ['nnnwwww', 27]], [335, ['nwnwnnnn', 26]], [232, ['wwnwnnw', 27]], [397, ['wnnnwwwn', 30]], [147, ['nnwnwnn', 23]], [225, ['wwnnnwn', 25]]], [[2, None], [229, ['wwnnwwn', 27]], [157, ['nnwwwwn', 27]], [19, ['nwnn', 12]], [27, ['wwnn', 14]], [36, ['nnwnw', 17]], [75, ['nnwwnn', 20]], [228, ['wwnnwnw', 27]]], [[1, None], [2, None], [157, ['nnwwwwn', 27]], [228, ['wwnnwnw', 27]], [361, ['nwwnwnwn', 30]], [153, ['nnwwnwn', 25]], [326, ['nwnnnwww', 30]], [188, ['nwwwwnw', 29]]]]
labels = ["regression: minimum 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 fixtureActualExpectedOutcome
regression: minimum encodable value 0NoneNonePassed
repair trap 1['w', 3]NoneFailed
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['nnwnwnwn', 28]['nnwnwnwn', 28]Passed

SHA-256 / 8ecbd3ff8359d42aa5642a6d2e7aa1ed05a72b87c21237a32c334ef473df68d8

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 = [[[1, None], [2, None], [34, ['nnnww', 17]], [306, ['nnwwnnww', 30]], [371, ['nwwwnwnn', 30]], [120, ['wwwnnw', 24]], [98, ['wnnnww', 22]], [297, ['nnwnwnwn', 28]]], [[2, None], [6, ['ww', 8]], [85, ['nwnwwn', 22]], [155, ['nnwwwnn', 25]], [306, ['nnwwnnww', 30]], [201, ['wnnwnwn', 25]], [146, ['nnwnnww', 25]], [240, ['wwwnnnw', 27]]], [[1, None], [2, None], [142, ['nnnwwww', 27]], [335, ['nwnwnnnn', 26]], [232, ['wwnwnnw', 27]], [397, ['wnnnwwwn', 30]], [147, ['nnwnwnn', 23]], [225, ['wwnnnwn', 25]]], [[2, None], [229, ['wwnnwwn', 27]], [157, ['nnwwwwn', 27]], [19, ['nwnn', 12]], [27, ['wwnn', 14]], [36, ['nnwnw', 17]], [75, ['nnwwnn', 20]], [228, ['wwnnwnw', 27]]], [[1, None], [2, None], [157, ['nnwwwwn', 27]], [228, ['wwnnwnw', 27]], [361, ['nwwnwnwn', 30]], [153, ['nnwwnwn', 25]], [326, ['nwnnnwww', 30]], [188, ['nwwwwnw', 29]]]]
labels = ["regression: minimum 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 fixtureActualExpectedOutcome
regression: minimum encodable value 0NoneNonePassed
repair trap 1NoneNonePassed
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['nnwnwnwn', 28]['nnwnwnwn', 28]Passed

SHA-256 / 062c2a659a6769ff340d49b3e3609b1a803a89a41ad8ffc4f9af8de38f919b66

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 2026-09-29T14:49:48.200653+00:00.

Case digest / 48006931c433fe163e3f1e6ca329fd74edb5ce5cc71aff6855e3905d1a2a1f07