FA-79751 / Barcode symbology encoding / Open access
Wide bars are drawn as separate one-module bars · case 01
With bar width reduction every wide bar shows hairline gaps between its modules.
ROOT CAUSE
Each bar module is emitted separately instead of merging runs.
VERIFIED REPAIR
Merge consecutive bar modules into one bar.
Unsuccessful approach: Capping a run at three modules still splits the four-module bars of wider symbologies.
Case contract
Render a module string ("1" bar, "0" space) at xn/xd device pixels per module after `quiet` leading quiet-zone modules. Module boundary k lies at round-half-up((quiet + k) * X), computed from the exact fraction so errors do not accumulate. Adjacent bar modules merge into one bar [start, end); bar width reduction shaves `bwr` pixels from the right edge of each bar, but a bar is never narrower than 1 pixel.
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
import math
from fractions import Fraction
N = 1
observations = []
def solve(mods, xn, xd, bwr, quiet):
X = Fraction(xn, xd)
def edge(i):
return math.floor((quiet + i) * X + Fraction(1, 2))
bars = []
i = 0
n = len(mods)
while i < n:
if mods[i] == '1':
j = i
while j < i + 1 and mods[j] == '1':
j += 1
s, e = edge(i), edge(j) - bwr
if e - s < 1:
e = s + 1
bars.append([s, e])
i = j
else:
i += 1
return bars
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('0001111', 2, 1, 0, 1), [[8, 16]]], [('000011011110', 4, 3, 1, 1), [[7, 8], [11, 15]]], [('00001010', 1, 1, 0, 1), [[5, 6], [7, 8]]], [('00101', 3, 1, 0, 0), [[6, 9], [12, 15]]], [('001', 9, 4, 0, 3), [[11, 14]]], [('000101', 4, 3, 0, 3), [[8, 9], [11, 12]]], [('10', 5, 2, 1, 10), [[25, 27]]], [('011', 5, 2, 1, 10), [[28, 32]]]], [[('0010101000110', 7, 3, 0, 0), [[5, 7], [9, 12], [14, 16], [23, 28]]], [('1100001111', 9, 4, 0, 0), [[0, 5], [14, 23]]], [('0101001111010', 7, 3, 0, 3), [[9, 12], [14, 16], [21, 30], [33, 35]]], [('00101', 3, 1, 1, 3), [[15, 17], [21, 23]]], [('0001001', 5, 2, 0, 10), [[33, 35], [40, 43]]], [('1', 4, 3, 1, 0), [[0, 1]]], [('000', 5, 2, 2, 3), []], [('1111', 9, 4, 2, 3), [[7, 14]]]], [[('00010110011', 7, 3, 2, 3), [[14, 15], [19, 21], [28, 31]]], [('101011111011', 11, 5, 0, 0), [[0, 2], [4, 7], [9, 20], [22, 26]]], [('0110111111', 11, 5, 2, 3), [[9, 11], [15, 27]]], [('001', 7, 3, 2, 10), [[28, 29]]], [('100000010', 9, 4, 1, 0), [[0, 1], [16, 17]]], [('000', 7, 3, 0, 0), []], [('010', 9, 4, 0, 3), [[9, 11]]], [('11000100111001', 5, 2, 1, 10), [[25, 29], [38, 39], [45, 52], [58, 59]]]], [[('01100', 2, 1, 0, 0), [[2, 6]]], [('111100000', 5, 2, 1, 0), [[0, 9]]], [('010011111100', 7, 3, 2, 1), [[5, 6], [12, 24]]], [('100000010010', 11, 5, 0, 1), [[2, 4], [18, 20], [24, 26]]], [('0100000100', 7, 3, 0, 1), [[5, 7], [19, 21]]], [('01001000000', 5, 2, 1, 1), [[5, 7], [13, 14]]], [('10100001', 1, 1, 0, 10), [[10, 11], [12, 13], [17, 18]]], [('0000111', 7, 3, 0, 0), [[9, 16]]]], [[('111', 4, 3, 2, 10), [[13, 15]]], [('1011111001100', 2, 1, 0, 3), [[6, 8], [10, 20], [24, 28]]], [('111100', 4, 3, 0, 1), [[1, 7]]], [('010', 7, 3, 1, 0), [[2, 4]]], [('10', 4, 3, 2, 0), [[0, 1]]], [('10', 2, 1, 1, 0), [[0, 1]]], [('1', 9, 4, 1, 1), [[2, 4]]], [('0010110011101', 3, 1, 1, 1), [[9, 11], [15, 20], [27, 35], [39, 41]]]]]
labels = ["regression: adjacent bar merging", "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: adjacent bar merging 0 | [[8, 10], [10, 12], [12, 14], [14, 16]] | [[8, 16]] | Failed |
| repair trap 1 | [[7, 8], [8, 9], [11, 12], [12, 13], [13, 14], [15, 16]] | [[7, 8], [11, 15]] | Failed |
| combined fault 2 | [[5, 6], [7, 8]] | [[5, 6], [7, 8]] | Passed |
| control 3 | [[6, 9], [12, 15]] | [[6, 9], [12, 15]] | Passed |
| control 4 | [[11, 14]] | [[11, 14]] | Passed |
| boundary 5 | [[8, 9], [11, 12]] | [[8, 9], [11, 12]] | Passed |
| boundary 6 | [[25, 27]] | [[25, 27]] | Passed |
| control 7 | [[28, 29], [30, 32]] | [[28, 32]] | Failed |
SHA-256 / b1c57c6bc135a7aacaeff62550a58a41d1ccc17c1e7bfda8de39d672369e4062
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(mods, xn, xd, bwr, quiet):
X = Fraction(xn, xd)
def edge(i):
return math.floor((quiet + i) * X + Fraction(1, 2))
bars = []
i = 0
n = len(mods)
while i < n:
if mods[i] == '1':
j = i
while j < n and mods[j] == '1' and j - i < 3:
j += 1
s, e = edge(i), edge(j) - bwr
if e - s < 1:
e = s + 1
bars.append([s, e])
i = j
else:
i += 1
return bars
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('0001111', 2, 1, 0, 1), [[8, 16]]], [('000011011110', 4, 3, 1, 1), [[7, 8], [11, 15]]], [('00001010', 1, 1, 0, 1), [[5, 6], [7, 8]]], [('00101', 3, 1, 0, 0), [[6, 9], [12, 15]]], [('001', 9, 4, 0, 3), [[11, 14]]], [('000101', 4, 3, 0, 3), [[8, 9], [11, 12]]], [('10', 5, 2, 1, 10), [[25, 27]]], [('011', 5, 2, 1, 10), [[28, 32]]]], [[('0010101000110', 7, 3, 0, 0), [[5, 7], [9, 12], [14, 16], [23, 28]]], [('1100001111', 9, 4, 0, 0), [[0, 5], [14, 23]]], [('0101001111010', 7, 3, 0, 3), [[9, 12], [14, 16], [21, 30], [33, 35]]], [('00101', 3, 1, 1, 3), [[15, 17], [21, 23]]], [('0001001', 5, 2, 0, 10), [[33, 35], [40, 43]]], [('1', 4, 3, 1, 0), [[0, 1]]], [('000', 5, 2, 2, 3), []], [('1111', 9, 4, 2, 3), [[7, 14]]]], [[('00010110011', 7, 3, 2, 3), [[14, 15], [19, 21], [28, 31]]], [('101011111011', 11, 5, 0, 0), [[0, 2], [4, 7], [9, 20], [22, 26]]], [('0110111111', 11, 5, 2, 3), [[9, 11], [15, 27]]], [('001', 7, 3, 2, 10), [[28, 29]]], [('100000010', 9, 4, 1, 0), [[0, 1], [16, 17]]], [('000', 7, 3, 0, 0), []], [('010', 9, 4, 0, 3), [[9, 11]]], [('11000100111001', 5, 2, 1, 10), [[25, 29], [38, 39], [45, 52], [58, 59]]]], [[('01100', 2, 1, 0, 0), [[2, 6]]], [('111100000', 5, 2, 1, 0), [[0, 9]]], [('010011111100', 7, 3, 2, 1), [[5, 6], [12, 24]]], [('100000010010', 11, 5, 0, 1), [[2, 4], [18, 20], [24, 26]]], [('0100000100', 7, 3, 0, 1), [[5, 7], [19, 21]]], [('01001000000', 5, 2, 1, 1), [[5, 7], [13, 14]]], [('10100001', 1, 1, 0, 10), [[10, 11], [12, 13], [17, 18]]], [('0000111', 7, 3, 0, 0), [[9, 16]]]], [[('111', 4, 3, 2, 10), [[13, 15]]], [('1011111001100', 2, 1, 0, 3), [[6, 8], [10, 20], [24, 28]]], [('111100', 4, 3, 0, 1), [[1, 7]]], [('010', 7, 3, 1, 0), [[2, 4]]], [('10', 4, 3, 2, 0), [[0, 1]]], [('10', 2, 1, 1, 0), [[0, 1]]], [('1', 9, 4, 1, 1), [[2, 4]]], [('0010110011101', 3, 1, 1, 1), [[9, 11], [15, 20], [27, 35], [39, 41]]]]]
labels = ["regression: adjacent bar merging", "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: adjacent bar merging 0 | [[8, 14], [14, 16]] | [[8, 16]] | Failed |
| repair trap 1 | [[7, 8], [11, 14], [15, 16]] | [[7, 8], [11, 15]] | Failed |
| combined fault 2 | [[5, 6], [7, 8]] | [[5, 6], [7, 8]] | Passed |
| control 3 | [[6, 9], [12, 15]] | [[6, 9], [12, 15]] | Passed |
| control 4 | [[11, 14]] | [[11, 14]] | Passed |
| boundary 5 | [[8, 9], [11, 12]] | [[8, 9], [11, 12]] | Passed |
| boundary 6 | [[25, 27]] | [[25, 27]] | Passed |
| control 7 | [[28, 32]] | [[28, 32]] | Passed |
SHA-256 / 476c7686308a1ff9ff24483b258e9f5e1e49e43c3cb6e32c7c3e10b4882f4025
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(mods, xn, xd, bwr, quiet):
X = Fraction(xn, xd)
def edge(i):
return math.floor((quiet + i) * X + Fraction(1, 2))
bars = []
i = 0
n = len(mods)
while i < n:
if mods[i] == '1':
j = i
while j < n and mods[j] == '1':
j += 1
s, e = edge(i), edge(j) - bwr
if e - s < 1:
e = s + 1
bars.append([s, e])
i = j
else:
i += 1
return bars
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[('0001111', 2, 1, 0, 1), [[8, 16]]], [('000011011110', 4, 3, 1, 1), [[7, 8], [11, 15]]], [('00001010', 1, 1, 0, 1), [[5, 6], [7, 8]]], [('00101', 3, 1, 0, 0), [[6, 9], [12, 15]]], [('001', 9, 4, 0, 3), [[11, 14]]], [('000101', 4, 3, 0, 3), [[8, 9], [11, 12]]], [('10', 5, 2, 1, 10), [[25, 27]]], [('011', 5, 2, 1, 10), [[28, 32]]]], [[('0010101000110', 7, 3, 0, 0), [[5, 7], [9, 12], [14, 16], [23, 28]]], [('1100001111', 9, 4, 0, 0), [[0, 5], [14, 23]]], [('0101001111010', 7, 3, 0, 3), [[9, 12], [14, 16], [21, 30], [33, 35]]], [('00101', 3, 1, 1, 3), [[15, 17], [21, 23]]], [('0001001', 5, 2, 0, 10), [[33, 35], [40, 43]]], [('1', 4, 3, 1, 0), [[0, 1]]], [('000', 5, 2, 2, 3), []], [('1111', 9, 4, 2, 3), [[7, 14]]]], [[('00010110011', 7, 3, 2, 3), [[14, 15], [19, 21], [28, 31]]], [('101011111011', 11, 5, 0, 0), [[0, 2], [4, 7], [9, 20], [22, 26]]], [('0110111111', 11, 5, 2, 3), [[9, 11], [15, 27]]], [('001', 7, 3, 2, 10), [[28, 29]]], [('100000010', 9, 4, 1, 0), [[0, 1], [16, 17]]], [('000', 7, 3, 0, 0), []], [('010', 9, 4, 0, 3), [[9, 11]]], [('11000100111001', 5, 2, 1, 10), [[25, 29], [38, 39], [45, 52], [58, 59]]]], [[('01100', 2, 1, 0, 0), [[2, 6]]], [('111100000', 5, 2, 1, 0), [[0, 9]]], [('010011111100', 7, 3, 2, 1), [[5, 6], [12, 24]]], [('100000010010', 11, 5, 0, 1), [[2, 4], [18, 20], [24, 26]]], [('0100000100', 7, 3, 0, 1), [[5, 7], [19, 21]]], [('01001000000', 5, 2, 1, 1), [[5, 7], [13, 14]]], [('10100001', 1, 1, 0, 10), [[10, 11], [12, 13], [17, 18]]], [('0000111', 7, 3, 0, 0), [[9, 16]]]], [[('111', 4, 3, 2, 10), [[13, 15]]], [('1011111001100', 2, 1, 0, 3), [[6, 8], [10, 20], [24, 28]]], [('111100', 4, 3, 0, 1), [[1, 7]]], [('010', 7, 3, 1, 0), [[2, 4]]], [('10', 4, 3, 2, 0), [[0, 1]]], [('10', 2, 1, 1, 0), [[0, 1]]], [('1', 9, 4, 1, 1), [[2, 4]]], [('0010110011101', 3, 1, 1, 1), [[9, 11], [15, 20], [27, 35], [39, 41]]]]]
labels = ["regression: adjacent bar merging", "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: adjacent bar merging 0 | [[8, 16]] | [[8, 16]] | Passed |
| repair trap 1 | [[7, 8], [11, 15]] | [[7, 8], [11, 15]] | Passed |
| combined fault 2 | [[5, 6], [7, 8]] | [[5, 6], [7, 8]] | Passed |
| control 3 | [[6, 9], [12, 15]] | [[6, 9], [12, 15]] | Passed |
| control 4 | [[11, 14]] | [[11, 14]] | Passed |
| boundary 5 | [[8, 9], [11, 12]] | [[8, 9], [11, 12]] | Passed |
| boundary 6 | [[25, 27]] | [[25, 27]] | Passed |
| control 7 | [[28, 32]] | [[28, 32]] | Passed |
SHA-256 / c2aeb72c737cbd65ebc67eb6b0d7b0d1f63b7170206ba9299d49db56dd128d58
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 2026-09-29T14:49:47.532235+00:00.
Case digest / f4a3e24ae375c6c4d9a1d6cf290cc975013860cebd1a4578cc60d7d056acb75e