FA-79746 / Barcode symbology encoding / Open access
Quiet zone offset is counted in pixels · case 01
At pitches above one pixel per module the quiet zone is too small and the symbol starts too close to the label edge.
ROOT CAUSE
The quiet zone count is added as pixels instead of modules.
VERIFIED REPAIR
Offset by quiet modules at the module pitch before rounding.
Unsuccessful approach: Rounding the quiet offset separately breaks the single rounding step for each edge.
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(i * X + Fraction(1, 2)) + quiet
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]]], [('11011', 5, 2, 2, 1), [[3, 6], [10, 13]]], [('010111110', 11, 5, 2, 0), [[2, 3], [7, 16]]], [('00001010', 1, 1, 0, 1), [[5, 6], [7, 8]]], [('101100101', 11, 5, 0, 0), [[0, 2], [4, 9], [13, 15], [18, 20]]], [('00101', 3, 1, 0, 0), [[6, 9], [12, 15]]], [('011', 5, 2, 1, 10), [[28, 32]]]], [[('0011000', 3, 1, 2, 3), [[15, 19]]], [('110', 11, 5, 0, 3), [[7, 11]]], [('11010001011', 11, 5, 1, 1), [[2, 6], [9, 10], [18, 19], [22, 25]]], [('0010101000110', 7, 3, 0, 0), [[5, 7], [9, 12], [14, 16], [23, 28]]], [('1100001111', 9, 4, 0, 0), [[0, 5], [14, 23]]], [('000010010001', 9, 4, 1, 0), [[9, 10], [16, 17], [25, 26]]], [('1000110000', 2, 1, 1, 0), [[0, 1], [8, 11]]], [('00101', 3, 1, 1, 3), [[15, 17], [21, 23]]]], [[('00010110011', 7, 3, 2, 3), [[14, 15], [19, 21], [28, 31]]], [('01001111110', 5, 2, 1, 3), [[10, 12], [18, 32]]], [('111000011001', 11, 5, 0, 1), [[2, 9], [18, 22], [26, 29]]], [('100110010100', 1, 1, 0, 1), [[1, 2], [4, 6], [8, 9], [10, 11]]], [('011100100', 1, 1, 2, 10), [[11, 12], [16, 17]]], [('01011', 3, 1, 0, 0), [[3, 6], [9, 15]]], [('100000010', 9, 4, 1, 0), [[0, 1], [16, 17]]], [('11000100111001', 5, 2, 1, 10), [[25, 29], [38, 39], [45, 52], [58, 59]]]], [[('00101011101', 7, 3, 1, 10), [[28, 29], [33, 34], [37, 43], [47, 48]]], [('1000010110000', 7, 3, 0, 1), [[2, 5], [14, 16], [19, 23]]], [('010110111001', 11, 5, 1, 1), [[4, 6], [9, 12], [15, 21], [26, 28]]], [('11001111', 2, 1, 2, 0), [[0, 2], [8, 14]]], [('1', 5, 2, 1, 0), [[0, 2]]], [('010011110', 7, 3, 2, 0), [[2, 3], [9, 17]]], [('0', 7, 3, 0, 0), []], [('0000001100111', 2, 1, 2, 3), [[18, 20], [26, 30]]]], [[('10111101000110', 7, 3, 0, 3), [[7, 9], [12, 21], [23, 26], [33, 37]]], [('00101011000', 9, 4, 0, 1), [[7, 9], [11, 14], [16, 20]]], [('0100100100', 4, 3, 0, 10), [[15, 16], [19, 20], [23, 24]]], [('0001011111001', 1, 1, 0, 1), [[4, 5], [6, 11], [13, 14]]], [('100011111110', 11, 5, 0, 0), [[0, 2], [9, 24]]], [('000011', 9, 4, 0, 0), [[9, 14]]], [('1110011100111', 1, 1, 2, 10), [[10, 11], [15, 16], [20, 21]]], [('0010110011101', 3, 1, 1, 1), [[9, 11], [15, 20], [27, 35], [39, 41]]]]]
labels = ["regression: quiet zone units", "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: quiet zone units 0 | [[7, 15]] | [[8, 16]] | Failed |
| repair trap 1 | [[6, 8], [10, 15]] | [[7, 8], [11, 15]] | Failed |
| combined fault 2 | [[1, 4], [9, 12]] | [[3, 6], [10, 13]] | Failed |
| control 3 | [[2, 3], [7, 16]] | [[2, 3], [7, 16]] | Passed |
| control 4 | [[5, 6], [7, 8]] | [[5, 6], [7, 8]] | Passed |
| boundary 5 | [[0, 2], [4, 9], [13, 15], [18, 20]] | [[0, 2], [4, 9], [13, 15], [18, 20]] | Passed |
| boundary 6 | [[6, 9], [12, 15]] | [[6, 9], [12, 15]] | Passed |
| control 7 | [[13, 17]] | [[28, 32]] | Failed |
SHA-256 / 51a14ca792f695346f87e2da4b5ed17e405adfd5aeced625438e15d2df523afa
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(i * X + Fraction(1, 2)) + math.floor(quiet * X)
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]]], [('11011', 5, 2, 2, 1), [[3, 6], [10, 13]]], [('010111110', 11, 5, 2, 0), [[2, 3], [7, 16]]], [('00001010', 1, 1, 0, 1), [[5, 6], [7, 8]]], [('101100101', 11, 5, 0, 0), [[0, 2], [4, 9], [13, 15], [18, 20]]], [('00101', 3, 1, 0, 0), [[6, 9], [12, 15]]], [('011', 5, 2, 1, 10), [[28, 32]]]], [[('0011000', 3, 1, 2, 3), [[15, 19]]], [('110', 11, 5, 0, 3), [[7, 11]]], [('11010001011', 11, 5, 1, 1), [[2, 6], [9, 10], [18, 19], [22, 25]]], [('0010101000110', 7, 3, 0, 0), [[5, 7], [9, 12], [14, 16], [23, 28]]], [('1100001111', 9, 4, 0, 0), [[0, 5], [14, 23]]], [('000010010001', 9, 4, 1, 0), [[9, 10], [16, 17], [25, 26]]], [('1000110000', 2, 1, 1, 0), [[0, 1], [8, 11]]], [('00101', 3, 1, 1, 3), [[15, 17], [21, 23]]]], [[('00010110011', 7, 3, 2, 3), [[14, 15], [19, 21], [28, 31]]], [('01001111110', 5, 2, 1, 3), [[10, 12], [18, 32]]], [('111000011001', 11, 5, 0, 1), [[2, 9], [18, 22], [26, 29]]], [('100110010100', 1, 1, 0, 1), [[1, 2], [4, 6], [8, 9], [10, 11]]], [('011100100', 1, 1, 2, 10), [[11, 12], [16, 17]]], [('01011', 3, 1, 0, 0), [[3, 6], [9, 15]]], [('100000010', 9, 4, 1, 0), [[0, 1], [16, 17]]], [('11000100111001', 5, 2, 1, 10), [[25, 29], [38, 39], [45, 52], [58, 59]]]], [[('00101011101', 7, 3, 1, 10), [[28, 29], [33, 34], [37, 43], [47, 48]]], [('1000010110000', 7, 3, 0, 1), [[2, 5], [14, 16], [19, 23]]], [('010110111001', 11, 5, 1, 1), [[4, 6], [9, 12], [15, 21], [26, 28]]], [('11001111', 2, 1, 2, 0), [[0, 2], [8, 14]]], [('1', 5, 2, 1, 0), [[0, 2]]], [('010011110', 7, 3, 2, 0), [[2, 3], [9, 17]]], [('0', 7, 3, 0, 0), []], [('0000001100111', 2, 1, 2, 3), [[18, 20], [26, 30]]]], [[('10111101000110', 7, 3, 0, 3), [[7, 9], [12, 21], [23, 26], [33, 37]]], [('00101011000', 9, 4, 0, 1), [[7, 9], [11, 14], [16, 20]]], [('0100100100', 4, 3, 0, 10), [[15, 16], [19, 20], [23, 24]]], [('0001011111001', 1, 1, 0, 1), [[4, 5], [6, 11], [13, 14]]], [('100011111110', 11, 5, 0, 0), [[0, 2], [9, 24]]], [('000011', 9, 4, 0, 0), [[9, 14]]], [('1110011100111', 1, 1, 2, 10), [[10, 11], [15, 16], [20, 21]]], [('0010110011101', 3, 1, 1, 1), [[9, 11], [15, 20], [27, 35], [39, 41]]]]]
labels = ["regression: quiet zone units", "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: quiet zone units 0 | [[8, 16]] | [[8, 16]] | Passed |
| repair trap 1 | [[6, 8], [10, 15]] | [[7, 8], [11, 15]] | Failed |
| combined fault 2 | [[2, 5], [10, 13]] | [[3, 6], [10, 13]] | Failed |
| control 3 | [[2, 3], [7, 16]] | [[2, 3], [7, 16]] | Passed |
| control 4 | [[5, 6], [7, 8]] | [[5, 6], [7, 8]] | Passed |
| boundary 5 | [[0, 2], [4, 9], [13, 15], [18, 20]] | [[0, 2], [4, 9], [13, 15], [18, 20]] | Passed |
| boundary 6 | [[6, 9], [12, 15]] | [[6, 9], [12, 15]] | Passed |
| control 7 | [[28, 32]] | [[28, 32]] | Passed |
SHA-256 / fc6388747337aac7df9883410e6b947ab1da9fa61aae770552019a013b7d7c70
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]]], [('11011', 5, 2, 2, 1), [[3, 6], [10, 13]]], [('010111110', 11, 5, 2, 0), [[2, 3], [7, 16]]], [('00001010', 1, 1, 0, 1), [[5, 6], [7, 8]]], [('101100101', 11, 5, 0, 0), [[0, 2], [4, 9], [13, 15], [18, 20]]], [('00101', 3, 1, 0, 0), [[6, 9], [12, 15]]], [('011', 5, 2, 1, 10), [[28, 32]]]], [[('0011000', 3, 1, 2, 3), [[15, 19]]], [('110', 11, 5, 0, 3), [[7, 11]]], [('11010001011', 11, 5, 1, 1), [[2, 6], [9, 10], [18, 19], [22, 25]]], [('0010101000110', 7, 3, 0, 0), [[5, 7], [9, 12], [14, 16], [23, 28]]], [('1100001111', 9, 4, 0, 0), [[0, 5], [14, 23]]], [('000010010001', 9, 4, 1, 0), [[9, 10], [16, 17], [25, 26]]], [('1000110000', 2, 1, 1, 0), [[0, 1], [8, 11]]], [('00101', 3, 1, 1, 3), [[15, 17], [21, 23]]]], [[('00010110011', 7, 3, 2, 3), [[14, 15], [19, 21], [28, 31]]], [('01001111110', 5, 2, 1, 3), [[10, 12], [18, 32]]], [('111000011001', 11, 5, 0, 1), [[2, 9], [18, 22], [26, 29]]], [('100110010100', 1, 1, 0, 1), [[1, 2], [4, 6], [8, 9], [10, 11]]], [('011100100', 1, 1, 2, 10), [[11, 12], [16, 17]]], [('01011', 3, 1, 0, 0), [[3, 6], [9, 15]]], [('100000010', 9, 4, 1, 0), [[0, 1], [16, 17]]], [('11000100111001', 5, 2, 1, 10), [[25, 29], [38, 39], [45, 52], [58, 59]]]], [[('00101011101', 7, 3, 1, 10), [[28, 29], [33, 34], [37, 43], [47, 48]]], [('1000010110000', 7, 3, 0, 1), [[2, 5], [14, 16], [19, 23]]], [('010110111001', 11, 5, 1, 1), [[4, 6], [9, 12], [15, 21], [26, 28]]], [('11001111', 2, 1, 2, 0), [[0, 2], [8, 14]]], [('1', 5, 2, 1, 0), [[0, 2]]], [('010011110', 7, 3, 2, 0), [[2, 3], [9, 17]]], [('0', 7, 3, 0, 0), []], [('0000001100111', 2, 1, 2, 3), [[18, 20], [26, 30]]]], [[('10111101000110', 7, 3, 0, 3), [[7, 9], [12, 21], [23, 26], [33, 37]]], [('00101011000', 9, 4, 0, 1), [[7, 9], [11, 14], [16, 20]]], [('0100100100', 4, 3, 0, 10), [[15, 16], [19, 20], [23, 24]]], [('0001011111001', 1, 1, 0, 1), [[4, 5], [6, 11], [13, 14]]], [('100011111110', 11, 5, 0, 0), [[0, 2], [9, 24]]], [('000011', 9, 4, 0, 0), [[9, 14]]], [('1110011100111', 1, 1, 2, 10), [[10, 11], [15, 16], [20, 21]]], [('0010110011101', 3, 1, 1, 1), [[9, 11], [15, 20], [27, 35], [39, 41]]]]]
labels = ["regression: quiet zone units", "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: quiet zone units 0 | [[8, 16]] | [[8, 16]] | Passed |
| repair trap 1 | [[7, 8], [11, 15]] | [[7, 8], [11, 15]] | Passed |
| combined fault 2 | [[3, 6], [10, 13]] | [[3, 6], [10, 13]] | Passed |
| control 3 | [[2, 3], [7, 16]] | [[2, 3], [7, 16]] | Passed |
| control 4 | [[5, 6], [7, 8]] | [[5, 6], [7, 8]] | Passed |
| boundary 5 | [[0, 2], [4, 9], [13, 15], [18, 20]] | [[0, 2], [4, 9], [13, 15], [18, 20]] | Passed |
| boundary 6 | [[6, 9], [12, 15]] | [[6, 9], [12, 15]] | Passed |
| control 7 | [[28, 32]] | [[28, 32]] | Passed |
SHA-256 / b60fd8a0c3e87df5e0f0fe551a68090de7ef19361806e30703394bfe80f1588c
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 2026-09-29T14:49:47.533309+00:00.
Case digest / a70d1a413736564bd3d4d5216399b86d78d784dd1e5d8c8e24a06a73da9407e6