FA-97496 / Knitting and sewing pattern grading / Open access

Neckband pick-up counter: per-edge rounding · case 01

A 22-row edge picks 16 stitches instead of 17.

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

ROOT CAUSE

Vertical pick-ups truncate instead of rounding half-up per edge.

VERIFIED REPAIR

Round each vertical edge half-up.

Unsuccessful approach: Rounding up adds a stitch whenever there is any fraction.

Case contract

Edges [kind, count]: vertical picks up 3 per 4 rows, diagonal 9 per 10 rows, each rounded half-up per edge; horizontal picks 1 per stitch; other kinds -> "error: edge". The rib needs a count of multiple*k + plus; adjust the total up to the next such count (unchanged if already valid). Return [raw_total, adjusted].

Why this case matters

Neckbands and button bands pick up stitches at edge ratios and must fit the rib repeat.

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(edges, multiple, plus):
    total = 0
    for kind, n in edges:
        if kind == 'vertical':
            total += 3 * n // 4
        elif kind == 'horizontal':
            total += n
        elif kind == 'diagonal':
            total += math.floor(Fraction(9 * n, 10) + Fraction(1, 2))
        else:
            return 'error: edge'
    r = (total - plus) % multiple
    adjusted = total if r == 0 else total + (multiple - r)
    return [total, adjusted]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['regression: per-edge rounding',
   [[['vertical', 30], ['diagonal', 7], ['vertical', 30], ['diagonal', 7]], 4, 0], [58, 60]],
  ['repair check: per-edge rounding', [[['vertical', 7], ['horizontal', 60], ['vertical', 22]], 6, 0],
   [82, 84]],
  ['generated control 1', [[['vertical', 20]], 1, 1], [15, 15]],
  ['generated control 2', [[['horizontal', 30], ['vertical', 10]], 6, 3], [38, 39]],
  ['generated control 3', [[['vertical', 20], ['diagonal', 18], ['vertical', 41]], 6, 0], [62, 66]]],
 [['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['unknown edge', [[['curve', 10]], 2, 0], 'error: edge'],
  ['regression: per-edge rounding', [[['vertical', 10], ['vertical', 7], ['vertical', 13]], 4, 2], [23, 26]],
  ['repair check: per-edge rounding', [[['vertical', 18], ['vertical', 7], ['diagonal', 60]], 1, 1],
   [73, 73]],
  ['generated control 1', [[['horizontal', 13]], 1, 2], [13, 13]],
  ['generated control 2', [[['vertical', 10], ['vertical', 10]], 4, 2], [16, 18]],
  ['generated control 3', [[['diagonal', 22], ['vertical', 30], ['vertical', 22], ['vertical', 18]], 6, 0],
   [74, 78]]],
 [['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['unknown edge', [[['curve', 10]], 2, 0], 'error: edge'],
  ['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['regression: per-edge rounding', [[['vertical', 30], ['vertical', 7]], 1, 0], [28, 28]],
  ['repair check: per-edge rounding', [[['vertical', 7], ['horizontal', 13], ['horizontal', 41]], 1, 3],
   [59, 59]],
  ['generated control 1', [[['vertical', 41], ['diagonal', 41], ['vertical', 22], ['vertical', 10]], 4, 1],
   [93, 93]],
  ['generated control 2', [[['horizontal', 30], ['diagonal', 7], ['horizontal', 60], ['vertical', 41]], 6, 1],
   [127, 127]],
  ['generated control 3', [[['vertical', 18], ['diagonal', 41], ['vertical', 41], ['vertical', 22]], 6, 3],
   [99, 99]]],
 [['unknown edge', [[['curve', 10]], 2, 0], 'error: edge'],
  ['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['regression: per-edge rounding',
   [[['vertical', 13], ['horizontal', 30], ['vertical', 18], ['vertical', 7]], 6, 2], [59, 62]],
  ['repair check: per-edge rounding', [[['vertical', 20], ['vertical', 7]], 2, 0], [20, 20]],
  ['generated control 1', [[['diagonal', 7]], 1, 1], [6, 6]],
  ['generated control 2', [[['diagonal', 18], ['horizontal', 18]], 1, 3], [34, 34]],
  ['generated control 3', [[['diagonal', 18]], 2, 1], [16, 17]]],
 [['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['regression: per-edge rounding', [[['vertical', 30], ['diagonal', 7]], 4, 1], [29, 29]],
  ['repair check: per-edge rounding', [[['vertical', 7], ['vertical', 18], ['vertical', 60]], 2, 2],
   [64, 64]],
  ['generated control 1',
   [[['vertical', 22], ['diagonal', 18], ['horizontal', 41], ['horizontal', 10]], 2, 3], [84, 85]],
  ['generated control 2', [[['vertical', 22]], 6, 2], [17, 20]],
  ['generated control 3', [[['diagonal', 22], ['horizontal', 41], ['vertical', 22]], 4, 3], [78, 79]]]]
for label, args, expected in fixtures[N - 1]:
    check(label, 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
front neck	`[82, 82]`	`[82, 82]`	Passed
already valid	`[22, 22]`	`[22, 22]`	Passed
diagonal edge	`[12, 12]`	`[12, 12]`	Passed
regression: per-edge rounding	`[56, 56]`	`[58, 60]`	Failed
repair check: per-edge rounding	`[81, 84]`	`[82, 84]`	Failed
generated control 1	`[15, 15]`	`[15, 15]`	Passed
generated control 2	`[37, 39]`	`[38, 39]`	Failed
generated control 3	`[61, 66]`	`[62, 66]`	Failed

SHA-256 / 623b70cea598772f614b03a7acc198f21aae44991c69a28245c89241bf90e30f

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(edges, multiple, plus):
    total = 0
    for kind, n in edges:
        if kind == 'vertical':
            total += math.ceil(Fraction(3 * n, 4))
        elif kind == 'horizontal':
            total += n
        elif kind == 'diagonal':
            total += math.floor(Fraction(9 * n, 10) + Fraction(1, 2))
        else:
            return 'error: edge'
    r = (total - plus) % multiple
    adjusted = total if r == 0 else total + (multiple - r)
    return [total, adjusted]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['regression: per-edge rounding',
   [[['vertical', 30], ['diagonal', 7], ['vertical', 30], ['diagonal', 7]], 4, 0], [58, 60]],
  ['repair check: per-edge rounding', [[['vertical', 7], ['horizontal', 60], ['vertical', 22]], 6, 0],
   [82, 84]],
  ['generated control 1', [[['vertical', 20]], 1, 1], [15, 15]],
  ['generated control 2', [[['horizontal', 30], ['vertical', 10]], 6, 3], [38, 39]],
  ['generated control 3', [[['vertical', 20], ['diagonal', 18], ['vertical', 41]], 6, 0], [62, 66]]],
 [['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['unknown edge', [[['curve', 10]], 2, 0], 'error: edge'],
  ['regression: per-edge rounding', [[['vertical', 10], ['vertical', 7], ['vertical', 13]], 4, 2], [23, 26]],
  ['repair check: per-edge rounding', [[['vertical', 18], ['vertical', 7], ['diagonal', 60]], 1, 1],
   [73, 73]],
  ['generated control 1', [[['horizontal', 13]], 1, 2], [13, 13]],
  ['generated control 2', [[['vertical', 10], ['vertical', 10]], 4, 2], [16, 18]],
  ['generated control 3', [[['diagonal', 22], ['vertical', 30], ['vertical', 22], ['vertical', 18]], 6, 0],
   [74, 78]]],
 [['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['unknown edge', [[['curve', 10]], 2, 0], 'error: edge'],
  ['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['regression: per-edge rounding', [[['vertical', 30], ['vertical', 7]], 1, 0], [28, 28]],
  ['repair check: per-edge rounding', [[['vertical', 7], ['horizontal', 13], ['horizontal', 41]], 1, 3],
   [59, 59]],
  ['generated control 1', [[['vertical', 41], ['diagonal', 41], ['vertical', 22], ['vertical', 10]], 4, 1],
   [93, 93]],
  ['generated control 2', [[['horizontal', 30], ['diagonal', 7], ['horizontal', 60], ['vertical', 41]], 6, 1],
   [127, 127]],
  ['generated control 3', [[['vertical', 18], ['diagonal', 41], ['vertical', 41], ['vertical', 22]], 6, 3],
   [99, 99]]],
 [['unknown edge', [[['curve', 10]], 2, 0], 'error: edge'],
  ['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['regression: per-edge rounding',
   [[['vertical', 13], ['horizontal', 30], ['vertical', 18], ['vertical', 7]], 6, 2], [59, 62]],
  ['repair check: per-edge rounding', [[['vertical', 20], ['vertical', 7]], 2, 0], [20, 20]],
  ['generated control 1', [[['diagonal', 7]], 1, 1], [6, 6]],
  ['generated control 2', [[['diagonal', 18], ['horizontal', 18]], 1, 3], [34, 34]],
  ['generated control 3', [[['diagonal', 18]], 2, 1], [16, 17]]],
 [['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['regression: per-edge rounding', [[['vertical', 30], ['diagonal', 7]], 4, 1], [29, 29]],
  ['repair check: per-edge rounding', [[['vertical', 7], ['vertical', 18], ['vertical', 60]], 2, 2],
   [64, 64]],
  ['generated control 1',
   [[['vertical', 22], ['diagonal', 18], ['horizontal', 41], ['horizontal', 10]], 2, 3], [84, 85]],
  ['generated control 2', [[['vertical', 22]], 6, 2], [17, 20]],
  ['generated control 3', [[['diagonal', 22], ['horizontal', 41], ['vertical', 22]], 4, 3], [78, 79]]]]
for label, args, expected in fixtures[N - 1]:
    check(label, 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
front neck	`[82, 82]`	`[82, 82]`	Passed
already valid	`[22, 22]`	`[22, 22]`	Passed
diagonal edge	`[12, 12]`	`[12, 12]`	Passed
regression: per-edge rounding	`[58, 60]`	`[58, 60]`	Passed
repair check: per-edge rounding	`[83, 84]`	`[82, 84]`	Failed
generated control 1	`[15, 15]`	`[15, 15]`	Passed
generated control 2	`[38, 39]`	`[38, 39]`	Passed
generated control 3	`[62, 66]`	`[62, 66]`	Passed

SHA-256 / fde5d8f6291dc29728bbad4b8665aa7449922d3ea4fa2874d3b09636757f8a10

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(edges, multiple, plus):
    total = 0
    for kind, n in edges:
        if kind == 'vertical':
            total += math.floor(Fraction(3 * n, 4) + Fraction(1, 2))
        elif kind == 'horizontal':
            total += n
        elif kind == 'diagonal':
            total += math.floor(Fraction(9 * n, 10) + Fraction(1, 2))
        else:
            return 'error: edge'
    r = (total - plus) % multiple
    adjusted = total if r == 0 else total + (multiple - r)
    return [total, adjusted]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['regression: per-edge rounding',
   [[['vertical', 30], ['diagonal', 7], ['vertical', 30], ['diagonal', 7]], 4, 0], [58, 60]],
  ['repair check: per-edge rounding', [[['vertical', 7], ['horizontal', 60], ['vertical', 22]], 6, 0],
   [82, 84]],
  ['generated control 1', [[['vertical', 20]], 1, 1], [15, 15]],
  ['generated control 2', [[['horizontal', 30], ['vertical', 10]], 6, 3], [38, 39]],
  ['generated control 3', [[['vertical', 20], ['diagonal', 18], ['vertical', 41]], 6, 0], [62, 66]]],
 [['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['unknown edge', [[['curve', 10]], 2, 0], 'error: edge'],
  ['regression: per-edge rounding', [[['vertical', 10], ['vertical', 7], ['vertical', 13]], 4, 2], [23, 26]],
  ['repair check: per-edge rounding', [[['vertical', 18], ['vertical', 7], ['diagonal', 60]], 1, 1],
   [73, 73]],
  ['generated control 1', [[['horizontal', 13]], 1, 2], [13, 13]],
  ['generated control 2', [[['vertical', 10], ['vertical', 10]], 4, 2], [16, 18]],
  ['generated control 3', [[['diagonal', 22], ['vertical', 30], ['vertical', 22], ['vertical', 18]], 6, 0],
   [74, 78]]],
 [['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['unknown edge', [[['curve', 10]], 2, 0], 'error: edge'],
  ['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['regression: per-edge rounding', [[['vertical', 30], ['vertical', 7]], 1, 0], [28, 28]],
  ['repair check: per-edge rounding', [[['vertical', 7], ['horizontal', 13], ['horizontal', 41]], 1, 3],
   [59, 59]],
  ['generated control 1', [[['vertical', 41], ['diagonal', 41], ['vertical', 22], ['vertical', 10]], 4, 1],
   [93, 93]],
  ['generated control 2', [[['horizontal', 30], ['diagonal', 7], ['horizontal', 60], ['vertical', 41]], 6, 1],
   [127, 127]],
  ['generated control 3', [[['vertical', 18], ['diagonal', 41], ['vertical', 41], ['vertical', 22]], 6, 3],
   [99, 99]]],
 [['unknown edge', [[['curve', 10]], 2, 0], 'error: edge'],
  ['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['regression: per-edge rounding',
   [[['vertical', 13], ['horizontal', 30], ['vertical', 18], ['vertical', 7]], 6, 2], [59, 62]],
  ['repair check: per-edge rounding', [[['vertical', 20], ['vertical', 7]], 2, 0], [20, 20]],
  ['generated control 1', [[['diagonal', 7]], 1, 1], [6, 6]],
  ['generated control 2', [[['diagonal', 18], ['horizontal', 18]], 1, 3], [34, 34]],
  ['generated control 3', [[['diagonal', 18]], 2, 1], [16, 17]]],
 [['front neck', [[['vertical', 40], ['horizontal', 22], ['vertical', 40]], 4, 2], [82, 82]],
  ['already valid', [[['horizontal', 22]], 4, 2], [22, 22]],
  ['diagonal edge', [[['diagonal', 13]], 2, 0], [12, 12]],
  ['regression: per-edge rounding', [[['vertical', 30], ['diagonal', 7]], 4, 1], [29, 29]],
  ['repair check: per-edge rounding', [[['vertical', 7], ['vertical', 18], ['vertical', 60]], 2, 2],
   [64, 64]],
  ['generated control 1',
   [[['vertical', 22], ['diagonal', 18], ['horizontal', 41], ['horizontal', 10]], 2, 3], [84, 85]],
  ['generated control 2', [[['vertical', 22]], 6, 2], [17, 20]],
  ['generated control 3', [[['diagonal', 22], ['horizontal', 41], ['vertical', 22]], 4, 3], [78, 79]]]]
for label, args, expected in fixtures[N - 1]:
    check(label, 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
front neck	`[82, 82]`	`[82, 82]`	Passed
already valid	`[22, 22]`	`[22, 22]`	Passed
diagonal edge	`[12, 12]`	`[12, 12]`	Passed
regression: per-edge rounding	`[58, 60]`	`[58, 60]`	Passed
repair check: per-edge rounding	`[82, 84]`	`[82, 84]`	Passed
generated control 1	`[15, 15]`	`[15, 15]`	Passed
generated control 2	`[38, 39]`	`[38, 39]`	Passed
generated control 3	`[62, 66]`	`[62, 66]`	Passed

SHA-256 / be024df7b42ad714f7c6076bb8dada618d2222ad5619b5c1896a622bdd972fd5

Verification & scope

A deterministic toy contract stated in full here; it is a bounded teaching model, not an authoritative reference or standards implementation. 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 2026-09-29T14:52:32.793740+00:00.

Case digest / 93ac6721b9edb9003cec2ce3c0b1557c8ced0e05889eaa77dfe62f1882303d9c