FA-97406 / Knitting and sewing pattern grading / Open access

Sleeve taper decrease schedule: row budget check · case 01

Fifteen decreases in ten rows produce "every 0 rows" instructions.

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

ROOT CAUSE

An interval of zero rows is not rejected.

VERIFIED REPAIR

Reject when rows are fewer than decrease rows.

Unsuccessful approach: Rejecting only zero rows still accepts impossible short tapers.

Case contract

Top-down sleeve from upper_sts to cuff_sts, decreasing 2 stitches per decrease row within rows rows. Errors: cuff wider ("error: cuff wider than upper arm"), odd difference ("error: odd difference"), rows fewer than decrease rows ("error: not enough rows"). pairs = difference/2; a = rows // pairs; y = rows - a*pairs decreases every a+1 rows, x = pairs-y every a rows. Return [[a, x], [a+1, y]] omitting a zero count; [] for no decreases.

Why this case matters

Pattern writers turn a stitch-count change over a length into "decrease every N rows X times".

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(cuff_sts, upper_sts, rows):
    diff = upper_sts - cuff_sts
    if diff < 0:
        return 'error: cuff wider than upper arm'
    if diff % 2:
        return 'error: odd difference'
    pairs = diff // 2
    if pairs == 0:
        return []
    a = rows // pairs
    if a < 0:
        return 'error: not enough rows'
    y = rows - a * pairs
    x = pairs - y
    plan = []
    if x:
        plan.append([a, x])
    if y:
        plan.append([a + 1, y])
    return plan
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['even schedule', [48, 64, 80], [[10, 8]]], ['two rates', [44, 60, 90], [[11, 6], [12, 2]]],
  ['odd difference', [48, 53, 60], 'error: odd difference'],
  ['regression: row budget check', [56, 86, 10], 'error: not enough rows'],
  ['repair check: row budget check', [48, 68, 5], 'error: not enough rows'],
  ['generated control 1', [40, 52, 90], [[15, 6]]],
  ['generated control 2', [50, 57, 90], 'error: odd difference'],
  ['generated control 3', [56, 64, 5], [[1, 3], [2, 1]]]],
 [['two rates', [44, 60, 90], [[11, 6], [12, 2]]], ['odd difference', [48, 53, 60], 'error: odd difference'],
  ['too few rows', [40, 70, 10], 'error: not enough rows'],
  ['regression: row budget check', [60, 90, 5], 'error: not enough rows'],
  ['repair check: row budget check', [45, 65, 5], 'error: not enough rows'],
  ['generated control 1', [45, 45, 72], []], ['generated control 2', [50, 57, 5], 'error: odd difference'],
  ['generated control 3', [50, 50, 40], []]],
 [['odd difference', [48, 53, 60], 'error: odd difference'],
  ['too few rows', [40, 70, 10], 'error: not enough rows'],
  ['cuff wider', [60, 50, 60], 'error: cuff wider than upper arm'],
  ['regression: row budget check', [40, 64, 5], 'error: not enough rows'],
  ['repair check: row budget check', [51, 71, 5], 'error: not enough rows'],
  ['generated control 1', [45, 52, 10], 'error: odd difference'],
  ['generated control 2', [50, 52, 40], [[40, 1]]],
  ['generated control 3', [45, 50, 40], 'error: odd difference']],
 [['too few rows', [40, 70, 10], 'error: not enough rows'],
  ['cuff wider', [60, 50, 60], 'error: cuff wider than upper arm'],
  ['even schedule', [48, 64, 80], [[10, 8]]],
  ['regression: row budget check', [60, 90, 10], 'error: not enough rows'],
  ['repair check: row budget check', [50, 66, 5], 'error: not enough rows'],
  ['generated control 1', [51, 56, 72], 'error: odd difference'], ['generated control 2', [40, 40, 60], []],
  ['generated control 3', [51, 51, 5], []]],
 [['cuff wider', [60, 50, 60], 'error: cuff wider than upper arm'],
  ['even schedule', [48, 64, 80], [[10, 8]]], ['two rates', [44, 60, 90], [[11, 6], [12, 2]]],
  ['regression: row budget check', [40, 60, 5], 'error: not enough rows'],
  ['repair check: row budget check', [50, 74, 5], 'error: not enough rows'],
  ['generated control 1', [60, 72, 100], [[16, 2], [17, 4]]],
  ['generated control 2', [48, 78, 100], [[6, 5], [7, 10]]],
  ['generated control 3', [50, 52, 60], [[60, 1]]]]]
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
even schedule	`[[10, 8]]`	`[[10, 8]]`	Passed
two rates	`[[11, 6], [12, 2]]`	`[[11, 6], [12, 2]]`	Passed
odd difference	`error: odd difference`	`error: odd difference`	Passed
regression: row budget check	`[[0, 5], [1, 10]]`	`error: not enough rows`	Failed
repair check: row budget check	`[[0, 5], [1, 5]]`	`error: not enough rows`	Failed
generated control 1	`[[15, 6]]`	`[[15, 6]]`	Passed
generated control 2	`error: odd difference`	`error: odd difference`	Passed
generated control 3	`[[1, 3], [2, 1]]`	`[[1, 3], [2, 1]]`	Passed

SHA-256 / ea26197d81fea9937094639eb22412d8e6b9d4c18df764574ac8010bf822d721

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(cuff_sts, upper_sts, rows):
    diff = upper_sts - cuff_sts
    if diff < 0:
        return 'error: cuff wider than upper arm'
    if diff % 2:
        return 'error: odd difference'
    pairs = diff // 2
    if pairs == 0:
        return []
    a = rows // pairs
    if a == 0 and rows == 0:
        return 'error: not enough rows'
    y = rows - a * pairs
    x = pairs - y
    plan = []
    if x:
        plan.append([a, x])
    if y:
        plan.append([a + 1, y])
    return plan
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['even schedule', [48, 64, 80], [[10, 8]]], ['two rates', [44, 60, 90], [[11, 6], [12, 2]]],
  ['odd difference', [48, 53, 60], 'error: odd difference'],
  ['regression: row budget check', [56, 86, 10], 'error: not enough rows'],
  ['repair check: row budget check', [48, 68, 5], 'error: not enough rows'],
  ['generated control 1', [40, 52, 90], [[15, 6]]],
  ['generated control 2', [50, 57, 90], 'error: odd difference'],
  ['generated control 3', [56, 64, 5], [[1, 3], [2, 1]]]],
 [['two rates', [44, 60, 90], [[11, 6], [12, 2]]], ['odd difference', [48, 53, 60], 'error: odd difference'],
  ['too few rows', [40, 70, 10], 'error: not enough rows'],
  ['regression: row budget check', [60, 90, 5], 'error: not enough rows'],
  ['repair check: row budget check', [45, 65, 5], 'error: not enough rows'],
  ['generated control 1', [45, 45, 72], []], ['generated control 2', [50, 57, 5], 'error: odd difference'],
  ['generated control 3', [50, 50, 40], []]],
 [['odd difference', [48, 53, 60], 'error: odd difference'],
  ['too few rows', [40, 70, 10], 'error: not enough rows'],
  ['cuff wider', [60, 50, 60], 'error: cuff wider than upper arm'],
  ['regression: row budget check', [40, 64, 5], 'error: not enough rows'],
  ['repair check: row budget check', [51, 71, 5], 'error: not enough rows'],
  ['generated control 1', [45, 52, 10], 'error: odd difference'],
  ['generated control 2', [50, 52, 40], [[40, 1]]],
  ['generated control 3', [45, 50, 40], 'error: odd difference']],
 [['too few rows', [40, 70, 10], 'error: not enough rows'],
  ['cuff wider', [60, 50, 60], 'error: cuff wider than upper arm'],
  ['even schedule', [48, 64, 80], [[10, 8]]],
  ['regression: row budget check', [60, 90, 10], 'error: not enough rows'],
  ['repair check: row budget check', [50, 66, 5], 'error: not enough rows'],
  ['generated control 1', [51, 56, 72], 'error: odd difference'], ['generated control 2', [40, 40, 60], []],
  ['generated control 3', [51, 51, 5], []]],
 [['cuff wider', [60, 50, 60], 'error: cuff wider than upper arm'],
  ['even schedule', [48, 64, 80], [[10, 8]]], ['two rates', [44, 60, 90], [[11, 6], [12, 2]]],
  ['regression: row budget check', [40, 60, 5], 'error: not enough rows'],
  ['repair check: row budget check', [50, 74, 5], 'error: not enough rows'],
  ['generated control 1', [60, 72, 100], [[16, 2], [17, 4]]],
  ['generated control 2', [48, 78, 100], [[6, 5], [7, 10]]],
  ['generated control 3', [50, 52, 60], [[60, 1]]]]]
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
even schedule	`[[10, 8]]`	`[[10, 8]]`	Passed
two rates	`[[11, 6], [12, 2]]`	`[[11, 6], [12, 2]]`	Passed
odd difference	`error: odd difference`	`error: odd difference`	Passed
regression: row budget check	`[[0, 5], [1, 10]]`	`error: not enough rows`	Failed
repair check: row budget check	`[[0, 5], [1, 5]]`	`error: not enough rows`	Failed
generated control 1	`[[15, 6]]`	`[[15, 6]]`	Passed
generated control 2	`error: odd difference`	`error: odd difference`	Passed
generated control 3	`[[1, 3], [2, 1]]`	`[[1, 3], [2, 1]]`	Passed

SHA-256 / a98df89059343014f8dba4b97ee4d3d3eccc233afb4540dab9061c87804ac9d0

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(cuff_sts, upper_sts, rows):
    diff = upper_sts - cuff_sts
    if diff < 0:
        return 'error: cuff wider than upper arm'
    if diff % 2:
        return 'error: odd difference'
    pairs = diff // 2
    if pairs == 0:
        return []
    a = rows // pairs
    if a == 0:
        return 'error: not enough rows'
    y = rows - a * pairs
    x = pairs - y
    plan = []
    if x:
        plan.append([a, x])
    if y:
        plan.append([a + 1, y])
    return plan
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['even schedule', [48, 64, 80], [[10, 8]]], ['two rates', [44, 60, 90], [[11, 6], [12, 2]]],
  ['odd difference', [48, 53, 60], 'error: odd difference'],
  ['regression: row budget check', [56, 86, 10], 'error: not enough rows'],
  ['repair check: row budget check', [48, 68, 5], 'error: not enough rows'],
  ['generated control 1', [40, 52, 90], [[15, 6]]],
  ['generated control 2', [50, 57, 90], 'error: odd difference'],
  ['generated control 3', [56, 64, 5], [[1, 3], [2, 1]]]],
 [['two rates', [44, 60, 90], [[11, 6], [12, 2]]], ['odd difference', [48, 53, 60], 'error: odd difference'],
  ['too few rows', [40, 70, 10], 'error: not enough rows'],
  ['regression: row budget check', [60, 90, 5], 'error: not enough rows'],
  ['repair check: row budget check', [45, 65, 5], 'error: not enough rows'],
  ['generated control 1', [45, 45, 72], []], ['generated control 2', [50, 57, 5], 'error: odd difference'],
  ['generated control 3', [50, 50, 40], []]],
 [['odd difference', [48, 53, 60], 'error: odd difference'],
  ['too few rows', [40, 70, 10], 'error: not enough rows'],
  ['cuff wider', [60, 50, 60], 'error: cuff wider than upper arm'],
  ['regression: row budget check', [40, 64, 5], 'error: not enough rows'],
  ['repair check: row budget check', [51, 71, 5], 'error: not enough rows'],
  ['generated control 1', [45, 52, 10], 'error: odd difference'],
  ['generated control 2', [50, 52, 40], [[40, 1]]],
  ['generated control 3', [45, 50, 40], 'error: odd difference']],
 [['too few rows', [40, 70, 10], 'error: not enough rows'],
  ['cuff wider', [60, 50, 60], 'error: cuff wider than upper arm'],
  ['even schedule', [48, 64, 80], [[10, 8]]],
  ['regression: row budget check', [60, 90, 10], 'error: not enough rows'],
  ['repair check: row budget check', [50, 66, 5], 'error: not enough rows'],
  ['generated control 1', [51, 56, 72], 'error: odd difference'], ['generated control 2', [40, 40, 60], []],
  ['generated control 3', [51, 51, 5], []]],
 [['cuff wider', [60, 50, 60], 'error: cuff wider than upper arm'],
  ['even schedule', [48, 64, 80], [[10, 8]]], ['two rates', [44, 60, 90], [[11, 6], [12, 2]]],
  ['regression: row budget check', [40, 60, 5], 'error: not enough rows'],
  ['repair check: row budget check', [50, 74, 5], 'error: not enough rows'],
  ['generated control 1', [60, 72, 100], [[16, 2], [17, 4]]],
  ['generated control 2', [48, 78, 100], [[6, 5], [7, 10]]],
  ['generated control 3', [50, 52, 60], [[60, 1]]]]]
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
even schedule	`[[10, 8]]`	`[[10, 8]]`	Passed
two rates	`[[11, 6], [12, 2]]`	`[[11, 6], [12, 2]]`	Passed
odd difference	`error: odd difference`	`error: odd difference`	Passed
regression: row budget check	`error: not enough rows`	`error: not enough rows`	Passed
repair check: row budget check	`error: not enough rows`	`error: not enough rows`	Passed
generated control 1	`[[15, 6]]`	`[[15, 6]]`	Passed
generated control 2	`error: odd difference`	`error: odd difference`	Passed
generated control 3	`[[1, 3], [2, 1]]`	`[[1, 3], [2, 1]]`	Passed

SHA-256 / 620114f9b94299af439b38f0b414b0806ce4b2ca5f810d37af934d7971e6514f

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 2026-09-29T14:52:31.874180+00:00.

Case digest / 5c3dfa5d181a519e916941429a02e1d7d2e82d97a9061112b40243e64424ff3f