FA-97391 / Knitting and sewing pattern grading / Open access

Sleeve taper decrease schedule: decrease pair count · case 01

A 16-stitch taper is scheduled as 16 decrease rows, removing 32 stitches.

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

ROOT CAUSE

Each decrease row removes two stitches but pairs counts single stitches.

VERIFIED REPAIR

Use half the stitch difference as the number of decrease rows.

Unsuccessful approach: Subtracting a setup decrease leaves the sleeve two stitches too wide.

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
    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: decrease pair count', [50, 62, 10], [[1, 2], [2, 4]]],
  ['repair check: decrease pair count', [45, 45, 5], []], ['generated control 1', [60, 62, 40], [[40, 1]]],
  ['generated control 2', [56, 61, 5], 'error: odd difference'],
  ['generated control 3', [60, 65, 72], 'error: odd difference']],
 [['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: decrease pair count', [56, 72, 90], [[11, 6], [12, 2]]],
  ['repair check: decrease pair count', [56, 64, 72], [[18, 4]]], ['generated control 1', [40, 40, 5], []],
  ['generated control 2', [40, 45, 60], 'error: odd difference'], ['generated control 3', [60, 60, 5], []]],
 [['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: decrease pair count', [60, 90, 90], [[6, 15]]],
  ['repair check: decrease pair count', [45, 69, 60], [[5, 12]]], ['generated control 1', [45, 45, 90], []],
  ['generated control 2', [60, 84, 40], [[3, 8], [4, 4]]], ['generated control 3', [60, 76, 72], [[9, 8]]]],
 [['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: decrease pair count', [50, 58, 40], [[10, 4]]],
  ['repair check: decrease pair count', [56, 86, 40], [[2, 5], [3, 10]]],
  ['generated control 1', [48, 78, 100], [[6, 5], [7, 10]]],
  ['generated control 2', [50, 66, 100], [[12, 4], [13, 4]]],
  ['generated control 3', [56, 61, 40], 'error: odd difference']],
 [['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: decrease pair count', [48, 64, 60], [[7, 4], [8, 4]]],
  ['repair check: decrease pair count', [56, 86, 60], [[4, 15]]],
  ['generated control 1', [45, 52, 100], 'error: odd difference'],
  ['generated control 2', [51, 75, 5], 'error: not enough rows'],
  ['generated control 3', [48, 50, 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	`[[5, 16]]`	`[[10, 8]]`	Failed
two rates	`[[5, 6], [6, 10]]`	`[[11, 6], [12, 2]]`	Failed
odd difference	`error: odd difference`	`error: odd difference`	Passed
regression: decrease pair count	`error: not enough rows`	`[[1, 2], [2, 4]]`	Failed
repair check: decrease pair count	`[]`	`[]`	Passed
generated control 1	`[[20, 2]]`	`[[40, 1]]`	Failed
generated control 2	`error: odd difference`	`error: odd difference`	Passed
generated control 3	`error: odd difference`	`error: odd difference`	Passed

SHA-256 / 1b83202c0254f54851728afaaa07d7af92d00fee54d382144b060c30ccafe25b

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) // 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: decrease pair count', [50, 62, 10], [[1, 2], [2, 4]]],
  ['repair check: decrease pair count', [45, 45, 5], []], ['generated control 1', [60, 62, 40], [[40, 1]]],
  ['generated control 2', [56, 61, 5], 'error: odd difference'],
  ['generated control 3', [60, 65, 72], 'error: odd difference']],
 [['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: decrease pair count', [56, 72, 90], [[11, 6], [12, 2]]],
  ['repair check: decrease pair count', [56, 64, 72], [[18, 4]]], ['generated control 1', [40, 40, 5], []],
  ['generated control 2', [40, 45, 60], 'error: odd difference'], ['generated control 3', [60, 60, 5], []]],
 [['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: decrease pair count', [60, 90, 90], [[6, 15]]],
  ['repair check: decrease pair count', [45, 69, 60], [[5, 12]]], ['generated control 1', [45, 45, 90], []],
  ['generated control 2', [60, 84, 40], [[3, 8], [4, 4]]], ['generated control 3', [60, 76, 72], [[9, 8]]]],
 [['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: decrease pair count', [50, 58, 40], [[10, 4]]],
  ['repair check: decrease pair count', [56, 86, 40], [[2, 5], [3, 10]]],
  ['generated control 1', [48, 78, 100], [[6, 5], [7, 10]]],
  ['generated control 2', [50, 66, 100], [[12, 4], [13, 4]]],
  ['generated control 3', [56, 61, 40], 'error: odd difference']],
 [['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: decrease pair count', [48, 64, 60], [[7, 4], [8, 4]]],
  ['repair check: decrease pair count', [56, 86, 60], [[4, 15]]],
  ['generated control 1', [45, 52, 100], 'error: odd difference'],
  ['generated control 2', [51, 75, 5], 'error: not enough rows'],
  ['generated control 3', [48, 50, 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	`[[11, 4], [12, 3]]`	`[[10, 8]]`	Failed
two rates	`[[12, 1], [13, 6]]`	`[[11, 6], [12, 2]]`	Failed
odd difference	`error: odd difference`	`error: odd difference`	Passed
regression: decrease pair count	`[[2, 5]]`	`[[1, 2], [2, 4]]`	Failed
repair check: decrease pair count	`[[-5, -1]]`	`[]`	Failed
generated control 1	`[]`	`[[40, 1]]`	Failed
generated control 2	`error: odd difference`	`error: odd difference`	Passed
generated control 3	`error: odd difference`	`error: odd difference`	Passed

SHA-256 / 4c710b68d2e5167eccab7c2f58f5468c523565b5df5dea87a68f8ee7a7995327

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: decrease pair count', [50, 62, 10], [[1, 2], [2, 4]]],
  ['repair check: decrease pair count', [45, 45, 5], []], ['generated control 1', [60, 62, 40], [[40, 1]]],
  ['generated control 2', [56, 61, 5], 'error: odd difference'],
  ['generated control 3', [60, 65, 72], 'error: odd difference']],
 [['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: decrease pair count', [56, 72, 90], [[11, 6], [12, 2]]],
  ['repair check: decrease pair count', [56, 64, 72], [[18, 4]]], ['generated control 1', [40, 40, 5], []],
  ['generated control 2', [40, 45, 60], 'error: odd difference'], ['generated control 3', [60, 60, 5], []]],
 [['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: decrease pair count', [60, 90, 90], [[6, 15]]],
  ['repair check: decrease pair count', [45, 69, 60], [[5, 12]]], ['generated control 1', [45, 45, 90], []],
  ['generated control 2', [60, 84, 40], [[3, 8], [4, 4]]], ['generated control 3', [60, 76, 72], [[9, 8]]]],
 [['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: decrease pair count', [50, 58, 40], [[10, 4]]],
  ['repair check: decrease pair count', [56, 86, 40], [[2, 5], [3, 10]]],
  ['generated control 1', [48, 78, 100], [[6, 5], [7, 10]]],
  ['generated control 2', [50, 66, 100], [[12, 4], [13, 4]]],
  ['generated control 3', [56, 61, 40], 'error: odd difference']],
 [['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: decrease pair count', [48, 64, 60], [[7, 4], [8, 4]]],
  ['repair check: decrease pair count', [56, 86, 60], [[4, 15]]],
  ['generated control 1', [45, 52, 100], 'error: odd difference'],
  ['generated control 2', [51, 75, 5], 'error: not enough rows'],
  ['generated control 3', [48, 50, 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: decrease pair count	`[[1, 2], [2, 4]]`	`[[1, 2], [2, 4]]`	Passed
repair check: decrease pair count	`[]`	`[]`	Passed
generated control 1	`[[40, 1]]`	`[[40, 1]]`	Passed
generated control 2	`error: odd difference`	`error: odd difference`	Passed
generated control 3	`error: odd difference`	`error: odd difference`	Passed

SHA-256 / 819a57ee5e56f722c3875a159c8916c761656457b716a66171217280746e920e

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 2026-09-29T14:52:31.737819+00:00.

Case digest / b5205d37dc4c07dd9167eab450c138eede6079cda3e9b8c4251bcd2d344bd3d7