FA-97676 / Knitting and sewing pattern grading / Open access

Sleeve cap ease checker: armhole length · case 01

Every sleeve cap shows about 24 cm of ease.

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

ROOT CAUSE

Only the front armhole is subtracted.

VERIFIED REPAIR

Subtract front plus back armhole.

Unsuccessful approach: Doubling the front assumes a symmetric armhole, which the back often is not.

Case contract

Ease = cap - (front + back armhole). Allowed ease: woven 2.5-4.5, knit 0-1.5, leather 0-0.5 (inclusive; fabric trimmed, lower-case; other -> "error: fabric"). Verdict "too little", "too much" or "ok". Adjustment per side = (midpoint - ease)/2. Return [ease, verdict, adjust] with floats rounded to 2 decimals.

Why this case matters

Set-in sleeves need a fabric-dependent amount of cap ease to ease into the armhole.

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(cap, front, back, fabric):
    R = {'woven': (Fraction(5, 2), Fraction(9, 2)), 'knit': (Fraction(0), Fraction(3, 2)), 'leather': (Fraction(0), Fraction(1, 2))}
    f = fabric.strip().lower()
    if f not in R:
        return 'error: fabric'
    lo, hi = R[f]
    ease = Fraction(cap) - Fraction(front)
    if ease < lo:
        verdict = 'too little'
    elif ease > hi:
        verdict = 'too much'
    else:
        verdict = 'ok'
    adjust = ((lo + hi) / 2 - ease) / 2
    return [round(float(ease), 2), verdict, round(float(adjust), 2)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['regression: armhole length', ['52', '23.5', '22', 'leather'], [6.5, 'too much', -3.12]],
  ['repair check: armhole length', ['50.5', '24', '22', 'knit'], [4.5, 'too much', -1.88]],
  ['generated control 1', ['50.5', '24', '22', 'felt'], 'error: fabric'],
  ['generated control 2', ['49', '23.5', '24.5', 'Knit '], [1.0, 'ok', -0.12]],
  ['generated control 3', ['50.5', '22', '22', 'Knit '], [6.5, 'too much', -2.88]]],
 [['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['woven lower edge', ['50.5', '24', '24', 'woven'], [2.5, 'ok', 0.5]],
  ['regression: armhole length', ['52', '23.5', '23', 'knit'], [5.5, 'too much', -2.38]],
  ['repair check: armhole length', ['52', '23.5', '23', 'Knit '], [5.5, 'too much', -2.38]],
  ['generated control 1', ['50.5', '22', '23', 'Knit '], [5.5, 'too much', -2.38]],
  ['generated control 2', ['52', '22', '24.5', 'leather'], [5.5, 'too much', -2.62]],
  ['generated control 3', ['48', '23.5', '24.5', 'woven'], [0.0, 'too little', 1.75]]],
 [['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['woven lower edge', ['50.5', '24', '24', 'woven'], [2.5, 'ok', 0.5]],
  ['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['regression: armhole length', ['46', '23.5', '23', 'woven'], [-0.5, 'too little', 2.0]],
  ['repair check: armhole length', ['52', '22', '23', 'woven'], [7.0, 'too much', -1.75]],
  ['generated control 1', ['52', '22', '24.5', 'woven'], [5.5, 'too much', -1.0]],
  ['generated control 2', ['46', '22', '22', 'woven'], [2.0, 'too little', 0.75]],
  ['generated control 3', ['49', '24', '24.5', 'leather'], [0.5, 'ok', -0.12]]],
 [['woven lower edge', ['50.5', '24', '24', 'woven'], [2.5, 'ok', 0.5]],
  ['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['regression: armhole length', ['46', '22', '24.5', 'knit'], [-0.5, 'too little', 0.62]],
  ['repair check: armhole length', ['49', '22', '24.5', 'leather'], [2.5, 'too much', -1.12]],
  ['generated control 1', ['49', '22', '24.5', 'felt'], 'error: fabric'],
  ['generated control 2', ['49', '24', '24.5', 'woven'], [0.5, 'too little', 1.5]],
  ['generated control 3', ['50.5', '22', '22', 'Knit '], [6.5, 'too much', -2.88]]],
 [['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['regression: armhole length', ['49', '22', '24.5', 'woven'], [2.5, 'ok', 0.5]],
  ['repair check: armhole length', ['52', '22', '23', 'knit'], [7.0, 'too much', -3.12]],
  ['generated control 1', ['46', '22', '22', 'Knit '], [2.0, 'too much', -0.62]],
  ['generated control 2', ['52', '23.5', '22', 'felt'], 'error: fabric'],
  ['generated control 3', ['48', '22', '22', 'woven'], [4.0, 'ok', -0.25]]]]
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
woven ok	`[27.0, 'too much', -11.75]`	`[3.0, 'ok', 0.25]`	Failed
knit too much	`[28.0, 'too much', -13.62]`	`[3.5, 'too much', -1.38]`	Failed
leather at lower bound	`[23.0, 'too much', -11.38]`	`[0.0, 'ok', 0.12]`	Failed
regression: armhole length	`[28.5, 'too much', -14.12]`	`[6.5, 'too much', -3.12]`	Failed
repair check: armhole length	`[26.5, 'too much', -12.88]`	`[4.5, 'too much', -1.88]`	Failed
generated control 1	`error: fabric`	`error: fabric`	Passed
generated control 2	`[25.5, 'too much', -12.38]`	`[1.0, 'ok', -0.12]`	Failed
generated control 3	`[28.5, 'too much', -13.88]`	`[6.5, 'too much', -2.88]`	Failed

SHA-256 / 8ba9d2c0e2825df9c41550fb367bded00866acc8d00456a4e356e4b57452a73f

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(cap, front, back, fabric):
    R = {'woven': (Fraction(5, 2), Fraction(9, 2)), 'knit': (Fraction(0), Fraction(3, 2)), 'leather': (Fraction(0), Fraction(1, 2))}
    f = fabric.strip().lower()
    if f not in R:
        return 'error: fabric'
    lo, hi = R[f]
    ease = Fraction(cap) - 2 * Fraction(front)
    if ease < lo:
        verdict = 'too little'
    elif ease > hi:
        verdict = 'too much'
    else:
        verdict = 'ok'
    adjust = ((lo + hi) / 2 - ease) / 2
    return [round(float(ease), 2), verdict, round(float(adjust), 2)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['regression: armhole length', ['52', '23.5', '22', 'leather'], [6.5, 'too much', -3.12]],
  ['repair check: armhole length', ['50.5', '24', '22', 'knit'], [4.5, 'too much', -1.88]],
  ['generated control 1', ['50.5', '24', '22', 'felt'], 'error: fabric'],
  ['generated control 2', ['49', '23.5', '24.5', 'Knit '], [1.0, 'ok', -0.12]],
  ['generated control 3', ['50.5', '22', '22', 'Knit '], [6.5, 'too much', -2.88]]],
 [['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['woven lower edge', ['50.5', '24', '24', 'woven'], [2.5, 'ok', 0.5]],
  ['regression: armhole length', ['52', '23.5', '23', 'knit'], [5.5, 'too much', -2.38]],
  ['repair check: armhole length', ['52', '23.5', '23', 'Knit '], [5.5, 'too much', -2.38]],
  ['generated control 1', ['50.5', '22', '23', 'Knit '], [5.5, 'too much', -2.38]],
  ['generated control 2', ['52', '22', '24.5', 'leather'], [5.5, 'too much', -2.62]],
  ['generated control 3', ['48', '23.5', '24.5', 'woven'], [0.0, 'too little', 1.75]]],
 [['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['woven lower edge', ['50.5', '24', '24', 'woven'], [2.5, 'ok', 0.5]],
  ['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['regression: armhole length', ['46', '23.5', '23', 'woven'], [-0.5, 'too little', 2.0]],
  ['repair check: armhole length', ['52', '22', '23', 'woven'], [7.0, 'too much', -1.75]],
  ['generated control 1', ['52', '22', '24.5', 'woven'], [5.5, 'too much', -1.0]],
  ['generated control 2', ['46', '22', '22', 'woven'], [2.0, 'too little', 0.75]],
  ['generated control 3', ['49', '24', '24.5', 'leather'], [0.5, 'ok', -0.12]]],
 [['woven lower edge', ['50.5', '24', '24', 'woven'], [2.5, 'ok', 0.5]],
  ['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['regression: armhole length', ['46', '22', '24.5', 'knit'], [-0.5, 'too little', 0.62]],
  ['repair check: armhole length', ['49', '22', '24.5', 'leather'], [2.5, 'too much', -1.12]],
  ['generated control 1', ['49', '22', '24.5', 'felt'], 'error: fabric'],
  ['generated control 2', ['49', '24', '24.5', 'woven'], [0.5, 'too little', 1.5]],
  ['generated control 3', ['50.5', '22', '22', 'Knit '], [6.5, 'too much', -2.88]]],
 [['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['regression: armhole length', ['49', '22', '24.5', 'woven'], [2.5, 'ok', 0.5]],
  ['repair check: armhole length', ['52', '22', '23', 'knit'], [7.0, 'too much', -3.12]],
  ['generated control 1', ['46', '22', '22', 'Knit '], [2.0, 'too much', -0.62]],
  ['generated control 2', ['52', '23.5', '22', 'felt'], 'error: fabric'],
  ['generated control 3', ['48', '22', '22', 'woven'], [4.0, 'ok', -0.25]]]]
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
woven ok	`[4.0, 'ok', -0.25]`	`[3.0, 'ok', 0.25]`	Failed
knit too much	`[4.0, 'too much', -1.62]`	`[3.5, 'too much', -1.38]`	Failed
leather at lower bound	`[0.0, 'ok', 0.12]`	`[0.0, 'ok', 0.12]`	Passed
regression: armhole length	`[5.0, 'too much', -2.38]`	`[6.5, 'too much', -3.12]`	Failed
repair check: armhole length	`[2.5, 'too much', -0.88]`	`[4.5, 'too much', -1.88]`	Failed
generated control 1	`error: fabric`	`error: fabric`	Passed
generated control 2	`[2.0, 'too much', -0.62]`	`[1.0, 'ok', -0.12]`	Failed
generated control 3	`[6.5, 'too much', -2.88]`	`[6.5, 'too much', -2.88]`	Passed

SHA-256 / b1032114594dfe78e7e418d7d47c7b41723326ca78ca185543636d7e79341903

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(cap, front, back, fabric):
    R = {'woven': (Fraction(5, 2), Fraction(9, 2)), 'knit': (Fraction(0), Fraction(3, 2)), 'leather': (Fraction(0), Fraction(1, 2))}
    f = fabric.strip().lower()
    if f not in R:
        return 'error: fabric'
    lo, hi = R[f]
    ease = Fraction(cap) - (Fraction(front) + Fraction(back))
    if ease < lo:
        verdict = 'too little'
    elif ease > hi:
        verdict = 'too much'
    else:
        verdict = 'ok'
    adjust = ((lo + hi) / 2 - ease) / 2
    return [round(float(ease), 2), verdict, round(float(adjust), 2)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['regression: armhole length', ['52', '23.5', '22', 'leather'], [6.5, 'too much', -3.12]],
  ['repair check: armhole length', ['50.5', '24', '22', 'knit'], [4.5, 'too much', -1.88]],
  ['generated control 1', ['50.5', '24', '22', 'felt'], 'error: fabric'],
  ['generated control 2', ['49', '23.5', '24.5', 'Knit '], [1.0, 'ok', -0.12]],
  ['generated control 3', ['50.5', '22', '22', 'Knit '], [6.5, 'too much', -2.88]]],
 [['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['woven lower edge', ['50.5', '24', '24', 'woven'], [2.5, 'ok', 0.5]],
  ['regression: armhole length', ['52', '23.5', '23', 'knit'], [5.5, 'too much', -2.38]],
  ['repair check: armhole length', ['52', '23.5', '23', 'Knit '], [5.5, 'too much', -2.38]],
  ['generated control 1', ['50.5', '22', '23', 'Knit '], [5.5, 'too much', -2.38]],
  ['generated control 2', ['52', '22', '24.5', 'leather'], [5.5, 'too much', -2.62]],
  ['generated control 3', ['48', '23.5', '24.5', 'woven'], [0.0, 'too little', 1.75]]],
 [['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['woven lower edge', ['50.5', '24', '24', 'woven'], [2.5, 'ok', 0.5]],
  ['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['regression: armhole length', ['46', '23.5', '23', 'woven'], [-0.5, 'too little', 2.0]],
  ['repair check: armhole length', ['52', '22', '23', 'woven'], [7.0, 'too much', -1.75]],
  ['generated control 1', ['52', '22', '24.5', 'woven'], [5.5, 'too much', -1.0]],
  ['generated control 2', ['46', '22', '22', 'woven'], [2.0, 'too little', 0.75]],
  ['generated control 3', ['49', '24', '24.5', 'leather'], [0.5, 'ok', -0.12]]],
 [['woven lower edge', ['50.5', '24', '24', 'woven'], [2.5, 'ok', 0.5]],
  ['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['regression: armhole length', ['46', '22', '24.5', 'knit'], [-0.5, 'too little', 0.62]],
  ['repair check: armhole length', ['49', '22', '24.5', 'leather'], [2.5, 'too much', -1.12]],
  ['generated control 1', ['49', '22', '24.5', 'felt'], 'error: fabric'],
  ['generated control 2', ['49', '24', '24.5', 'woven'], [0.5, 'too little', 1.5]],
  ['generated control 3', ['50.5', '22', '22', 'Knit '], [6.5, 'too much', -2.88]]],
 [['woven ok', ['50', '23', '24', 'woven'], [3.0, 'ok', 0.25]],
  ['knit too much', ['52', '24', '24.5', 'knit'], [3.5, 'too much', -1.38]],
  ['leather at lower bound', ['46', '23', '23', 'leather'], [0.0, 'ok', 0.12]],
  ['regression: armhole length', ['49', '22', '24.5', 'woven'], [2.5, 'ok', 0.5]],
  ['repair check: armhole length', ['52', '22', '23', 'knit'], [7.0, 'too much', -3.12]],
  ['generated control 1', ['46', '22', '22', 'Knit '], [2.0, 'too much', -0.62]],
  ['generated control 2', ['52', '23.5', '22', 'felt'], 'error: fabric'],
  ['generated control 3', ['48', '22', '22', 'woven'], [4.0, 'ok', -0.25]]]]
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
woven ok	`[3.0, 'ok', 0.25]`	`[3.0, 'ok', 0.25]`	Passed
knit too much	`[3.5, 'too much', -1.38]`	`[3.5, 'too much', -1.38]`	Passed
leather at lower bound	`[0.0, 'ok', 0.12]`	`[0.0, 'ok', 0.12]`	Passed
regression: armhole length	`[6.5, 'too much', -3.12]`	`[6.5, 'too much', -3.12]`	Passed
repair check: armhole length	`[4.5, 'too much', -1.88]`	`[4.5, 'too much', -1.88]`	Passed
generated control 1	`error: fabric`	`error: fabric`	Passed
generated control 2	`[1.0, 'ok', -0.12]`	`[1.0, 'ok', -0.12]`	Passed
generated control 3	`[6.5, 'too much', -2.88]`	`[6.5, 'too much', -2.88]`	Passed

SHA-256 / 9f26548385c3498855c980dd88d3c3adea082acef7295afae67521e613f98112

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 2026-09-29T14:52:34.457000+00:00.

Case digest / 5d378bc163b99dc88e836f172e9ab95e676ab05a5bd2593f9f4281af68bb2d58