FAILURE MAP
← Case archive

FA-86016 / Game economy crafting balance / Open access

Repair bill: Discounted bill truncates fractional copper · case 01

Discounted repairs are a copper cheaper than the ceiling rule.

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

ROOT CAUSE

The final price is truncated instead of rounded up.

VERIFIED REPAIR

Restore `math.ceil(price)` at the final rounding step.

Unsuccessful approach: Banker rounding still rounds fractional copper down below one half.

Case contract

Per item cost = max(0, max-dur) * (ilvl//4 + 1) copper. Discount percentages stack multiplicatively on the exact total; the result is rounded up once to copper. Return [gold, silver, copper] with 100 copper per silver and 100 silver per gold.

Why this case matters

Game economies leak or destroy currency when one crafting or pricing rule is off by one boundary, rounding stage or state update; the defect is observable in exact integer outcomes.

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(items, discounts):
    total = 0
    for it in items:
        missing = max(0, it['max'] - it['dur'])
        total += missing * (it['ilvl'] // 4 + 1)
    price = Fraction(total)
    for pct in discounts:
        price = price * (100 - pct) / 100
    cost = int(price)
    return [cost // 10000, cost // 100 % 100, cost % 100]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('fault site final rounding #1',
   [[{'ilvl': 1, 'dur': 120, 'max': 120},
     {'ilvl': 4, 'dur': 84, 'max': 100},
     {'ilvl': 3, 'dur': 40, 'max': 40},
     {'ilvl': 3, 'dur': 0, 'max': 120}],
    [10, 33]],
   [0, 0, 92]),
  ('fault site final rounding #2',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression final rounding #1',
   [[{'ilvl': 113, 'dur': 4, 'max': 40},
     {'ilvl': 84, 'dur': 100, 'max': 100},
     {'ilvl': 276, 'dur': 62, 'max': 100},
     {'ilvl': 4, 'dur': 0, 'max': 120}],
    [33]],
   [0, 26, 43]),
  ('regression final rounding #2',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('fault site final rounding #1',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression final rounding #1',
   [[{'ilvl': 113, 'dur': 4, 'max': 40},
     {'ilvl': 84, 'dur': 100, 'max': 100},
     {'ilvl': 276, 'dur': 62, 'max': 100},
     {'ilvl': 4, 'dur': 0, 'max': 120}],
    [33]],
   [0, 26, 43]),
  ('regression final rounding #2',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('regression final rounding #3',
   [[{'ilvl': 4, 'dur': 29, 'max': 100}, {'ilvl': 7, 'dur': 0, 'max': 100}], [20, 10]],
   [0, 2, 47]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression final rounding #1',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('fault site final rounding #1',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('regression final rounding #2', [[{'ilvl': 1, 'dur': 89, 'max': 100}], [33]], [0, 0, 8]),
  ('regression final rounding #3',
   [[{'ilvl': 1, 'dur': 69, 'max': 120},
     {'ilvl': 254, 'dur': 20, 'max': 60},
     {'ilvl': 7, 'dur': 0, 'max': 120},
     {'ilvl': 1, 'dur': 103, 'max': 100}],
    [33]],
   [0, 19, 11]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression final rounding #1',
   [[{'ilvl': 4, 'dur': 29, 'max': 100}, {'ilvl': 7, 'dur': 0, 'max': 100}], [20, 10]],
   [0, 2, 47]),
  ('regression final rounding #2', [[{'ilvl': 1, 'dur': 89, 'max': 100}], [33]], [0, 0, 8]),
  ('regression final rounding #3',
   [[{'ilvl': 8, 'dur': 0, 'max': 120}, {'ilvl': 4, 'dur': 63, 'max': 60}, {'ilvl': 7, 'dur': 60, 'max': 60}],
    [10, 33]],
   [0, 2, 18]),
  ('regression final rounding #4',
   [[{'ilvl': 7, 'dur': 44, 'max': 120}, {'ilvl': 8, 'dur': 60, 'max': 60}], [5, 15, 10]],
   [0, 1, 11]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1',
   [[{'ilvl': 4, 'dur': 63, 'max': 60},
     {'ilvl': 130, 'dur': 63, 'max': 60},
     {'ilvl': 3, 'dur': 60, 'max': 60}],
    [25, 25]],
   [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('fault site final rounding #1',
   [[{'ilvl': 8, 'dur': 43, 'max': 40},
     {'ilvl': 7, 'dur': 0, 'max': 40},
     {'ilvl': 316, 'dur': 123, 'max': 120}],
    [15, 25, 10]],
   [0, 0, 46]),
  ('fault site final rounding #2',
   [[{'ilvl': 7, 'dur': 100, 'max': 100},
     {'ilvl': 1, 'dur': 37, 'max': 40},
     {'ilvl': 7, 'dur': 103, 'max': 100}],
    [25, 15]],
   [0, 0, 2]),
  ('regression final rounding #1',
   [[{'ilvl': 7, 'dur': 0, 'max': 100}, {'ilvl': 4, 'dur': 44, 'max': 60}], [20, 20]],
   [0, 1, 49]),
  ('regression final rounding #2',
   [[{'ilvl': 8, 'dur': 120, 'max': 120},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 8, 'dur': 16, 'max': 40},
     {'ilvl': 1, 'dur': 120, 'max': 120}],
    [5, 25, 20]],
   [0, 0, 99]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 111, 'dur': 123, 'max': 120}], []], [0, 0, 0])]]
for label, args, expected in cases[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 fixtureActualExpectedOutcome
two stacked discounts #1[0, 22, 46][0, 22, 47]Failed
fault site final rounding #1[0, 0, 91][0, 0, 92]Failed
fault site final rounding #2[0, 5, 95][0, 5, 96]Failed
regression final rounding #1[0, 26, 42][0, 26, 43]Failed
regression final rounding #2[0, 0, 32][0, 0, 33]Failed
over-repaired piece #1[0, 0, 60][0, 0, 60]Passed
nothing to repair #1[0, 0, 0][0, 0, 0]Passed
control #1[0, 0, 0][0, 0, 0]Passed

SHA-256 / d6c23dec836798b6a95149152d39adc44a57a28699298375ea9b1026099e01be

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(items, discounts):
    total = 0
    for it in items:
        missing = max(0, it['max'] - it['dur'])
        total += missing * (it['ilvl'] // 4 + 1)
    price = Fraction(total)
    for pct in discounts:
        price = price * (100 - pct) / 100
    cost = round(price)
    return [cost // 10000, cost // 100 % 100, cost % 100]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('fault site final rounding #1',
   [[{'ilvl': 1, 'dur': 120, 'max': 120},
     {'ilvl': 4, 'dur': 84, 'max': 100},
     {'ilvl': 3, 'dur': 40, 'max': 40},
     {'ilvl': 3, 'dur': 0, 'max': 120}],
    [10, 33]],
   [0, 0, 92]),
  ('fault site final rounding #2',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression final rounding #1',
   [[{'ilvl': 113, 'dur': 4, 'max': 40},
     {'ilvl': 84, 'dur': 100, 'max': 100},
     {'ilvl': 276, 'dur': 62, 'max': 100},
     {'ilvl': 4, 'dur': 0, 'max': 120}],
    [33]],
   [0, 26, 43]),
  ('regression final rounding #2',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('fault site final rounding #1',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression final rounding #1',
   [[{'ilvl': 113, 'dur': 4, 'max': 40},
     {'ilvl': 84, 'dur': 100, 'max': 100},
     {'ilvl': 276, 'dur': 62, 'max': 100},
     {'ilvl': 4, 'dur': 0, 'max': 120}],
    [33]],
   [0, 26, 43]),
  ('regression final rounding #2',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('regression final rounding #3',
   [[{'ilvl': 4, 'dur': 29, 'max': 100}, {'ilvl': 7, 'dur': 0, 'max': 100}], [20, 10]],
   [0, 2, 47]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression final rounding #1',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('fault site final rounding #1',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('regression final rounding #2', [[{'ilvl': 1, 'dur': 89, 'max': 100}], [33]], [0, 0, 8]),
  ('regression final rounding #3',
   [[{'ilvl': 1, 'dur': 69, 'max': 120},
     {'ilvl': 254, 'dur': 20, 'max': 60},
     {'ilvl': 7, 'dur': 0, 'max': 120},
     {'ilvl': 1, 'dur': 103, 'max': 100}],
    [33]],
   [0, 19, 11]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression final rounding #1',
   [[{'ilvl': 4, 'dur': 29, 'max': 100}, {'ilvl': 7, 'dur': 0, 'max': 100}], [20, 10]],
   [0, 2, 47]),
  ('regression final rounding #2', [[{'ilvl': 1, 'dur': 89, 'max': 100}], [33]], [0, 0, 8]),
  ('regression final rounding #3',
   [[{'ilvl': 8, 'dur': 0, 'max': 120}, {'ilvl': 4, 'dur': 63, 'max': 60}, {'ilvl': 7, 'dur': 60, 'max': 60}],
    [10, 33]],
   [0, 2, 18]),
  ('regression final rounding #4',
   [[{'ilvl': 7, 'dur': 44, 'max': 120}, {'ilvl': 8, 'dur': 60, 'max': 60}], [5, 15, 10]],
   [0, 1, 11]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1',
   [[{'ilvl': 4, 'dur': 63, 'max': 60},
     {'ilvl': 130, 'dur': 63, 'max': 60},
     {'ilvl': 3, 'dur': 60, 'max': 60}],
    [25, 25]],
   [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('fault site final rounding #1',
   [[{'ilvl': 8, 'dur': 43, 'max': 40},
     {'ilvl': 7, 'dur': 0, 'max': 40},
     {'ilvl': 316, 'dur': 123, 'max': 120}],
    [15, 25, 10]],
   [0, 0, 46]),
  ('fault site final rounding #2',
   [[{'ilvl': 7, 'dur': 100, 'max': 100},
     {'ilvl': 1, 'dur': 37, 'max': 40},
     {'ilvl': 7, 'dur': 103, 'max': 100}],
    [25, 15]],
   [0, 0, 2]),
  ('regression final rounding #1',
   [[{'ilvl': 7, 'dur': 0, 'max': 100}, {'ilvl': 4, 'dur': 44, 'max': 60}], [20, 20]],
   [0, 1, 49]),
  ('regression final rounding #2',
   [[{'ilvl': 8, 'dur': 120, 'max': 120},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 8, 'dur': 16, 'max': 40},
     {'ilvl': 1, 'dur': 120, 'max': 120}],
    [5, 25, 20]],
   [0, 0, 99]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 111, 'dur': 123, 'max': 120}], []], [0, 0, 0])]]
for label, args, expected in cases[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 fixtureActualExpectedOutcome
two stacked discounts #1[0, 22, 46][0, 22, 47]Failed
fault site final rounding #1[0, 0, 92][0, 0, 92]Passed
fault site final rounding #2[0, 5, 96][0, 5, 96]Passed
regression final rounding #1[0, 26, 42][0, 26, 43]Failed
regression final rounding #2[0, 0, 32][0, 0, 33]Failed
over-repaired piece #1[0, 0, 60][0, 0, 60]Passed
nothing to repair #1[0, 0, 0][0, 0, 0]Passed
control #1[0, 0, 0][0, 0, 0]Passed

SHA-256 / 19faa68bc862debeb205014e845528acde8d2277993fcf817604608e1f0f40ee

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(items, discounts):
    total = 0
    for it in items:
        missing = max(0, it['max'] - it['dur'])
        total += missing * (it['ilvl'] // 4 + 1)
    price = Fraction(total)
    for pct in discounts:
        price = price * (100 - pct) / 100
    cost = math.ceil(price)
    return [cost // 10000, cost // 100 % 100, cost % 100]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('fault site final rounding #1',
   [[{'ilvl': 1, 'dur': 120, 'max': 120},
     {'ilvl': 4, 'dur': 84, 'max': 100},
     {'ilvl': 3, 'dur': 40, 'max': 40},
     {'ilvl': 3, 'dur': 0, 'max': 120}],
    [10, 33]],
   [0, 0, 92]),
  ('fault site final rounding #2',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression final rounding #1',
   [[{'ilvl': 113, 'dur': 4, 'max': 40},
     {'ilvl': 84, 'dur': 100, 'max': 100},
     {'ilvl': 276, 'dur': 62, 'max': 100},
     {'ilvl': 4, 'dur': 0, 'max': 120}],
    [33]],
   [0, 26, 43]),
  ('regression final rounding #2',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('fault site final rounding #1',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression final rounding #1',
   [[{'ilvl': 113, 'dur': 4, 'max': 40},
     {'ilvl': 84, 'dur': 100, 'max': 100},
     {'ilvl': 276, 'dur': 62, 'max': 100},
     {'ilvl': 4, 'dur': 0, 'max': 120}],
    [33]],
   [0, 26, 43]),
  ('regression final rounding #2',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('regression final rounding #3',
   [[{'ilvl': 4, 'dur': 29, 'max': 100}, {'ilvl': 7, 'dur': 0, 'max': 100}], [20, 10]],
   [0, 2, 47]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression final rounding #1',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('fault site final rounding #1',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('regression final rounding #2', [[{'ilvl': 1, 'dur': 89, 'max': 100}], [33]], [0, 0, 8]),
  ('regression final rounding #3',
   [[{'ilvl': 1, 'dur': 69, 'max': 120},
     {'ilvl': 254, 'dur': 20, 'max': 60},
     {'ilvl': 7, 'dur': 0, 'max': 120},
     {'ilvl': 1, 'dur': 103, 'max': 100}],
    [33]],
   [0, 19, 11]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression final rounding #1',
   [[{'ilvl': 4, 'dur': 29, 'max': 100}, {'ilvl': 7, 'dur': 0, 'max': 100}], [20, 10]],
   [0, 2, 47]),
  ('regression final rounding #2', [[{'ilvl': 1, 'dur': 89, 'max': 100}], [33]], [0, 0, 8]),
  ('regression final rounding #3',
   [[{'ilvl': 8, 'dur': 0, 'max': 120}, {'ilvl': 4, 'dur': 63, 'max': 60}, {'ilvl': 7, 'dur': 60, 'max': 60}],
    [10, 33]],
   [0, 2, 18]),
  ('regression final rounding #4',
   [[{'ilvl': 7, 'dur': 44, 'max': 120}, {'ilvl': 8, 'dur': 60, 'max': 60}], [5, 15, 10]],
   [0, 1, 11]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1',
   [[{'ilvl': 4, 'dur': 63, 'max': 60},
     {'ilvl': 130, 'dur': 63, 'max': 60},
     {'ilvl': 3, 'dur': 60, 'max': 60}],
    [25, 25]],
   [0, 0, 0])],
 [('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('fault site final rounding #1',
   [[{'ilvl': 8, 'dur': 43, 'max': 40},
     {'ilvl': 7, 'dur': 0, 'max': 40},
     {'ilvl': 316, 'dur': 123, 'max': 120}],
    [15, 25, 10]],
   [0, 0, 46]),
  ('fault site final rounding #2',
   [[{'ilvl': 7, 'dur': 100, 'max': 100},
     {'ilvl': 1, 'dur': 37, 'max': 40},
     {'ilvl': 7, 'dur': 103, 'max': 100}],
    [25, 15]],
   [0, 0, 2]),
  ('regression final rounding #1',
   [[{'ilvl': 7, 'dur': 0, 'max': 100}, {'ilvl': 4, 'dur': 44, 'max': 60}], [20, 20]],
   [0, 1, 49]),
  ('regression final rounding #2',
   [[{'ilvl': 8, 'dur': 120, 'max': 120},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 8, 'dur': 16, 'max': 40},
     {'ilvl': 1, 'dur': 120, 'max': 120}],
    [5, 25, 20]],
   [0, 0, 99]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 111, 'dur': 123, 'max': 120}], []], [0, 0, 0])]]
for label, args, expected in cases[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 fixtureActualExpectedOutcome
two stacked discounts #1[0, 22, 47][0, 22, 47]Passed
fault site final rounding #1[0, 0, 92][0, 0, 92]Passed
fault site final rounding #2[0, 5, 96][0, 5, 96]Passed
regression final rounding #1[0, 26, 43][0, 26, 43]Passed
regression final rounding #2[0, 0, 33][0, 0, 33]Passed
over-repaired piece #1[0, 0, 60][0, 0, 60]Passed
nothing to repair #1[0, 0, 0][0, 0, 0]Passed
control #1[0, 0, 0][0, 0, 0]Passed

SHA-256 / 2e6dfc235ffd9414de6f33ac1f3c693c64d7d49e6d624724e0b397f130ca4c06

Verification & scope

Deterministic toy contract stipulated for this model; integer or exact arithmetic only, not a reproduction of any specific game engine. 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 2026-09-29T14:50:45.671654+00:00.

Case digest / f59f0ccdb407f45fed6cf5b31ddd0fe0c749774e56126f7a4c3c023be50ee20c