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FA-86006 / Game economy crafting balance / Open access

Repair bill: Low-level repairs are free · case 01

Items below item level 4 cost nothing to repair.

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

ROOT CAUSE

The per-point price drops the one-copper base.

VERIFIED REPAIR

Restore `(it['ilvl'] // 4 + 1)` at the per-point price step.

Unsuccessful approach: Shifting the item level before dividing still yields zero for the lowest levels.

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)
    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 = [[('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression per-point price #1',
   [[{'ilvl': 8, 'dur': 18, 'max': 120}, {'ilvl': 3, 'dur': 41, 'max': 60}], [20]],
   [0, 2, 60]),
  ('regression per-point price #2',
   [[{'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]),
  ('regression per-point price #3',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression per-point price #4',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('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]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('regression per-point price #1',
   [[{'ilvl': 8, 'dur': 18, 'max': 120}, {'ilvl': 3, 'dur': 41, 'max': 60}], [20]],
   [0, 2, 60]),
  ('regression per-point price #2',
   [[{'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]),
  ('regression per-point price #3',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression per-point price #4',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression per-point price #1',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('fault site per-point price #1',
   [[{'ilvl': 7, 'dur': 0, 'max': 100}, {'ilvl': 3, 'dur': 78, 'max': 120}], []],
   [0, 2, 42]),
  ('regression per-point price #2',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('regression per-point price #3', [[{'ilvl': 4, 'dur': 0, 'max': 60}], [25]], [0, 0, 90]),
  ('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]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('regression per-point price #1',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('regression per-point price #2', [[{'ilvl': 4, 'dur': 0, 'max': 60}], [25]], [0, 0, 90]),
  ('regression per-point price #3',
   [[{'ilvl': 8, 'dur': 103, 'max': 100}, {'ilvl': 204, 'dur': 26, 'max': 60}], []],
   [0, 17, 68]),
  ('regression per-point price #4',
   [[{'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]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 111, 'dur': 123, 'max': 120}], []], [0, 0, 0])],
 [('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression per-point price #1',
   [[{'ilvl': 8, 'dur': 103, 'max': 100}, {'ilvl': 204, 'dur': 26, 'max': 60}], []],
   [0, 17, 68]),
  ('regression per-point price #2',
   [[{'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 per-point price #3',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('regression per-point price #4',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1',
   [[{'ilvl': 113, 'dur': 123, 'max': 120}, {'ilvl': 8, 'dur': 103, 'max': 100}], []],
   [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
over-repaired piece #1[0, 0, 50][0, 0, 60]Failed
two stacked discounts #1[0, 21, 60][0, 22, 47]Failed
regression per-point price #1[0, 1, 64][0, 2, 60]Failed
regression per-point price #2[0, 0, 10][0, 0, 92]Failed
regression per-point price #3[0, 5, 6][0, 5, 96]Failed
regression per-point price #4[0, 58, 25][0, 59, 46]Failed
nothing to repair #1[0, 0, 0][0, 0, 0]Passed
control #1[0, 0, 0][0, 0, 0]Passed

SHA-256 / 06c8ef7df84a9661df34a4342223742bf0cd2543a1d601ece709d11ec9c9bc05

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'] + 1) // 4)
    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 = [[('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression per-point price #1',
   [[{'ilvl': 8, 'dur': 18, 'max': 120}, {'ilvl': 3, 'dur': 41, 'max': 60}], [20]],
   [0, 2, 60]),
  ('regression per-point price #2',
   [[{'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]),
  ('regression per-point price #3',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression per-point price #4',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('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]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('regression per-point price #1',
   [[{'ilvl': 8, 'dur': 18, 'max': 120}, {'ilvl': 3, 'dur': 41, 'max': 60}], [20]],
   [0, 2, 60]),
  ('regression per-point price #2',
   [[{'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]),
  ('regression per-point price #3',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression per-point price #4',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression per-point price #1',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('fault site per-point price #1',
   [[{'ilvl': 7, 'dur': 0, 'max': 100}, {'ilvl': 3, 'dur': 78, 'max': 120}], []],
   [0, 2, 42]),
  ('regression per-point price #2',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('regression per-point price #3', [[{'ilvl': 4, 'dur': 0, 'max': 60}], [25]], [0, 0, 90]),
  ('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]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('regression per-point price #1',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('regression per-point price #2', [[{'ilvl': 4, 'dur': 0, 'max': 60}], [25]], [0, 0, 90]),
  ('regression per-point price #3',
   [[{'ilvl': 8, 'dur': 103, 'max': 100}, {'ilvl': 204, 'dur': 26, 'max': 60}], []],
   [0, 17, 68]),
  ('regression per-point price #4',
   [[{'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]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 111, 'dur': 123, 'max': 120}], []], [0, 0, 0])],
 [('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression per-point price #1',
   [[{'ilvl': 8, 'dur': 103, 'max': 100}, {'ilvl': 204, 'dur': 26, 'max': 60}], []],
   [0, 17, 68]),
  ('regression per-point price #2',
   [[{'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 per-point price #3',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('regression per-point price #4',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1',
   [[{'ilvl': 113, 'dur': 123, 'max': 120}, {'ilvl': 8, 'dur': 103, 'max': 100}], []],
   [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
over-repaired piece #1[0, 0, 50][0, 0, 60]Failed
two stacked discounts #1[0, 21, 60][0, 22, 47]Failed
regression per-point price #1[0, 1, 79][0, 2, 60]Failed
regression per-point price #2[0, 0, 83][0, 0, 92]Failed
regression per-point price #3[0, 5, 67][0, 5, 96]Failed
regression per-point price #4[0, 58, 84][0, 59, 46]Failed
nothing to repair #1[0, 0, 0][0, 0, 0]Passed
control #1[0, 0, 0][0, 0, 0]Passed

SHA-256 / 8d8d7f7cc330ada5c45a62ccb8eced0ee008384207a9238f9239d59a1de48ed6

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 = [[('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression per-point price #1',
   [[{'ilvl': 8, 'dur': 18, 'max': 120}, {'ilvl': 3, 'dur': 41, 'max': 60}], [20]],
   [0, 2, 60]),
  ('regression per-point price #2',
   [[{'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]),
  ('regression per-point price #3',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression per-point price #4',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('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]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('regression per-point price #1',
   [[{'ilvl': 8, 'dur': 18, 'max': 120}, {'ilvl': 3, 'dur': 41, 'max': 60}], [20]],
   [0, 2, 60]),
  ('regression per-point price #2',
   [[{'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]),
  ('regression per-point price #3',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('regression per-point price #4',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 7, 'dur': 40, 'max': 40}], [20]], [0, 0, 0])],
 [('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression per-point price #1',
   [[{'ilvl': 69, 'dur': 5, 'max': 40},
     {'ilvl': 3, 'dur': 49, 'max': 120},
     {'ilvl': 139, 'dur': 63, 'max': 60}],
    [15]],
   [0, 5, 96]),
  ('fault site per-point price #1',
   [[{'ilvl': 7, 'dur': 0, 'max': 100}, {'ilvl': 3, 'dur': 78, 'max': 120}], []],
   [0, 2, 42]),
  ('regression per-point price #2',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('regression per-point price #3', [[{'ilvl': 4, 'dur': 0, 'max': 60}], [25]], [0, 0, 90]),
  ('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]),
  ('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('regression per-point price #1',
   [[{'ilvl': 1, 'dur': 123, 'max': 120},
     {'ilvl': 7, 'dur': 61, 'max': 120},
     {'ilvl': 3, 'dur': 120, 'max': 120},
     {'ilvl': 374, 'dur': 38, 'max': 100}],
    []],
   [0, 59, 46]),
  ('regression per-point price #2', [[{'ilvl': 4, 'dur': 0, 'max': 60}], [25]], [0, 0, 90]),
  ('regression per-point price #3',
   [[{'ilvl': 8, 'dur': 103, 'max': 100}, {'ilvl': 204, 'dur': 26, 'max': 60}], []],
   [0, 17, 68]),
  ('regression per-point price #4',
   [[{'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]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1', [[{'ilvl': 111, 'dur': 123, 'max': 120}], []], [0, 0, 0])],
 [('over-repaired piece #1',
   [[{'ilvl': 20, 'dur': 105, 'max': 100}, {'ilvl': 20, 'dur': 90, 'max': 100}], []],
   [0, 0, 60]),
  ('two stacked discounts #1', [[{'ilvl': 100, 'dur': 0, 'max': 120}], [10, 20]], [0, 22, 47]),
  ('regression per-point price #1',
   [[{'ilvl': 8, 'dur': 103, 'max': 100}, {'ilvl': 204, 'dur': 26, 'max': 60}], []],
   [0, 17, 68]),
  ('regression per-point price #2',
   [[{'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 per-point price #3',
   [[{'ilvl': 1, 'dur': 47, 'max': 60},
     {'ilvl': 3, 'dur': 97, 'max': 120},
     {'ilvl': 4, 'dur': 103, 'max': 100}],
    [10]],
   [0, 0, 33]),
  ('regression per-point price #4',
   [[{'ilvl': 377, 'dur': 103, 'max': 100},
     {'ilvl': 1, 'dur': 0, 'max': 100},
     {'ilvl': 1, 'dur': 5, 'max': 60}],
    [15, 10]],
   [0, 1, 19]),
  ('nothing to repair #1', [[], [15]], [0, 0, 0]),
  ('control #1',
   [[{'ilvl': 113, 'dur': 123, 'max': 120}, {'ilvl': 8, 'dur': 103, 'max': 100}], []],
   [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
over-repaired piece #1[0, 0, 60][0, 0, 60]Passed
two stacked discounts #1[0, 22, 47][0, 22, 47]Passed
regression per-point price #1[0, 2, 60][0, 2, 60]Passed
regression per-point price #2[0, 0, 92][0, 0, 92]Passed
regression per-point price #3[0, 5, 96][0, 5, 96]Passed
regression per-point price #4[0, 59, 46][0, 59, 46]Passed
nothing to repair #1[0, 0, 0][0, 0, 0]Passed
control #1[0, 0, 0][0, 0, 0]Passed

SHA-256 / dd884131bd964862b78c10a963572482a3f39a332e965ee4c89755506f758bf4

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 2026-09-29T14:50:45.637386+00:00.

Case digest / d3fdb5c80e8d16f0b7e09c78f2b04a61999eb681001c02d3da62fd8d25f429bb