FA-86296 / Game economy crafting balance / Open access
Crafting station queue: Jobs wait for every station · case 01
Parallel stations behave like one serial station.
ROOT CAUSE
A job starts when the busiest station frees instead of its own station.
VERIFIED REPAIR
Restore `start = free[s]` at the start time step.
Unsuccessful approach: Adding a one-second gap delays every job.
Case contract
jobs = [[name, duration], ...] in queue order. Effective duration = max(1, floor(duration*(100-speed)/100)). Each job starts on the station that frees earliest (lowest index on ties) at that station free time. Return names of jobs finished by now (finish <= now) ordered by finish time then queue position.
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
N = 1
observations = []
def solve(jobs, stations, speed, now):
free = [0] * stations
done = []
for idx, (name, dur) in enumerate(jobs):
d = max(1, dur * (100 - speed) // 100)
s = min(range(stations), key=lambda k: (free[k], k))
start = max(free)
free[s] = start + d
done.append((free[s], idx, name))
return [name for fin, idx, name in sorted(done) if fin <= now]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('regression start time #1',
[[['flask', 2], ['bow', 10], ['cape', 1], ['dagger', 2], ['anvil', 10], ['ember', 10]], 2, 10, 5],
['flask', 'cape', 'dagger']),
('fault site start time #1',
[[['anvil', 2], ['flask', 2], ['cape', 1], ['dagger', 103], ['ember', 5]], 2, 10, 60],
['anvil', 'flask', 'cape', 'ember']),
('finish exactly now #1', [[['a', 30]], 1, 0, 30], ['a']),
('partial repair boundary #1',
[[['flask', 1], ['cape', 60], ['ember', 1], ['bow', 1], ['anvil', 2], ['dagger', 33]], 2, 25, 1],
['flask']),
('control #1',
[[['dagger', 10], ['bow', 119], ['cape', 1], ['flask', 2], ['ember', 60], ['anvil', 5]], 1, 0, 60],
['dagger']),
('control #2', [[['dagger', 1], ['bow', 5]], 1, 99, 161], ['dagger', 'bow'])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('fault site start time #1',
[[['anvil', 2], ['flask', 2], ['cape', 1], ['dagger', 103], ['ember', 5]], 2, 10, 60],
['anvil', 'flask', 'cape', 'ember']),
('regression start time #1',
[[['anvil', 10], ['bow', 1], ['dagger', 10], ['cape', 60]], 2, 25, 1],
['bow']),
('finish exactly now #1', [[['a', 30]], 1, 0, 30], ['a']),
('regression start time #2',
[[['flask', 2], ['bow', 10], ['cape', 1], ['dagger', 2], ['anvil', 10], ['ember', 10]], 2, 10, 5],
['flask', 'cape', 'dagger']),
('control #1',
[[['dagger', 60], ['flask', 1], ['anvil', 60], ['cape', 1], ['ember', 5], ['bow', 33]], 1, 99, 154],
['dagger', 'flask', 'anvil', 'cape', 'ember', 'bow']),
('control #2', [[['flask', 60]], 1, 25, 30], [])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('finish exactly now #1', [[['a', 30]], 1, 0, 30], ['a']),
('regression start time #1',
[[['cape', 1], ['dagger', 73], ['bow', 1], ['anvil', 2], ['flask', 5], ['ember', 32]], 2, 0, 5],
['cape', 'bow', 'anvil']),
('fault site start time #1',
[[['anvil', 10], ['bow', 60], ['cape', 10]], 2, 50, 260],
['anvil', 'cape', 'bow']),
('partial repair boundary #1',
[[['flask', 1], ['cape', 60], ['ember', 1], ['bow', 1], ['anvil', 2], ['dagger', 33]], 2, 25, 1],
['flask']),
('partial repair boundary #2', [[['anvil', 2]], 3, 90, 1], ['anvil']),
('control #1',
[[['anvil', 105], ['dagger', 10], ['ember', 1], ['flask', 5], ['cape', 5], ['bow', 5]], 1, 99, 0],
[]),
('control #2', [[['flask', 60]], 1, 90, 174], ['flask'])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('regression start time #1',
[[['anvil', 2], ['cape', 60], ['bow', 5], ['ember', 1]], 2, 50, 5],
['anvil', 'bow', 'ember']),
('regression start time #2',
[[['flask', 5], ['bow', 10], ['anvil', 1], ['dagger', 2], ['cape', 78]], 2, 50, 208],
['flask', 'anvil', 'dagger', 'bow', 'cape']),
('partial repair boundary #1', [[['anvil', 2], ['dagger', 2], ['flask', 5]], 1, 90, 1], ['anvil']),
('partial repair boundary #2', [[['anvil', 5], ['dagger', 10], ['cape', 1]], 1, 90, 1], ['anvil']),
('control #1', [[['bow', 5]], 3, 0, 0], []),
('control #2', [[['flask', 10], ['bow', 60]], 1, 90, 5], ['flask'])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('regression start time #1', [[['ember', 1], ['cape', 1], ['bow', 60]], 3, 50, 1], ['ember', 'cape']),
('fault site start time #1',
[[['bow', 60], ['anvil', 60], ['ember', 5], ['dagger', 5]], 3, 0, 133],
['ember', 'dagger', 'bow', 'anvil']),
('regression start time #2',
[[['anvil', 10], ['bow', 1], ['dagger', 10], ['cape', 60]], 2, 25, 1],
['bow']),
('regression start time #3',
[[['cape', 1], ['dagger', 73], ['bow', 1], ['anvil', 2], ['flask', 5], ['ember', 32]], 2, 0, 5],
['cape', 'bow', 'anvil']),
('control #1', [[['dagger', 60], ['cape', 5], ['flask', 1]], 3, 25, 0], []),
('control #2', [[['bow', 100], ['ember', 2], ['flask', 5], ['dagger', 60]], 1, 0, 30], [])]]
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| two stations tie #1 | ['a'] | ['a', 'b', 'c'] | Failed |
| speed floor #1 | ['x', 'y'] | ['x', 'y'] | Passed |
| regression start time #1 | ['flask'] | ['flask', 'cape', 'dagger'] | Failed |
| fault site start time #1 | ['anvil', 'flask', 'cape'] | ['anvil', 'flask', 'cape', 'ember'] | Failed |
| finish exactly now #1 | ['a'] | ['a'] | Passed |
| partial repair boundary #1 | ['flask'] | ['flask'] | Passed |
| control #1 | ['dagger'] | ['dagger'] | Passed |
| control #2 | ['dagger', 'bow'] | ['dagger', 'bow'] | Passed |
SHA-256 / 468bb21ce40af5caf7ee08950b91594459af453eeb3c66e76db052ace082839a
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(jobs, stations, speed, now):
free = [0] * stations
done = []
for idx, (name, dur) in enumerate(jobs):
d = max(1, dur * (100 - speed) // 100)
s = min(range(stations), key=lambda k: (free[k], k))
start = free[s] + 1
free[s] = start + d
done.append((free[s], idx, name))
return [name for fin, idx, name in sorted(done) if fin <= now]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('regression start time #1',
[[['flask', 2], ['bow', 10], ['cape', 1], ['dagger', 2], ['anvil', 10], ['ember', 10]], 2, 10, 5],
['flask', 'cape', 'dagger']),
('fault site start time #1',
[[['anvil', 2], ['flask', 2], ['cape', 1], ['dagger', 103], ['ember', 5]], 2, 10, 60],
['anvil', 'flask', 'cape', 'ember']),
('finish exactly now #1', [[['a', 30]], 1, 0, 30], ['a']),
('partial repair boundary #1',
[[['flask', 1], ['cape', 60], ['ember', 1], ['bow', 1], ['anvil', 2], ['dagger', 33]], 2, 25, 1],
['flask']),
('control #1',
[[['dagger', 10], ['bow', 119], ['cape', 1], ['flask', 2], ['ember', 60], ['anvil', 5]], 1, 0, 60],
['dagger']),
('control #2', [[['dagger', 1], ['bow', 5]], 1, 99, 161], ['dagger', 'bow'])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('fault site start time #1',
[[['anvil', 2], ['flask', 2], ['cape', 1], ['dagger', 103], ['ember', 5]], 2, 10, 60],
['anvil', 'flask', 'cape', 'ember']),
('regression start time #1',
[[['anvil', 10], ['bow', 1], ['dagger', 10], ['cape', 60]], 2, 25, 1],
['bow']),
('finish exactly now #1', [[['a', 30]], 1, 0, 30], ['a']),
('regression start time #2',
[[['flask', 2], ['bow', 10], ['cape', 1], ['dagger', 2], ['anvil', 10], ['ember', 10]], 2, 10, 5],
['flask', 'cape', 'dagger']),
('control #1',
[[['dagger', 60], ['flask', 1], ['anvil', 60], ['cape', 1], ['ember', 5], ['bow', 33]], 1, 99, 154],
['dagger', 'flask', 'anvil', 'cape', 'ember', 'bow']),
('control #2', [[['flask', 60]], 1, 25, 30], [])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('finish exactly now #1', [[['a', 30]], 1, 0, 30], ['a']),
('regression start time #1',
[[['cape', 1], ['dagger', 73], ['bow', 1], ['anvil', 2], ['flask', 5], ['ember', 32]], 2, 0, 5],
['cape', 'bow', 'anvil']),
('fault site start time #1',
[[['anvil', 10], ['bow', 60], ['cape', 10]], 2, 50, 260],
['anvil', 'cape', 'bow']),
('partial repair boundary #1',
[[['flask', 1], ['cape', 60], ['ember', 1], ['bow', 1], ['anvil', 2], ['dagger', 33]], 2, 25, 1],
['flask']),
('partial repair boundary #2', [[['anvil', 2]], 3, 90, 1], ['anvil']),
('control #1',
[[['anvil', 105], ['dagger', 10], ['ember', 1], ['flask', 5], ['cape', 5], ['bow', 5]], 1, 99, 0],
[]),
('control #2', [[['flask', 60]], 1, 90, 174], ['flask'])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('regression start time #1',
[[['anvil', 2], ['cape', 60], ['bow', 5], ['ember', 1]], 2, 50, 5],
['anvil', 'bow', 'ember']),
('regression start time #2',
[[['flask', 5], ['bow', 10], ['anvil', 1], ['dagger', 2], ['cape', 78]], 2, 50, 208],
['flask', 'anvil', 'dagger', 'bow', 'cape']),
('partial repair boundary #1', [[['anvil', 2], ['dagger', 2], ['flask', 5]], 1, 90, 1], ['anvil']),
('partial repair boundary #2', [[['anvil', 5], ['dagger', 10], ['cape', 1]], 1, 90, 1], ['anvil']),
('control #1', [[['bow', 5]], 3, 0, 0], []),
('control #2', [[['flask', 10], ['bow', 60]], 1, 90, 5], ['flask'])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('regression start time #1', [[['ember', 1], ['cape', 1], ['bow', 60]], 3, 50, 1], ['ember', 'cape']),
('fault site start time #1',
[[['bow', 60], ['anvil', 60], ['ember', 5], ['dagger', 5]], 3, 0, 133],
['ember', 'dagger', 'bow', 'anvil']),
('regression start time #2',
[[['anvil', 10], ['bow', 1], ['dagger', 10], ['cape', 60]], 2, 25, 1],
['bow']),
('regression start time #3',
[[['cape', 1], ['dagger', 73], ['bow', 1], ['anvil', 2], ['flask', 5], ['ember', 32]], 2, 0, 5],
['cape', 'bow', 'anvil']),
('control #1', [[['dagger', 60], ['cape', 5], ['flask', 1]], 3, 25, 0], []),
('control #2', [[['bow', 100], ['ember', 2], ['flask', 5], ['dagger', 60]], 1, 0, 30], [])]]
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| two stations tie #1 | ['a', 'b'] | ['a', 'b', 'c'] | Failed |
| speed floor #1 | ['x'] | ['x', 'y'] | Failed |
| regression start time #1 | ['flask', 'cape'] | ['flask', 'cape', 'dagger'] | Failed |
| fault site start time #1 | ['anvil', 'flask', 'cape', 'ember'] | ['anvil', 'flask', 'cape', 'ember'] | Passed |
| finish exactly now #1 | [] | ['a'] | Failed |
| partial repair boundary #1 | [] | ['flask'] | Failed |
| control #1 | ['dagger'] | ['dagger'] | Passed |
| control #2 | ['dagger', 'bow'] | ['dagger', 'bow'] | Passed |
SHA-256 / e8d04e4079c020856fe4c128ca7207181efe7393eb172b737ae82adc929afe63
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(jobs, stations, speed, now):
free = [0] * stations
done = []
for idx, (name, dur) in enumerate(jobs):
d = max(1, dur * (100 - speed) // 100)
s = min(range(stations), key=lambda k: (free[k], k))
start = free[s]
free[s] = start + d
done.append((free[s], idx, name))
return [name for fin, idx, name in sorted(done) if fin <= now]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('regression start time #1',
[[['flask', 2], ['bow', 10], ['cape', 1], ['dagger', 2], ['anvil', 10], ['ember', 10]], 2, 10, 5],
['flask', 'cape', 'dagger']),
('fault site start time #1',
[[['anvil', 2], ['flask', 2], ['cape', 1], ['dagger', 103], ['ember', 5]], 2, 10, 60],
['anvil', 'flask', 'cape', 'ember']),
('finish exactly now #1', [[['a', 30]], 1, 0, 30], ['a']),
('partial repair boundary #1',
[[['flask', 1], ['cape', 60], ['ember', 1], ['bow', 1], ['anvil', 2], ['dagger', 33]], 2, 25, 1],
['flask']),
('control #1',
[[['dagger', 10], ['bow', 119], ['cape', 1], ['flask', 2], ['ember', 60], ['anvil', 5]], 1, 0, 60],
['dagger']),
('control #2', [[['dagger', 1], ['bow', 5]], 1, 99, 161], ['dagger', 'bow'])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('fault site start time #1',
[[['anvil', 2], ['flask', 2], ['cape', 1], ['dagger', 103], ['ember', 5]], 2, 10, 60],
['anvil', 'flask', 'cape', 'ember']),
('regression start time #1',
[[['anvil', 10], ['bow', 1], ['dagger', 10], ['cape', 60]], 2, 25, 1],
['bow']),
('finish exactly now #1', [[['a', 30]], 1, 0, 30], ['a']),
('regression start time #2',
[[['flask', 2], ['bow', 10], ['cape', 1], ['dagger', 2], ['anvil', 10], ['ember', 10]], 2, 10, 5],
['flask', 'cape', 'dagger']),
('control #1',
[[['dagger', 60], ['flask', 1], ['anvil', 60], ['cape', 1], ['ember', 5], ['bow', 33]], 1, 99, 154],
['dagger', 'flask', 'anvil', 'cape', 'ember', 'bow']),
('control #2', [[['flask', 60]], 1, 25, 30], [])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('finish exactly now #1', [[['a', 30]], 1, 0, 30], ['a']),
('regression start time #1',
[[['cape', 1], ['dagger', 73], ['bow', 1], ['anvil', 2], ['flask', 5], ['ember', 32]], 2, 0, 5],
['cape', 'bow', 'anvil']),
('fault site start time #1',
[[['anvil', 10], ['bow', 60], ['cape', 10]], 2, 50, 260],
['anvil', 'cape', 'bow']),
('partial repair boundary #1',
[[['flask', 1], ['cape', 60], ['ember', 1], ['bow', 1], ['anvil', 2], ['dagger', 33]], 2, 25, 1],
['flask']),
('partial repair boundary #2', [[['anvil', 2]], 3, 90, 1], ['anvil']),
('control #1',
[[['anvil', 105], ['dagger', 10], ['ember', 1], ['flask', 5], ['cape', 5], ['bow', 5]], 1, 99, 0],
[]),
('control #2', [[['flask', 60]], 1, 90, 174], ['flask'])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('regression start time #1',
[[['anvil', 2], ['cape', 60], ['bow', 5], ['ember', 1]], 2, 50, 5],
['anvil', 'bow', 'ember']),
('regression start time #2',
[[['flask', 5], ['bow', 10], ['anvil', 1], ['dagger', 2], ['cape', 78]], 2, 50, 208],
['flask', 'anvil', 'dagger', 'bow', 'cape']),
('partial repair boundary #1', [[['anvil', 2], ['dagger', 2], ['flask', 5]], 1, 90, 1], ['anvil']),
('partial repair boundary #2', [[['anvil', 5], ['dagger', 10], ['cape', 1]], 1, 90, 1], ['anvil']),
('control #1', [[['bow', 5]], 3, 0, 0], []),
('control #2', [[['flask', 10], ['bow', 60]], 1, 90, 5], ['flask'])],
[('two stations tie #1', [[['a', 10], ['b', 10], ['c', 5]], 2, 0, 15], ['a', 'b', 'c']),
('speed floor #1', [[['x', 1], ['y', 1]], 1, 90, 2], ['x', 'y']),
('regression start time #1', [[['ember', 1], ['cape', 1], ['bow', 60]], 3, 50, 1], ['ember', 'cape']),
('fault site start time #1',
[[['bow', 60], ['anvil', 60], ['ember', 5], ['dagger', 5]], 3, 0, 133],
['ember', 'dagger', 'bow', 'anvil']),
('regression start time #2',
[[['anvil', 10], ['bow', 1], ['dagger', 10], ['cape', 60]], 2, 25, 1],
['bow']),
('regression start time #3',
[[['cape', 1], ['dagger', 73], ['bow', 1], ['anvil', 2], ['flask', 5], ['ember', 32]], 2, 0, 5],
['cape', 'bow', 'anvil']),
('control #1', [[['dagger', 60], ['cape', 5], ['flask', 1]], 3, 25, 0], []),
('control #2', [[['bow', 100], ['ember', 2], ['flask', 5], ['dagger', 60]], 1, 0, 30], [])]]
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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| two stations tie #1 | ['a', 'b', 'c'] | ['a', 'b', 'c'] | Passed |
| speed floor #1 | ['x', 'y'] | ['x', 'y'] | Passed |
| regression start time #1 | ['flask', 'cape', 'dagger'] | ['flask', 'cape', 'dagger'] | Passed |
| fault site start time #1 | ['anvil', 'flask', 'cape', 'ember'] | ['anvil', 'flask', 'cape', 'ember'] | Passed |
| finish exactly now #1 | ['a'] | ['a'] | Passed |
| partial repair boundary #1 | ['flask'] | ['flask'] | Passed |
| control #1 | ['dagger'] | ['dagger'] | Passed |
| control #2 | ['dagger', 'bow'] | ['dagger', 'bow'] | Passed |
SHA-256 / 90fd24de9c91ae9498db3103b1ca07684cc38ecbf57fb9ef7e57ca0e2b310542
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 2026-09-29T14:50:48.230680+00:00.
Case digest / a3137481340b3302c5079aa736d4e34eab45d5eb0b0b73aeef5ec4374320034e