FAILURE MAP
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FA-40526 / Heap invariants / Open access

Loser tree propagates the winner to the next match rather than the stored loser · case 01

The bounded loser match certificate reports an incorrect continuation.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Loser tree propagates the winner to the next match rather than the stored loser.

VERIFIED REPAIR

Derive continuation using None if win is None else win[0] under the stated bounded certificate contract.

Unsuccessful approach: The local patch uses a[0] and still violates the stated relation.

Case contract

A loser-tree match compares challenger [run,key,active] and defender likewise. Exhausted entries lose to active entries, ties prefer lower run id, both exhausted produce no winner. Return winner run, stored loser run, active match cost, exhausted runs, winning key, and replay continuation run.

Why this case matters

This isolates an internal heap representation or priority-structure invariant using deterministic finite records.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    a=d['challenger']; b=d['defender']; active=[x for x in (a,b) if x[2]]; win=min(active,key=lambda x:(x[1],x[0])) if active else None; lose=None if win is None else (b if win is a else a)
    return {'winner': None if win is None else win[0],
    'stored_loser': None if lose is None else lose[0],
    'comparisons': int(len(active)==2),
    'exhausted': [x[0] for x in (a,b) if not x[2]],
    'key': None if win is None else win[1],
    'continuation': None if lose is None else lose[0]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 2, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 3, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 4, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 4, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 5, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 5, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 6, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 6, 'continuation': 3})]][N-1]
check('regression certificate 1', solve(cases[0][0]), cases[0][1])
check('regression certificate 2', solve(cases[1][0]), cases[1][1])
check('regression certificate 3', solve(cases[2][0]), cases[2][1])
check('regression certificate 4', solve(cases[3][0]), cases[3][1])
check('regression certificate 5', solve(cases[4][0]), cases[4][1])
check('regression certificate 6', solve(cases[5][0]), cases[5][1])
check('variant-dependent certificate', solve(cases[6][0]), cases[6][1])
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
regression certificate 1{'comparisons': 0, 'continuation': 1, 'exhausted': [1], 'key': 5, 'stored_loser': 1, 'winner': 2}{'comparisons': 0, 'continuation': 2, 'exhausted': [1], 'key': 5, 'stored_loser': 1, 'winner': 2}Failed
regression certificate 2{'comparisons': 1, 'continuation': 7, 'exhausted': [], 'key': 3, 'stored_loser': 7, 'winner': 2}{'comparisons': 1, 'continuation': 2, 'exhausted': [], 'key': 3, 'stored_loser': 7, 'winner': 2}Failed
regression certificate 3{'comparisons': 1, 'continuation': 4, 'exhausted': [], 'key': 2, 'stored_loser': 4, 'winner': 3}{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 2, 'stored_loser': 4, 'winner': 3}Failed
regression certificate 4{'comparisons': 0, 'continuation': 2, 'exhausted': [2], 'key': 0, 'stored_loser': 2, 'winner': 1}{'comparisons': 0, 'continuation': 1, 'exhausted': [2], 'key': 0, 'stored_loser': 2, 'winner': 1}Failed
regression certificate 5{'comparisons': 0, 'continuation': None, 'exhausted': [1, 2], 'key': None, 'stored_loser': None, 'winner': None}{'comparisons': 0, 'continuation': None, 'exhausted': [1, 2], 'key': None, 'stored_loser': None, 'winner': None}Passed
regression certificate 6{'comparisons': 1, 'continuation': 7, 'exhausted': [], 'key': 1, 'stored_loser': 7, 'winner': 3}{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 1, 'stored_loser': 7, 'winner': 3}Failed
variant-dependent certificate{'comparisons': 1, 'continuation': 7, 'exhausted': [], 'key': 2, 'stored_loser': 7, 'winner': 3}{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 2, 'stored_loser': 7, 'winner': 3}Failed

SHA-256 / 89183f947c2d13528c901e161a55aa141992c91d35de81dcc69bc6395ae58b06

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    a=d['challenger']; b=d['defender']; active=[x for x in (a,b) if x[2]]; win=min(active,key=lambda x:(x[1],x[0])) if active else None; lose=None if win is None else (b if win is a else a)
    return {'winner': None if win is None else win[0],
    'stored_loser': None if lose is None else lose[0],
    'comparisons': int(len(active)==2),
    'exhausted': [x[0] for x in (a,b) if not x[2]],
    'key': None if win is None else win[1],
    'continuation': a[0]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 2, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 3, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 4, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 4, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 5, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 5, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 6, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 6, 'continuation': 3})]][N-1]
check('regression certificate 1', solve(cases[0][0]), cases[0][1])
check('regression certificate 2', solve(cases[1][0]), cases[1][1])
check('regression certificate 3', solve(cases[2][0]), cases[2][1])
check('regression certificate 4', solve(cases[3][0]), cases[3][1])
check('regression certificate 5', solve(cases[4][0]), cases[4][1])
check('regression certificate 6', solve(cases[5][0]), cases[5][1])
check('variant-dependent certificate', solve(cases[6][0]), cases[6][1])
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
regression certificate 1{'comparisons': 0, 'continuation': 1, 'exhausted': [1], 'key': 5, 'stored_loser': 1, 'winner': 2}{'comparisons': 0, 'continuation': 2, 'exhausted': [1], 'key': 5, 'stored_loser': 1, 'winner': 2}Failed
regression certificate 2{'comparisons': 1, 'continuation': 7, 'exhausted': [], 'key': 3, 'stored_loser': 7, 'winner': 2}{'comparisons': 1, 'continuation': 2, 'exhausted': [], 'key': 3, 'stored_loser': 7, 'winner': 2}Failed
regression certificate 3{'comparisons': 1, 'continuation': 4, 'exhausted': [], 'key': 2, 'stored_loser': 4, 'winner': 3}{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 2, 'stored_loser': 4, 'winner': 3}Failed
regression certificate 4{'comparisons': 0, 'continuation': 1, 'exhausted': [2], 'key': 0, 'stored_loser': 2, 'winner': 1}{'comparisons': 0, 'continuation': 1, 'exhausted': [2], 'key': 0, 'stored_loser': 2, 'winner': 1}Passed
regression certificate 5{'comparisons': 0, 'continuation': 1, 'exhausted': [1, 2], 'key': None, 'stored_loser': None, 'winner': None}{'comparisons': 0, 'continuation': None, 'exhausted': [1, 2], 'key': None, 'stored_loser': None, 'winner': None}Failed
regression certificate 6{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 1, 'stored_loser': 7, 'winner': 3}{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 1, 'stored_loser': 7, 'winner': 3}Passed
variant-dependent certificate{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 2, 'stored_loser': 7, 'winner': 3}{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 2, 'stored_loser': 7, 'winner': 3}Passed

SHA-256 / 7eaefe7c3a18fb7fb2491bf16a115f5c48af6bcc78441ffff9ee7c54717c6e04

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    a=d['challenger']; b=d['defender']; active=[x for x in (a,b) if x[2]]; win=min(active,key=lambda x:(x[1],x[0])) if active else None; lose=None if win is None else (b if win is a else a)
    return {'winner': None if win is None else win[0],
    'stored_loser': None if lose is None else lose[0],
    'comparisons': int(len(active)==2),
    'exhausted': [x[0] for x in (a,b) if not x[2]],
    'key': None if win is None else win[1],
    'continuation': None if win is None else win[0]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 2, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 3, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 4, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 4, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 5, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 5, 'continuation': 3})], [({'challenger': [1, 0, False], 'defender': [2, 5, True]}, {'winner': 2, 'stored_loser': 1, 'comparisons': 0, 'exhausted': [1], 'key': 5, 'continuation': 2}), ({'challenger': [7, 3, True], 'defender': [2, 3, True]}, {'winner': 2, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 3, 'continuation': 2}), ({'challenger': [4, 8, True], 'defender': [3, 2, True]}, {'winner': 3, 'stored_loser': 4, 'comparisons': 1, 'exhausted': [], 'key': 2, 'continuation': 3}), ({'challenger': [1, 0, True], 'defender': [2, 9, False]}, {'winner': 1, 'stored_loser': 2, 'comparisons': 0, 'exhausted': [2], 'key': 0, 'continuation': 1}), ({'challenger': [1, -9, False], 'defender': [2, 4, False]}, {'winner': None, 'stored_loser': None, 'comparisons': 0, 'exhausted': [1, 2], 'key': None, 'continuation': None}), ({'challenger': [3, 1, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 1, 'continuation': 3}), ({'challenger': [3, 6, True], 'defender': [7, 9, True]}, {'winner': 3, 'stored_loser': 7, 'comparisons': 1, 'exhausted': [], 'key': 6, 'continuation': 3})]][N-1]
check('regression certificate 1', solve(cases[0][0]), cases[0][1])
check('regression certificate 2', solve(cases[1][0]), cases[1][1])
check('regression certificate 3', solve(cases[2][0]), cases[2][1])
check('regression certificate 4', solve(cases[3][0]), cases[3][1])
check('regression certificate 5', solve(cases[4][0]), cases[4][1])
check('regression certificate 6', solve(cases[5][0]), cases[5][1])
check('variant-dependent certificate', solve(cases[6][0]), cases[6][1])
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
regression certificate 1{'comparisons': 0, 'continuation': 2, 'exhausted': [1], 'key': 5, 'stored_loser': 1, 'winner': 2}{'comparisons': 0, 'continuation': 2, 'exhausted': [1], 'key': 5, 'stored_loser': 1, 'winner': 2}Passed
regression certificate 2{'comparisons': 1, 'continuation': 2, 'exhausted': [], 'key': 3, 'stored_loser': 7, 'winner': 2}{'comparisons': 1, 'continuation': 2, 'exhausted': [], 'key': 3, 'stored_loser': 7, 'winner': 2}Passed
regression certificate 3{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 2, 'stored_loser': 4, 'winner': 3}{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 2, 'stored_loser': 4, 'winner': 3}Passed
regression certificate 4{'comparisons': 0, 'continuation': 1, 'exhausted': [2], 'key': 0, 'stored_loser': 2, 'winner': 1}{'comparisons': 0, 'continuation': 1, 'exhausted': [2], 'key': 0, 'stored_loser': 2, 'winner': 1}Passed
regression certificate 5{'comparisons': 0, 'continuation': None, 'exhausted': [1, 2], 'key': None, 'stored_loser': None, 'winner': None}{'comparisons': 0, 'continuation': None, 'exhausted': [1, 2], 'key': None, 'stored_loser': None, 'winner': None}Passed
regression certificate 6{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 1, 'stored_loser': 7, 'winner': 3}{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 1, 'stored_loser': 7, 'winner': 3}Passed
variant-dependent certificate{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 2, 'stored_loser': 7, 'winner': 3}{'comparisons': 1, 'continuation': 3, 'exhausted': [], 'key': 2, 'stored_loser': 7, 'winner': 3}Passed

SHA-256 / bad47467b71916815b670651657eb7c3c43807c896cbacd09450b6cdc662d36e

Verification & scope

A stipulated offline diagnostic model; it does not implement a production allocator, concurrency protocol, or complete heap library. 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 2026-09-29T14:43:31.965541+00:00.

Case digest / 09c70cd9b5023f6f96161583c83c7490aa9172c127710f4103ac24b15bc76700