FA-40496 / Heap invariants / Open access
Winner tournament replay preserves all other leaf payloads · case 01
The bounded tournament path certificate reports an incorrect untouched.
ROOT CAUSE
Winner tournament replay preserves all other leaf payloads.
VERIFIED REPAIR
Derive untouched using [i for i in range(c) if i!=s] under the stated bounded certificate contract.
Unsuccessful approach: The local patch uses [] and still violates the stated relation.
Case contract
A complete winner tournament has power-of-two leaf capacity c and updated leaf slot s. Tree leaves occupy c+s. Report ancestors in bottom-up replay order, sibling indices along that path, root index, comparison count, leaf index, and unaffected leaf slots. Capacity at least one; slot is in range.
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):
c=d['capacity']; s=d['slot']; leaf=c+s; path=[]; siblings=[]; v=leaf
while v>1:
siblings.append(v^1); v//=2; path.append(v)
return {'replay': path,
'siblings': siblings,
'root': 1,
'comparisons': len(path),
'leaf': leaf,
'untouched': [i for i in range(c) if i!=leaf]}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 1}, {'replay': [8, 4, 2, 1], 'siblings': [16, 9, 5, 3], 'root': 1, 'comparisons': 4, 'leaf': 17, 'untouched': [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 2}, {'replay': [9, 4, 2, 1], 'siblings': [19, 8, 5, 3], 'root': 1, 'comparisons': 4, 'leaf': 18, 'untouched': [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 3}, {'replay': [9, 4, 2, 1], 'siblings': [18, 8, 5, 3], 'root': 1, 'comparisons': 4, 'leaf': 19, 'untouched': [0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 4}, {'replay': [10, 5, 2, 1], 'siblings': [21, 11, 4, 3], 'root': 1, 'comparisons': 4, 'leaf': 20, 'untouched': [0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 5}, {'replay': [10, 5, 2, 1], 'siblings': [20, 11, 4, 3], 'root': 1, 'comparisons': 4, 'leaf': 21, 'untouched': [0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})]][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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression certificate 1 | {'comparisons': 0, 'leaf': 1, 'replay': [], 'root': 1, 'siblings': [], 'untouched': [0]} | {'comparisons': 0, 'leaf': 1, 'replay': [], 'root': 1, 'siblings': [], 'untouched': []} | Failed |
| regression certificate 2 | {'comparisons': 1, 'leaf': 3, 'replay': [1], 'root': 1, 'siblings': [2], 'untouched': [0, 1]} | {'comparisons': 1, 'leaf': 3, 'replay': [1], 'root': 1, 'siblings': [2], 'untouched': [0]} | Failed |
| regression certificate 3 | {'comparisons': 2, 'leaf': 4, 'replay': [2, 1], 'root': 1, 'siblings': [5, 3], 'untouched': [0, 1, 2, 3]} | {'comparisons': 2, 'leaf': 4, 'replay': [2, 1], 'root': 1, 'siblings': [5, 3], 'untouched': [1, 2, 3]} | Failed |
| regression certificate 4 | {'comparisons': 2, 'leaf': 7, 'replay': [3, 1], 'root': 1, 'siblings': [6, 2], 'untouched': [0, 1, 2, 3]} | {'comparisons': 2, 'leaf': 7, 'replay': [3, 1], 'root': 1, 'siblings': [6, 2], 'untouched': [0, 1, 2]} | Failed |
| regression certificate 5 | {'comparisons': 3, 'leaf': 13, 'replay': [6, 3, 1], 'root': 1, 'siblings': [12, 7, 2], 'untouched': [0, 1, 2, 3, 4, 5, 6, 7]} | {'comparisons': 3, 'leaf': 13, 'replay': [6, 3, 1], 'root': 1, 'siblings': [12, 7, 2], 'untouched': [0, 1, 2, 3, 4, 6, 7]} | Failed |
| regression certificate 6 | {'comparisons': 4, 'leaf': 26, 'replay': [13, 6, 3, 1], 'root': 1, 'siblings': [27, 12, 7, 2], 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]} | {'comparisons': 4, 'leaf': 26, 'replay': [13, 6, 3, 1], 'root': 1, 'siblings': [27, 12, 7, 2], 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]} | Failed |
| variant-dependent certificate | {'comparisons': 4, 'leaf': 17, 'replay': [8, 4, 2, 1], 'root': 1, 'siblings': [16, 9, 5, 3], 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]} | {'comparisons': 4, 'leaf': 17, 'replay': [8, 4, 2, 1], 'root': 1, 'siblings': [16, 9, 5, 3], 'untouched': [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]} | Failed |
SHA-256 / 2a28124241e9f9ad4caaf8b68b44c0068b12383722bfe91b5d92937351782371
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(d):
c=d['capacity']; s=d['slot']; leaf=c+s; path=[]; siblings=[]; v=leaf
while v>1:
siblings.append(v^1); v//=2; path.append(v)
return {'replay': path,
'siblings': siblings,
'root': 1,
'comparisons': len(path),
'leaf': leaf,
'untouched': []}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 1}, {'replay': [8, 4, 2, 1], 'siblings': [16, 9, 5, 3], 'root': 1, 'comparisons': 4, 'leaf': 17, 'untouched': [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 2}, {'replay': [9, 4, 2, 1], 'siblings': [19, 8, 5, 3], 'root': 1, 'comparisons': 4, 'leaf': 18, 'untouched': [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 3}, {'replay': [9, 4, 2, 1], 'siblings': [18, 8, 5, 3], 'root': 1, 'comparisons': 4, 'leaf': 19, 'untouched': [0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 4}, {'replay': [10, 5, 2, 1], 'siblings': [21, 11, 4, 3], 'root': 1, 'comparisons': 4, 'leaf': 20, 'untouched': [0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 5}, {'replay': [10, 5, 2, 1], 'siblings': [20, 11, 4, 3], 'root': 1, 'comparisons': 4, 'leaf': 21, 'untouched': [0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})]][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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression certificate 1 | {'comparisons': 0, 'leaf': 1, 'replay': [], 'root': 1, 'siblings': [], 'untouched': []} | {'comparisons': 0, 'leaf': 1, 'replay': [], 'root': 1, 'siblings': [], 'untouched': []} | Passed |
| regression certificate 2 | {'comparisons': 1, 'leaf': 3, 'replay': [1], 'root': 1, 'siblings': [2], 'untouched': []} | {'comparisons': 1, 'leaf': 3, 'replay': [1], 'root': 1, 'siblings': [2], 'untouched': [0]} | Failed |
| regression certificate 3 | {'comparisons': 2, 'leaf': 4, 'replay': [2, 1], 'root': 1, 'siblings': [5, 3], 'untouched': []} | {'comparisons': 2, 'leaf': 4, 'replay': [2, 1], 'root': 1, 'siblings': [5, 3], 'untouched': [1, 2, 3]} | Failed |
| regression certificate 4 | {'comparisons': 2, 'leaf': 7, 'replay': [3, 1], 'root': 1, 'siblings': [6, 2], 'untouched': []} | {'comparisons': 2, 'leaf': 7, 'replay': [3, 1], 'root': 1, 'siblings': [6, 2], 'untouched': [0, 1, 2]} | Failed |
| regression certificate 5 | {'comparisons': 3, 'leaf': 13, 'replay': [6, 3, 1], 'root': 1, 'siblings': [12, 7, 2], 'untouched': []} | {'comparisons': 3, 'leaf': 13, 'replay': [6, 3, 1], 'root': 1, 'siblings': [12, 7, 2], 'untouched': [0, 1, 2, 3, 4, 6, 7]} | Failed |
| regression certificate 6 | {'comparisons': 4, 'leaf': 26, 'replay': [13, 6, 3, 1], 'root': 1, 'siblings': [27, 12, 7, 2], 'untouched': []} | {'comparisons': 4, 'leaf': 26, 'replay': [13, 6, 3, 1], 'root': 1, 'siblings': [27, 12, 7, 2], 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]} | Failed |
| variant-dependent certificate | {'comparisons': 4, 'leaf': 17, 'replay': [8, 4, 2, 1], 'root': 1, 'siblings': [16, 9, 5, 3], 'untouched': []} | {'comparisons': 4, 'leaf': 17, 'replay': [8, 4, 2, 1], 'root': 1, 'siblings': [16, 9, 5, 3], 'untouched': [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]} | Failed |
SHA-256 / c814a868a3b52a8731e45f2263707b53d1a2a89ca2f03aae6843b10f0bf1d229
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(d):
c=d['capacity']; s=d['slot']; leaf=c+s; path=[]; siblings=[]; v=leaf
while v>1:
siblings.append(v^1); v//=2; path.append(v)
return {'replay': path,
'siblings': siblings,
'root': 1,
'comparisons': len(path),
'leaf': leaf,
'untouched': [i for i in range(c) if i!=s]}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 1}, {'replay': [8, 4, 2, 1], 'siblings': [16, 9, 5, 3], 'root': 1, 'comparisons': 4, 'leaf': 17, 'untouched': [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 2}, {'replay': [9, 4, 2, 1], 'siblings': [19, 8, 5, 3], 'root': 1, 'comparisons': 4, 'leaf': 18, 'untouched': [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 3}, {'replay': [9, 4, 2, 1], 'siblings': [18, 8, 5, 3], 'root': 1, 'comparisons': 4, 'leaf': 19, 'untouched': [0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 4}, {'replay': [10, 5, 2, 1], 'siblings': [21, 11, 4, 3], 'root': 1, 'comparisons': 4, 'leaf': 20, 'untouched': [0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})], [({'capacity': 1, 'slot': 0}, {'replay': [], 'siblings': [], 'root': 1, 'comparisons': 0, 'leaf': 1, 'untouched': []}), ({'capacity': 2, 'slot': 1}, {'replay': [1], 'siblings': [2], 'root': 1, 'comparisons': 1, 'leaf': 3, 'untouched': [0]}), ({'capacity': 4, 'slot': 0}, {'replay': [2, 1], 'siblings': [5, 3], 'root': 1, 'comparisons': 2, 'leaf': 4, 'untouched': [1, 2, 3]}), ({'capacity': 4, 'slot': 3}, {'replay': [3, 1], 'siblings': [6, 2], 'root': 1, 'comparisons': 2, 'leaf': 7, 'untouched': [0, 1, 2]}), ({'capacity': 8, 'slot': 5}, {'replay': [6, 3, 1], 'siblings': [12, 7, 2], 'root': 1, 'comparisons': 3, 'leaf': 13, 'untouched': [0, 1, 2, 3, 4, 6, 7]}), ({'capacity': 16, 'slot': 10}, {'replay': [13, 6, 3, 1], 'siblings': [27, 12, 7, 2], 'root': 1, 'comparisons': 4, 'leaf': 26, 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]}), ({'capacity': 16, 'slot': 5}, {'replay': [10, 5, 2, 1], 'siblings': [20, 11, 4, 3], 'root': 1, 'comparisons': 4, 'leaf': 21, 'untouched': [0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]})]][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 fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression certificate 1 | {'comparisons': 0, 'leaf': 1, 'replay': [], 'root': 1, 'siblings': [], 'untouched': []} | {'comparisons': 0, 'leaf': 1, 'replay': [], 'root': 1, 'siblings': [], 'untouched': []} | Passed |
| regression certificate 2 | {'comparisons': 1, 'leaf': 3, 'replay': [1], 'root': 1, 'siblings': [2], 'untouched': [0]} | {'comparisons': 1, 'leaf': 3, 'replay': [1], 'root': 1, 'siblings': [2], 'untouched': [0]} | Passed |
| regression certificate 3 | {'comparisons': 2, 'leaf': 4, 'replay': [2, 1], 'root': 1, 'siblings': [5, 3], 'untouched': [1, 2, 3]} | {'comparisons': 2, 'leaf': 4, 'replay': [2, 1], 'root': 1, 'siblings': [5, 3], 'untouched': [1, 2, 3]} | Passed |
| regression certificate 4 | {'comparisons': 2, 'leaf': 7, 'replay': [3, 1], 'root': 1, 'siblings': [6, 2], 'untouched': [0, 1, 2]} | {'comparisons': 2, 'leaf': 7, 'replay': [3, 1], 'root': 1, 'siblings': [6, 2], 'untouched': [0, 1, 2]} | Passed |
| regression certificate 5 | {'comparisons': 3, 'leaf': 13, 'replay': [6, 3, 1], 'root': 1, 'siblings': [12, 7, 2], 'untouched': [0, 1, 2, 3, 4, 6, 7]} | {'comparisons': 3, 'leaf': 13, 'replay': [6, 3, 1], 'root': 1, 'siblings': [12, 7, 2], 'untouched': [0, 1, 2, 3, 4, 6, 7]} | Passed |
| regression certificate 6 | {'comparisons': 4, 'leaf': 26, 'replay': [13, 6, 3, 1], 'root': 1, 'siblings': [27, 12, 7, 2], 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]} | {'comparisons': 4, 'leaf': 26, 'replay': [13, 6, 3, 1], 'root': 1, 'siblings': [27, 12, 7, 2], 'untouched': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15]} | Passed |
| variant-dependent certificate | {'comparisons': 4, 'leaf': 17, 'replay': [8, 4, 2, 1], 'root': 1, 'siblings': [16, 9, 5, 3], 'untouched': [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]} | {'comparisons': 4, 'leaf': 17, 'replay': [8, 4, 2, 1], 'root': 1, 'siblings': [16, 9, 5, 3], 'untouched': [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]} | Passed |
SHA-256 / 83dc30358577aec25ac5b289cc4d0e6a2646988f56c9a8004756f4444acc5438
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 2026-09-29T14:43:31.620403+00:00.
Case digest / 1f32c4db8972f9e0374ab8337f578e52cbe63772b2be6f1fec49ec46af4ad28a