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FA-40721 / Heap invariants / Open access

Pairing cut successor points to the preceding sibling or parent according to cut position · case 01

The bounded pairing cut splice certificate reports an incorrect successor previous.

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

ROOT CAUSE

Pairing cut successor points to the preceding sibling or parent according to cut position.

THE FAILURE

Pairing cut successor points to the preceding sibling or parent according to cut position.

Unsuccessful approach: The local patch uses None if not after else [after[0],c] and still violates the stated relation.

Case contract

A pairing-heap cut input contains parent id, ordered child ids, selected child, and preexisting roots. Remove the child while preserving sibling order. Return remaining children, new first child, successor previous pointer (parent if selected was first), predecessor next pointer, promoted root list, and detached child links [parent,previous,next] all None.

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):
    p=d['parent']; cs=d['children']; c=d['child']; k=cs.index(c); before=cs[:k]; after=cs[k+1:]; kept=before+after
    return {'children': kept,
    'first': kept[0] if kept else None,
    'successor_previous': None if not after else [after[0],p],
    'predecessor_next': None if not before else [before[-1],after[0] if after else None],
    'roots': d["roots"]+[c],
    'detached': [None,None,None]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100], 'child': 100, 'roots': [9, 8]}, {'children': [1, 2, 3], 'first': 1, 'successor_previous': None, 'predecessor_next': [3, None], 'roots': [9, 8, 100], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101], 'child': 101, 'roots': [9, 8]}, {'children': [1, 2, 3, 100], 'first': 1, 'successor_previous': None, 'predecessor_next': [100, None], 'roots': [9, 8, 101], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102], 'child': 102, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101], 'first': 1, 'successor_previous': None, 'predecessor_next': [101, None], 'roots': [9, 8, 102], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102, 103], 'child': 103, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101, 102], 'first': 1, 'successor_previous': None, 'predecessor_next': [102, None], 'roots': [9, 8, 103], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102, 103, 104], 'child': 104, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101, 102, 103], 'first': 1, 'successor_previous': None, 'predecessor_next': [103, None], 'roots': [9, 8, 104], 'detached': [None, None, None]})]][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{'children': [], 'detached': [None, None, None], 'first': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': None}{'children': [], 'detached': [None, None, None], 'first': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': None}Passed
regression certificate 2{'children': [2], 'detached': [None, None, None], 'first': 2, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': [2, 9]}{'children': [2], 'detached': [None, None, None], 'first': 2, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': [2, 9]}Passed
regression certificate 3{'children': [1], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'successor_previous': None}{'children': [1], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'successor_previous': None}Passed
regression certificate 4{'children': [1, 3], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'successor_previous': [3, 9]}{'children': [1, 3], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'successor_previous': [3, 1]}Failed
regression certificate 5{'children': [1, 2, 4], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'successor_previous': [4, 9]}{'children': [1, 2, 4], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'successor_previous': [4, 2]}Failed
regression certificate 6{'children': [2, 3], 'detached': [None, None, None], 'first': 2, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': [2, 9]}{'children': [2, 3], 'detached': [None, None, None], 'first': 2, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': [2, 9]}Passed
variant-dependent certificate{'children': [1, 2, 3], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [3, None], 'roots': [9, 8, 100], 'successor_previous': None}{'children': [1, 2, 3], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [3, None], 'roots': [9, 8, 100], 'successor_previous': None}Passed

SHA-256 / 1342f6112287ecf46d39835fe1b934806015f1667712cde422ce86b4ce9d618d

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    p=d['parent']; cs=d['children']; c=d['child']; k=cs.index(c); before=cs[:k]; after=cs[k+1:]; kept=before+after
    return {'children': kept,
    'first': kept[0] if kept else None,
    'successor_previous': None if not after else [after[0],c],
    'predecessor_next': None if not before else [before[-1],after[0] if after else None],
    'roots': d["roots"]+[c],
    'detached': [None,None,None]}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100], 'child': 100, 'roots': [9, 8]}, {'children': [1, 2, 3], 'first': 1, 'successor_previous': None, 'predecessor_next': [3, None], 'roots': [9, 8, 100], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101], 'child': 101, 'roots': [9, 8]}, {'children': [1, 2, 3, 100], 'first': 1, 'successor_previous': None, 'predecessor_next': [100, None], 'roots': [9, 8, 101], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102], 'child': 102, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101], 'first': 1, 'successor_previous': None, 'predecessor_next': [101, None], 'roots': [9, 8, 102], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102, 103], 'child': 103, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101, 102], 'first': 1, 'successor_previous': None, 'predecessor_next': [102, None], 'roots': [9, 8, 103], 'detached': [None, None, None]})], [({'parent': 9, 'children': [1], 'child': 1, 'roots': [9, 8]}, {'children': [], 'first': None, 'successor_previous': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 1, 'roots': [9, 8]}, {'children': [2], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2], 'child': 2, 'roots': [9, 8]}, {'children': [1], 'first': 1, 'successor_previous': None, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 2, 'roots': [9, 8]}, {'children': [1, 3], 'first': 1, 'successor_previous': [3, 1], 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 4], 'child': 3, 'roots': [9, 8]}, {'children': [1, 2, 4], 'first': 1, 'successor_previous': [4, 2], 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3], 'child': 1, 'roots': [9, 8]}, {'children': [2, 3], 'first': 2, 'successor_previous': [2, 9], 'predecessor_next': None, 'roots': [9, 8, 1], 'detached': [None, None, None]}), ({'parent': 9, 'children': [1, 2, 3, 100, 101, 102, 103, 104], 'child': 104, 'roots': [9, 8]}, {'children': [1, 2, 3, 100, 101, 102, 103], 'first': 1, 'successor_previous': None, 'predecessor_next': [103, None], 'roots': [9, 8, 104], 'detached': [None, None, None]})]][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{'children': [], 'detached': [None, None, None], 'first': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': None}{'children': [], 'detached': [None, None, None], 'first': None, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': None}Passed
regression certificate 2{'children': [2], 'detached': [None, None, None], 'first': 2, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': [2, 1]}{'children': [2], 'detached': [None, None, None], 'first': 2, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': [2, 9]}Failed
regression certificate 3{'children': [1], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'successor_previous': None}{'children': [1], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [1, None], 'roots': [9, 8, 2], 'successor_previous': None}Passed
regression certificate 4{'children': [1, 3], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'successor_previous': [3, 2]}{'children': [1, 3], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [1, 3], 'roots': [9, 8, 2], 'successor_previous': [3, 1]}Failed
regression certificate 5{'children': [1, 2, 4], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'successor_previous': [4, 3]}{'children': [1, 2, 4], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [2, 4], 'roots': [9, 8, 3], 'successor_previous': [4, 2]}Failed
regression certificate 6{'children': [2, 3], 'detached': [None, None, None], 'first': 2, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': [2, 1]}{'children': [2, 3], 'detached': [None, None, None], 'first': 2, 'predecessor_next': None, 'roots': [9, 8, 1], 'successor_previous': [2, 9]}Failed
variant-dependent certificate{'children': [1, 2, 3], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [3, None], 'roots': [9, 8, 100], 'successor_previous': None}{'children': [1, 2, 3], 'detached': [None, None, None], 'first': 1, 'predecessor_next': [3, None], 'roots': [9, 8, 100], 'successor_previous': None}Passed

SHA-256 / dac86f40572c9406ab7474e0389abb59fe6f9f45ae6cdfaf1879264c0b3bca4b

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:43:33.994539+00:00.

Case digest / e900b0227c6fb9c6eb9c0c6c011d606bfdd69ec6385c242bb2bef8055db18504