FAILURE MAP
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FA-40111 / Heap invariants / Open access

Fibonacci cascading cut stops at the first unmarked ancestor · case 01

The bounded fibonacci cascade certificate reports an incorrect cuts.

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

ROOT CAUSE

Fibonacci cascading cut stops at the first unmarked ancestor.

THE FAILURE

Fibonacci cascading cut stops at the first unmarked ancestor.

Unsuccessful approach: The local patch uses [x[0] for x in path if not x[1]] and still violates the stated relation.

Case contract

A cascading-cut path runs from the parent of an initially cut node upward as [id,is_root,marked]. Stop at a root or first unmarked nonroot; mark that first unmarked node. Previously marked nonroots are cut and unmarked. Report cut ids, marked stop, cleared ids, visited count, promoted count, and potential change roots+2*marks.

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):
    path=d['path']; cut=[]; marked=None; visited=0
    for ident,root,mark in path:
        visited+=1
        if root: break
        if not mark:
            marked=ident; break
        cut.append(ident)
    return {'cuts': [x[0] for x in path if x[2]],
    'new_mark': marked,
    'cleared': cut,
    'visits': visited,
    'promoted_count': len(cut),
    'potential_delta': -len(cut)+(2 if marked is not None else 0)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100], 'new_mark': 1, 'cleared': [100], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101], 'new_mark': 1, 'cleared': [100, 101], 'visits': 3, 'promoted_count': 2, 'potential_delta': 0})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102], 'new_mark': 1, 'cleared': [100, 101, 102], 'visits': 4, 'promoted_count': 3, 'potential_delta': -1})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [103, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102, 103], 'new_mark': 1, 'cleared': [100, 101, 102, 103], 'visits': 5, 'promoted_count': 4, 'potential_delta': -2})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [103, False, True], [104, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102, 103, 104], 'new_mark': 1, 'cleared': [100, 101, 102, 103, 104], 'visits': 6, 'promoted_count': 5, 'potential_delta': -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{'cleared': [], 'cuts': [], 'new_mark': None, 'potential_delta': 0, 'promoted_count': 0, 'visits': 0}{'cleared': [], 'cuts': [], 'new_mark': None, 'potential_delta': 0, 'promoted_count': 0, 'visits': 0}Passed
regression certificate 2{'cleared': [], 'cuts': [], 'new_mark': None, 'potential_delta': 0, 'promoted_count': 0, 'visits': 1}{'cleared': [], 'cuts': [], 'new_mark': None, 'potential_delta': 0, 'promoted_count': 0, 'visits': 1}Passed
regression certificate 3{'cleared': [], 'cuts': [], 'new_mark': 1, 'potential_delta': 2, 'promoted_count': 0, 'visits': 1}{'cleared': [], 'cuts': [], 'new_mark': 1, 'potential_delta': 2, 'promoted_count': 0, 'visits': 1}Passed
regression certificate 4{'cleared': [1], 'cuts': [1], 'new_mark': 2, 'potential_delta': 1, 'promoted_count': 1, 'visits': 2}{'cleared': [1], 'cuts': [1], 'new_mark': 2, 'potential_delta': 1, 'promoted_count': 1, 'visits': 2}Passed
regression certificate 5{'cleared': [1, 2], 'cuts': [1, 2, 3], 'new_mark': None, 'potential_delta': -2, 'promoted_count': 2, 'visits': 3}{'cleared': [1, 2], 'cuts': [1, 2], 'new_mark': None, 'potential_delta': -2, 'promoted_count': 2, 'visits': 3}Failed
regression certificate 6{'cleared': [], 'cuts': [2], 'new_mark': 1, 'potential_delta': 2, 'promoted_count': 0, 'visits': 1}{'cleared': [], 'cuts': [], 'new_mark': 1, 'potential_delta': 2, 'promoted_count': 0, 'visits': 1}Failed
variant-dependent certificate{'cleared': [100], 'cuts': [100, 2], 'new_mark': 1, 'potential_delta': 1, 'promoted_count': 1, 'visits': 2}{'cleared': [100], 'cuts': [100], 'new_mark': 1, 'potential_delta': 1, 'promoted_count': 1, 'visits': 2}Failed

SHA-256 / 67811f31a0ca1e1df722f7ef0ea48eea351df7b1fc72912e7a43fd7fb6720c6b

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    path=d['path']; cut=[]; marked=None; visited=0
    for ident,root,mark in path:
        visited+=1
        if root: break
        if not mark:
            marked=ident; break
        cut.append(ident)
    return {'cuts': [x[0] for x in path if not x[1]],
    'new_mark': marked,
    'cleared': cut,
    'visits': visited,
    'promoted_count': len(cut),
    'potential_delta': -len(cut)+(2 if marked is not None else 0)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100], 'new_mark': 1, 'cleared': [100], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101], 'new_mark': 1, 'cleared': [100, 101], 'visits': 3, 'promoted_count': 2, 'potential_delta': 0})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102], 'new_mark': 1, 'cleared': [100, 101, 102], 'visits': 4, 'promoted_count': 3, 'potential_delta': -1})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [103, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102, 103], 'new_mark': 1, 'cleared': [100, 101, 102, 103], 'visits': 5, 'promoted_count': 4, 'potential_delta': -2})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [103, False, True], [104, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102, 103, 104], 'new_mark': 1, 'cleared': [100, 101, 102, 103, 104], 'visits': 6, 'promoted_count': 5, 'potential_delta': -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{'cleared': [], 'cuts': [], 'new_mark': None, 'potential_delta': 0, 'promoted_count': 0, 'visits': 0}{'cleared': [], 'cuts': [], 'new_mark': None, 'potential_delta': 0, 'promoted_count': 0, 'visits': 0}Passed
regression certificate 2{'cleared': [], 'cuts': [], 'new_mark': None, 'potential_delta': 0, 'promoted_count': 0, 'visits': 1}{'cleared': [], 'cuts': [], 'new_mark': None, 'potential_delta': 0, 'promoted_count': 0, 'visits': 1}Passed
regression certificate 3{'cleared': [], 'cuts': [1], 'new_mark': 1, 'potential_delta': 2, 'promoted_count': 0, 'visits': 1}{'cleared': [], 'cuts': [], 'new_mark': 1, 'potential_delta': 2, 'promoted_count': 0, 'visits': 1}Failed
regression certificate 4{'cleared': [1], 'cuts': [1, 2], 'new_mark': 2, 'potential_delta': 1, 'promoted_count': 1, 'visits': 2}{'cleared': [1], 'cuts': [1], 'new_mark': 2, 'potential_delta': 1, 'promoted_count': 1, 'visits': 2}Failed
regression certificate 5{'cleared': [1, 2], 'cuts': [1, 2], 'new_mark': None, 'potential_delta': -2, 'promoted_count': 2, 'visits': 3}{'cleared': [1, 2], 'cuts': [1, 2], 'new_mark': None, 'potential_delta': -2, 'promoted_count': 2, 'visits': 3}Passed
regression certificate 6{'cleared': [], 'cuts': [1, 2], 'new_mark': 1, 'potential_delta': 2, 'promoted_count': 0, 'visits': 1}{'cleared': [], 'cuts': [], 'new_mark': 1, 'potential_delta': 2, 'promoted_count': 0, 'visits': 1}Failed
variant-dependent certificate{'cleared': [100], 'cuts': [100, 1, 2], 'new_mark': 1, 'potential_delta': 1, 'promoted_count': 1, 'visits': 2}{'cleared': [100], 'cuts': [100], 'new_mark': 1, 'potential_delta': 1, 'promoted_count': 1, 'visits': 2}Failed

SHA-256 / 8037c96bc8116caf68ec083489cfb741210287fbadc49b5fa3482d12f449e21e

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 2026-09-29T14:43:28.081876+00:00.

Case digest / 54eee34810b5cd2f7203f9808283e1a1968371e4f50276bf2ee353ded5b1f020