FA-41296 / Heap invariants / Open access

Rank-loss repair preserves unvisited ranks and applies the full local decrease · case 01

The bounded rank loss propagation certificate reports an incorrect prefix ranks.

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

ROOT CAUSE

Rank-loss repair preserves unvisited ranks and applies the full local decrease.

VERIFIED REPAIR

Derive prefix ranks using [r if x[0] in changed else x[1] for x,r in zip(a,actual)] under the stated bounded certificate contract.

Unsuccessful approach: The local patch uses [x[1]-1 if x[0] in changed else x[1] for x in a] and still violates the stated relation.

Case contract

A stipulated rank-balanced heap repair trace supplies bottom-up nodes [id,stored_rank,left_rank,right_rank], with null child rank -1. Recomputed rank is max child rank if child ranks differ, otherwise child rank+1. A decrease propagates while computed rank is smaller, stopping at first unchanged node. Report local recomputed ranks, decreased ids, stopping id, new prefix ranks, rank drops, and visited count. This models the stated rule only, not every rank-pairing heap variant.

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['nodes']; actual=[max(x[2],x[3]) if x[2]!=x[3] else x[2]+1 for x in a]; changed=[]; stop=None; visited=0
    for x,r in zip(a,actual):
        visited+=1
        if r>=x[1]: stop=x[0]; break
        changed.append(x[0])
    return {'computed': actual,
    'decreased': changed,
    'stop': stop,
    'prefix_ranks': actual,
    'drops': [x[1]-r for x,r in zip(a,actual) if x[0] in changed],
    'visited': visited}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 5, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [2, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 6, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [3, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 7, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [4, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 8, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [5, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 9, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [6, 1], 'visited': 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 fixture	Actual	Expected	Outcome
regression certificate 1	`{'computed': [], 'decreased': [], 'drops': [], 'prefix_ranks': [], 'stop': None, 'visited': 0}`	`{'computed': [], 'decreased': [], 'drops': [], 'prefix_ranks': [], 'stop': None, 'visited': 0}`	Passed
regression certificate 2	`{'computed': [0], 'decreased': [], 'drops': [], 'prefix_ranks': [0], 'stop': 'a', 'visited': 1}`	`{'computed': [0], 'decreased': [], 'drops': [], 'prefix_ranks': [0], 'stop': 'a', 'visited': 1}`	Passed
regression certificate 3	`{'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'drops': [2, 2], 'prefix_ranks': [1, 2, 3], 'stop': 'c', 'visited': 3}`	`{'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'drops': [2, 2], 'prefix_ranks': [1, 2, 3], 'stop': 'c', 'visited': 3}`	Passed
regression certificate 4	`{'computed': [1, 2], 'decreased': [], 'drops': [], 'prefix_ranks': [1, 2], 'stop': 'a', 'visited': 1}`	`{'computed': [1, 2], 'decreased': [], 'drops': [], 'prefix_ranks': [1, 5], 'stop': 'a', 'visited': 1}`	Failed
regression certificate 5	`{'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'drops': [2, 2, 4], 'prefix_ranks': [0, 2, 3], 'stop': None, 'visited': 3}`	`{'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'drops': [2, 2, 4], 'prefix_ranks': [0, 2, 3], 'stop': None, 'visited': 3}`	Passed
regression certificate 6	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [1, 1], 'prefix_ranks': [3, 3, 3, 1], 'stop': 'c', 'visited': 3}`	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [1, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}`	Failed
variant-dependent certificate	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [2, 1], 'prefix_ranks': [3, 3, 3, 1], 'stop': 'c', 'visited': 3}`	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [2, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}`	Failed

SHA-256 / 6384af9dd1b5ab6d1781ce7b124cfb7c4b9dbb25c77d38639cfe21863e54b97d

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(d):
    a=d['nodes']; actual=[max(x[2],x[3]) if x[2]!=x[3] else x[2]+1 for x in a]; changed=[]; stop=None; visited=0
    for x,r in zip(a,actual):
        visited+=1
        if r>=x[1]: stop=x[0]; break
        changed.append(x[0])
    return {'computed': actual,
    'decreased': changed,
    'stop': stop,
    'prefix_ranks': [x[1]-1 if x[0] in changed else x[1] for x in a],
    'drops': [x[1]-r for x,r in zip(a,actual) if x[0] in changed],
    'visited': visited}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 5, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [2, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 6, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [3, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 7, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [4, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 8, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [5, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 9, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [6, 1], 'visited': 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 fixture	Actual	Expected	Outcome
regression certificate 1	`{'computed': [], 'decreased': [], 'drops': [], 'prefix_ranks': [], 'stop': None, 'visited': 0}`	`{'computed': [], 'decreased': [], 'drops': [], 'prefix_ranks': [], 'stop': None, 'visited': 0}`	Passed
regression certificate 2	`{'computed': [0], 'decreased': [], 'drops': [], 'prefix_ranks': [0], 'stop': 'a', 'visited': 1}`	`{'computed': [0], 'decreased': [], 'drops': [], 'prefix_ranks': [0], 'stop': 'a', 'visited': 1}`	Passed
regression certificate 3	`{'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'drops': [2, 2], 'prefix_ranks': [2, 3, 3], 'stop': 'c', 'visited': 3}`	`{'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'drops': [2, 2], 'prefix_ranks': [1, 2, 3], 'stop': 'c', 'visited': 3}`	Failed
regression certificate 4	`{'computed': [1, 2], 'decreased': [], 'drops': [], 'prefix_ranks': [1, 5], 'stop': 'a', 'visited': 1}`	`{'computed': [1, 2], 'decreased': [], 'drops': [], 'prefix_ranks': [1, 5], 'stop': 'a', 'visited': 1}`	Passed
regression certificate 5	`{'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'drops': [2, 2, 4], 'prefix_ranks': [1, 3, 6], 'stop': None, 'visited': 3}`	`{'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'drops': [2, 2, 4], 'prefix_ranks': [0, 2, 3], 'stop': None, 'visited': 3}`	Failed
regression certificate 6	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [1, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}`	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [1, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}`	Passed
variant-dependent certificate	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [2, 1], 'prefix_ranks': [4, 3, 3, 8], 'stop': 'c', 'visited': 3}`	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [2, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}`	Failed

SHA-256 / ddf2c56a4e5788a7173969b48e0e35a0def47ce461ee7660720eed0db3f7e750

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(d):
    a=d['nodes']; actual=[max(x[2],x[3]) if x[2]!=x[3] else x[2]+1 for x in a]; changed=[]; stop=None; visited=0
    for x,r in zip(a,actual):
        visited+=1
        if r>=x[1]: stop=x[0]; break
        changed.append(x[0])
    return {'computed': actual,
    'decreased': changed,
    'stop': stop,
    'prefix_ranks': [r if x[0] in changed else x[1] for x,r in zip(a,actual)],
    'drops': [x[1]-r for x,r in zip(a,actual) if x[0] in changed],
    'visited': visited}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 5, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [2, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 6, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [3, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 7, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [4, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 8, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [5, 1], 'visited': 3})], [({'nodes': []}, {'computed': [], 'decreased': [], 'stop': None, 'prefix_ranks': [], 'drops': [], 'visited': 0}), ({'nodes': [['a', 0, -1, -1]]}, {'computed': [0], 'decreased': [], 'stop': 'a', 'prefix_ranks': [0], 'drops': [], 'visited': 1}), ({'nodes': [['a', 3, 0, 0], ['b', 4, 2, 1], ['c', 3, 2, 2]]}, {'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [1, 2, 3], 'drops': [2, 2], 'visited': 3}), ({'nodes': [['a', 1, 0, 0], ['b', 5, 1, 1]]}, {'computed': [1, 2], 'decreased': [], 'stop': 'a', 'prefix_ranks': [1, 5], 'drops': [], 'visited': 1}), ({'nodes': [['a', 2, 0, -1], ['b', 4, 0, 2], ['c', 7, 2, 3]]}, {'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'stop': None, 'prefix_ranks': [0, 2, 3], 'drops': [2, 2, 4], 'visited': 3}), ({'nodes': [['a', 4, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [1, 1], 'visited': 3}), ({'nodes': [['a', 9, 2, 2], ['b', 4, 3, 2], ['c', 3, 2, 2], ['d', 8, 1, 0]]}, {'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'stop': 'c', 'prefix_ranks': [3, 3, 3, 8], 'drops': [6, 1], 'visited': 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 fixture	Actual	Expected	Outcome
regression certificate 1	`{'computed': [], 'decreased': [], 'drops': [], 'prefix_ranks': [], 'stop': None, 'visited': 0}`	`{'computed': [], 'decreased': [], 'drops': [], 'prefix_ranks': [], 'stop': None, 'visited': 0}`	Passed
regression certificate 2	`{'computed': [0], 'decreased': [], 'drops': [], 'prefix_ranks': [0], 'stop': 'a', 'visited': 1}`	`{'computed': [0], 'decreased': [], 'drops': [], 'prefix_ranks': [0], 'stop': 'a', 'visited': 1}`	Passed
regression certificate 3	`{'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'drops': [2, 2], 'prefix_ranks': [1, 2, 3], 'stop': 'c', 'visited': 3}`	`{'computed': [1, 2, 3], 'decreased': ['a', 'b'], 'drops': [2, 2], 'prefix_ranks': [1, 2, 3], 'stop': 'c', 'visited': 3}`	Passed
regression certificate 4	`{'computed': [1, 2], 'decreased': [], 'drops': [], 'prefix_ranks': [1, 5], 'stop': 'a', 'visited': 1}`	`{'computed': [1, 2], 'decreased': [], 'drops': [], 'prefix_ranks': [1, 5], 'stop': 'a', 'visited': 1}`	Passed
regression certificate 5	`{'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'drops': [2, 2, 4], 'prefix_ranks': [0, 2, 3], 'stop': None, 'visited': 3}`	`{'computed': [0, 2, 3], 'decreased': ['a', 'b', 'c'], 'drops': [2, 2, 4], 'prefix_ranks': [0, 2, 3], 'stop': None, 'visited': 3}`	Passed
regression certificate 6	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [1, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}`	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [1, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}`	Passed
variant-dependent certificate	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [2, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}`	`{'computed': [3, 3, 3, 1], 'decreased': ['a', 'b'], 'drops': [2, 1], 'prefix_ranks': [3, 3, 3, 8], 'stop': 'c', 'visited': 3}`	Passed

SHA-256 / cac4df40074fc937c5243cab79703cb5e19ee24332533b61fd9c7c9777e8c071

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 2026-09-29T14:43:39.589421+00:00.

Case digest / 6006c16dee912fdfec515d31b424f9c2f9b03f50e7fc8ec567941975237ac1b1