FAILURE MAP
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FA-40426 / Heap invariants / Open access

Interval heap minimum is the root lower endpoint · case 01

The bounded interval endpoints certificate reports an incorrect minimum.

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

ROOT CAUSE

Interval heap minimum is the root lower endpoint.

VERIFIED REPAIR

Derive minimum using lows[0] if a else None under the stated bounded certificate contract.

Unsuccessful approach: The local patch uses lows[-1] if a else None and still violates the stated relation.

Case contract

An interval heap stores ordered pairs [lo,hi] except the last node may be singleton [x]. Report reversed intervals, low-end heap violations, high-end heap violations treating singleton as both endpoints, global minimum, global maximum, and member count.

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['intervals']; n=len(a); lows=[x[0] for x in a]; highs=[x[-1] for x in a]
    return {'reversed': [i for i,x in enumerate(a) if x[0]>x[-1]],
    'low_order': [i for i in range(1,n) if lows[i]<lows[(i-1)//2]],
    'high_order': [i for i in range(1,n) if highs[i]>highs[(i-1)//2]],
    'minimum': min(highs) if a else None,
    'maximum': highs[0] if a else None,
    'members': sum(len(x) for x in a)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 10], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 10, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 11], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 11, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 12], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 12, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 13], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 13, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 14], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 14, 'members': 8})]][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{'high_order': [], 'low_order': [], 'maximum': None, 'members': 0, 'minimum': None, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': None, 'members': 0, 'minimum': None, 'reversed': []}Passed
regression certificate 2{'high_order': [], 'low_order': [], 'maximum': 4, 'members': 1, 'minimum': 4, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 4, 'members': 1, 'minimum': 4, 'reversed': []}Passed
regression certificate 3{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 5, 'minimum': 3, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 5, 'minimum': 1, 'reversed': []}Failed
regression certificate 4{'high_order': [2], 'low_order': [], 'maximum': 8, 'members': 5, 'minimum': 7, 'reversed': []}{'high_order': [2], 'low_order': [], 'maximum': 8, 'members': 5, 'minimum': 1, 'reversed': []}Failed
regression certificate 5{'high_order': [1, 2], 'low_order': [1, 2], 'maximum': 3, 'members': 6, 'minimum': 3, 'reversed': [0]}{'high_order': [1, 2], 'low_order': [1, 2], 'maximum': 3, 'members': 6, 'minimum': 5, 'reversed': [0]}Failed
regression certificate 6{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 8, 'minimum': 4, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 8, 'minimum': 1, 'reversed': []}Failed
variant-dependent certificate{'high_order': [], 'low_order': [], 'maximum': 10, 'members': 8, 'minimum': 4, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 10, 'members': 8, 'minimum': 1, 'reversed': []}Failed

SHA-256 / 015f0b5933f1e1f400872549c69a7020eb21e7ed502a37fdbe868991b946c7de

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    a=d['intervals']; n=len(a); lows=[x[0] for x in a]; highs=[x[-1] for x in a]
    return {'reversed': [i for i,x in enumerate(a) if x[0]>x[-1]],
    'low_order': [i for i in range(1,n) if lows[i]<lows[(i-1)//2]],
    'high_order': [i for i in range(1,n) if highs[i]>highs[(i-1)//2]],
    'minimum': lows[-1] if a else None,
    'maximum': highs[0] if a else None,
    'members': sum(len(x) for x in a)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 10], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 10, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 11], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 11, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 12], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 12, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 13], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 13, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 14], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 14, 'members': 8})]][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{'high_order': [], 'low_order': [], 'maximum': None, 'members': 0, 'minimum': None, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': None, 'members': 0, 'minimum': None, 'reversed': []}Passed
regression certificate 2{'high_order': [], 'low_order': [], 'maximum': 4, 'members': 1, 'minimum': 4, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 4, 'members': 1, 'minimum': 4, 'reversed': []}Passed
regression certificate 3{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 5, 'minimum': 3, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 5, 'minimum': 1, 'reversed': []}Failed
regression certificate 4{'high_order': [2], 'low_order': [], 'maximum': 8, 'members': 5, 'minimum': 9, 'reversed': []}{'high_order': [2], 'low_order': [], 'maximum': 8, 'members': 5, 'minimum': 1, 'reversed': []}Failed
regression certificate 5{'high_order': [1, 2], 'low_order': [1, 2], 'maximum': 3, 'members': 6, 'minimum': 4, 'reversed': [0]}{'high_order': [1, 2], 'low_order': [1, 2], 'maximum': 3, 'members': 6, 'minimum': 5, 'reversed': [0]}Failed
regression certificate 6{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 8, 'minimum': 4, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 8, 'minimum': 1, 'reversed': []}Failed
variant-dependent certificate{'high_order': [], 'low_order': [], 'maximum': 10, 'members': 8, 'minimum': 4, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 10, 'members': 8, 'minimum': 1, 'reversed': []}Failed

SHA-256 / e1f7233b78b126b28b0b8e34c00e4acba1e9a2a5316fe6ea6928e670d15247a4

3 / The verified repair

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

N = 1
observations = []
def solve(d):
    a=d['intervals']; n=len(a); lows=[x[0] for x in a]; highs=[x[-1] for x in a]
    return {'reversed': [i for i,x in enumerate(a) if x[0]>x[-1]],
    'low_order': [i for i in range(1,n) if lows[i]<lows[(i-1)//2]],
    'high_order': [i for i in range(1,n) if highs[i]>highs[(i-1)//2]],
    'minimum': lows[0] if a else None,
    'maximum': highs[0] if a else None,
    'members': sum(len(x) for x in a)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 10], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 10, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 11], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 11, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 12], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 12, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 13], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 13, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 14], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 14, 'members': 8})]][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{'high_order': [], 'low_order': [], 'maximum': None, 'members': 0, 'minimum': None, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': None, 'members': 0, 'minimum': None, 'reversed': []}Passed
regression certificate 2{'high_order': [], 'low_order': [], 'maximum': 4, 'members': 1, 'minimum': 4, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 4, 'members': 1, 'minimum': 4, 'reversed': []}Passed
regression certificate 3{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 5, 'minimum': 1, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 5, 'minimum': 1, 'reversed': []}Passed
regression certificate 4{'high_order': [2], 'low_order': [], 'maximum': 8, 'members': 5, 'minimum': 1, 'reversed': []}{'high_order': [2], 'low_order': [], 'maximum': 8, 'members': 5, 'minimum': 1, 'reversed': []}Passed
regression certificate 5{'high_order': [1, 2], 'low_order': [1, 2], 'maximum': 3, 'members': 6, 'minimum': 5, 'reversed': [0]}{'high_order': [1, 2], 'low_order': [1, 2], 'maximum': 3, 'members': 6, 'minimum': 5, 'reversed': [0]}Passed
regression certificate 6{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 8, 'minimum': 1, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 9, 'members': 8, 'minimum': 1, 'reversed': []}Passed
variant-dependent certificate{'high_order': [], 'low_order': [], 'maximum': 10, 'members': 8, 'minimum': 1, 'reversed': []}{'high_order': [], 'low_order': [], 'maximum': 10, 'members': 8, 'minimum': 1, 'reversed': []}Passed

SHA-256 / f85459689ba9f8267cd021e24f670f8584dd5b9561096043ca809993d3cc2ffe

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 2026-09-29T14:43:30.977206+00:00.

Case digest / f75182c75b635b2b0225398cb44889eb692426a58ba3a038ed103f1d03d4e70c