FA-2616 / Indexing / Open access

Composite index conflicts: Forgets NULL exemption in the first component · case 01

The query violates its result contract: forgets null exemption in the first component.

Verified by executionVariant 1 · 10 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Forgets NULL exemption in the first component. The faulty SQL is: SELECT k,v,COUNT() FROM a WHERE v IS NOT NULL GROUP BY k,v HAVING COUNT()>1

VERIFIED REPAIR

Use the required relational semantics: Return (k,v,count) for repeated fully known composite keys; any NULL component exempts a key. Correct SQL: SELECT k,v,COUNT(*) FROM a WHERE k IS NOT NULL AND v IS NOT NULL GROUP BY k,v HAVING COUNT(*)>1

Unsuccessful approach: The alternative query still fails because it treats NULL-containing keys as equal conflicts. Attempted SQL: SELECT k,v,COUNT(*) FROM a GROUP BY k,v HAVING COUNT(*)>1

Case contract

Return (k,v,count) for repeated fully known composite keys; any NULL component exempts a key. Inputs are finite relations a=rows and b=refs with columns (id,k,v,w,flag,parent). IDs are unique within each relation, None is SQL NULL, keys are ASCII strings or None, and other values are integers or None. Return an unordered result bag as lists sorted by repr, preserving multiplicity unless explicitly distinct.

Why this case matters

Executes actual in-memory SQLite relational semantics. The fixtures exercise empty inputs, nullable groups, duplicate facts, known zero, negative values, peer ties and partition boundaries. This models the specified query contract, not optimizer performance, disk durability or a complete migration transaction.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import sqlite3
N = 1
observations = []
def solve(rows, refs):
    db = sqlite3.connect(':memory:')
    try:
        for name, records in [('a', rows), ('b', refs)]:
            db.execute('CREATE TABLE ' + name + ' (id INTEGER PRIMARY KEY, k TEXT, v INTEGER, w INTEGER, flag INTEGER, parent INTEGER)')
            db.executemany('INSERT INTO ' + name + ' VALUES (?,?,?,?,?,?)', records)
        return sorted([list(row) for row in db.execute('SELECT k,v,COUNT(*) FROM a WHERE v IS NOT NULL GROUP BY k,v HAVING COUNT(*)>1')], key=repr)
    finally:
        db.close()
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[11, 'a', None, 8, None, None], [21, 'a', 0, 3, 0, 11], [31, 'a', 2, 1, 1, 21], [41, 'a', 2, 2, 2, 901], [51, 'a', -1, 4, -1, 31], [61, 'a', 3, 1, 1, 41], [71, 'b', -2, 2, 0, 11], [81, 'b', 2, 8, 1, 21], [91, 'b', None, 4, None, None], [101, None, None, 0, 1, 901], [111, None, 0, 5, 0, 11], [121, None, None, 7, None, 21], [131, 'c', None, 6, None, 31], [141, 'd', -1, 1, 0, 41], [151, 'A', 2, 2, 1, 51], [161, ' a ', 2, 8, 1, None], [171, '', None, 2, 0, None], [181, 'a', 2, 8, 1, 11], [191, 'd', 1, 3, 0, 41], [201, 'd', -1, 0, -1, 21]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[11, 'a', None, 0, 1, None], [21, 'a', 2, 2, 0, None], [31, 'a', 2, 3, 2, None], [41, 'a', 3, 4, None, None], [51, 'b', -2, 2, 1, None], [61, 'b', 0, 8, -1, None], [71, None, None, 2, 1, None], [81, None, 0, 5, None, None], [91, 'z', 3, 2, 0, None], [101, 'z', 3, 2, 1, None], [111, 'A', 2, 1, 1, None], [121, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[11, 'a', None, 8, None, None], [21, 'a', 0, 3, 0, 11], [31, 'a', 2, 1, 1, 21], [41, 'a', 2, 2, 2, 901], [51, 'a', -1, 4, -1, 31], [61, 'a', 3, 1, 1, 41], [71, 'b', -2, 2, 0, 11], [81, 'b', 2, 8, 1, 21], [91, 'b', None, 4, None, None], [101, None, None, 0, 1, 901], [111, None, 0, 5, 0, 11], [121, None, None, 7, None, 21], [131, 'c', None, 6, None, 31], [141, 'd', -1, 1, 0, 41], [151, 'A', 2, 2, 1, 51], [161, ' a ', 2, 8, 1, None], [171, '', None, 2, 0, None], [181, 'a', 2, 8, 1, 11], [191, 'd', 1, 3, 0, 41], [201, 'd', -1, 0, -1, 21]], [[11, 'a', None, 0, 1, None], [21, 'a', 2, 2, 0, None], [31, 'a', 2, 3, 2, None], [41, 'a', 3, 4, None, None], [51, 'b', -2, 2, 1, None], [61, 'b', 0, 8, -1, None], [71, None, None, 2, 1, None], [81, None, 0, 5, None, None], [91, 'z', 3, 2, 0, None], [101, 'z', 3, 2, 1, None], [111, 'A', 2, 1, 1, None], [121, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[11, None, None, 3, None, None], [21, None, None, 4, None, None], [31, 'x', None, 5, None, None]], [[11, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[11, 'a', 0, 9, 0, 11]], [[11, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[11, 'n', -2, 4, -1, 11], [21, 'n', None, 2, 0, 21], [31, 'n', -1, 0, 2, None]], [[11, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[11, 'p', 2, 1, 1, 11], [21, 'p', 2, 2, 1, 11], [31, 'p', 3, 0, 1, 11], [41, 'p', None, 1, 0, None]], [[11, 'p', 2, 1, 1, None], [21, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[11, '', 3, 7, 0, 191], [21, 'b', 3, 3, -1, 31], [31, 'c', None, 2, -1, 21], [41, ' a ', 3, 0, 2, 191], [51, ' a ', 1, 3, 2, 21], [61, 'b', None, 2, 0, 11], [71, 'a', -2, 2, -1, None], [81, 'c', None, 0, -1, None], [91, 'a', -1, 1, -1, 31], [101, ' a ', None, 3, 0, 31], [111, 'A', None, 1, 1, 31], [121, 'a', 3, 3, None, None]], [[11, 'c', 0, 2, None, 11], [21, '', 0, 3, 0, 21], [31, 'c', -1, 1, -1, 21], [41, 'a', 2, 2, -1, 191], [51, 'a', -1, 7, -1, 21], [61, ' a ', None, 2, -1, 11], [71, None, 2, 7, 2, 191], [81, 'a', None, 0, -1, 21], [91, None, 2, 1, None, 11], [101, 'b', 3, 2, 1, None], [111, ' a ', 2, 2, 0, 31]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[11, None, -2, 1, 0, 11], [21, 'b', None, 2, 1, 191], [31, None, 2, 7, 2, 191], [41, 'A', 3, 3, -1, 31], [51, ' a ', None, 7, 2, 11], [61, '', 1, 7, 2, None], [71, None, 2, 0, 2, 21], [81, 'A', None, 3, -1, 21], [91, 'a', 2, 7, 2, 191], [101, 'b', 3, 2, 0, None], [111, 'c', None, 3, 2, None], [121, 'A', 5, 2, None, None], [131, ' a ', 0, 1, 1, 21], [141, 'b', 2, 7, 2, None]], [[11, ' a ', -1, 1, 0, 31], [21, 'a', 5, 0, 0, None], [31, 'c', -3, 0, 1, 191], [41, ' a ', 2, 7, 1, None], [51, 'b', None, 7, -1, 11], [61, '', 2, 0, None, 31], [71, 'b', -3, 3, 1, None], [81, 'a', 0, 1, None, 191], [91, 'a', 5, 0, None, 11], [101, '', None, 3, 0, 191]]), [])
elif N == 2:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[12, 'a', None, 8, None, None], [22, 'a', 0, 3, 0, 12], [32, 'a', 2, 1, 1, 22], [42, 'a', 2, 2, 2, 902], [52, 'a', -1, 4, -1, 32], [62, 'a', 3, 1, 1, 42], [72, 'b', -2, 2, 0, 12], [82, 'b', 2, 8, 1, 22], [92, 'b', None, 4, None, None], [102, None, None, 0, 1, 902], [112, None, 0, 5, 0, 12], [122, None, None, 7, None, 22], [132, 'c', None, 6, None, 32], [142, 'd', -1, 1, 0, 42], [152, 'A', 2, 2, 1, 52], [162, ' a ', 2, 8, 1, None], [172, '', None, 2, 0, None], [182, 'a', 2, 8, 1, 12], [192, 'd', 1, 3, 0, 42], [202, 'd', -1, 0, -1, 22]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[12, 'a', None, 0, 1, None], [22, 'a', 2, 2, 0, None], [32, 'a', 2, 3, 2, None], [42, 'a', 3, 4, None, None], [52, 'b', -2, 2, 1, None], [62, 'b', 0, 8, -1, None], [72, None, None, 2, 1, None], [82, None, 0, 5, None, None], [92, 'z', 3, 2, 0, None], [102, 'z', 3, 2, 1, None], [112, 'A', 2, 1, 1, None], [122, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[12, 'a', None, 8, None, None], [22, 'a', 0, 3, 0, 12], [32, 'a', 2, 1, 1, 22], [42, 'a', 2, 2, 2, 902], [52, 'a', -1, 4, -1, 32], [62, 'a', 3, 1, 1, 42], [72, 'b', -2, 2, 0, 12], [82, 'b', 2, 8, 1, 22], [92, 'b', None, 4, None, None], [102, None, None, 0, 1, 902], [112, None, 0, 5, 0, 12], [122, None, None, 7, None, 22], [132, 'c', None, 6, None, 32], [142, 'd', -1, 1, 0, 42], [152, 'A', 2, 2, 1, 52], [162, ' a ', 2, 8, 1, None], [172, '', None, 2, 0, None], [182, 'a', 2, 8, 1, 12], [192, 'd', 1, 3, 0, 42], [202, 'd', -1, 0, -1, 22]], [[12, 'a', None, 0, 1, None], [22, 'a', 2, 2, 0, None], [32, 'a', 2, 3, 2, None], [42, 'a', 3, 4, None, None], [52, 'b', -2, 2, 1, None], [62, 'b', 0, 8, -1, None], [72, None, None, 2, 1, None], [82, None, 0, 5, None, None], [92, 'z', 3, 2, 0, None], [102, 'z', 3, 2, 1, None], [112, 'A', 2, 1, 1, None], [122, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[12, None, None, 3, None, None], [22, None, None, 4, None, None], [32, 'x', None, 5, None, None]], [[12, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[12, 'a', 0, 9, 0, 12]], [[12, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[12, 'n', -2, 4, -1, 12], [22, 'n', None, 2, 0, 22], [32, 'n', -1, 0, 2, None]], [[12, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[12, 'p', 2, 1, 1, 12], [22, 'p', 2, 2, 1, 12], [32, 'p', 3, 0, 1, 12], [42, 'p', None, 1, 0, None]], [[12, 'p', 2, 1, 1, None], [22, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[12, '', 3, 7, 0, 192], [22, 'b', 3, 3, -1, 32], [32, 'c', None, 2, -1, 22], [42, ' a ', 3, 0, 2, 192], [52, ' a ', 1, 3, 2, 22], [62, 'b', None, 2, 0, 12], [72, 'a', -2, 2, -1, None], [82, 'c', None, 0, -1, None], [92, 'a', -1, 1, -1, 32], [102, ' a ', None, 3, 0, 32], [112, 'A', None, 1, 1, 32], [122, 'a', 3, 3, None, None]], [[12, 'c', 0, 2, None, 12], [22, '', 0, 3, 0, 22], [32, 'c', -1, 1, -1, 22], [42, 'a', 2, 2, -1, 192], [52, 'a', -1, 7, -1, 22], [62, ' a ', None, 2, -1, 12], [72, None, 2, 7, 2, 192], [82, 'a', None, 0, -1, 22], [92, None, 2, 1, None, 12], [102, 'b', 3, 2, 1, None], [112, ' a ', 2, 2, 0, 32]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[12, None, -2, 1, 0, 12], [22, 'b', None, 2, 1, 192], [32, None, 2, 7, 2, 192], [42, 'A', 3, 3, -1, 32], [52, ' a ', None, 7, 2, 12], [62, '', 1, 7, 2, None], [72, None, 2, 0, 2, 22], [82, 'A', None, 3, -1, 22], [92, 'a', 2, 7, 2, 192], [102, 'b', 3, 2, 0, None], [112, 'c', None, 3, 2, None], [122, 'A', 5, 2, None, None], [132, ' a ', 0, 1, 1, 22], [142, 'b', 2, 7, 2, None]], [[12, ' a ', -1, 1, 0, 32], [22, 'a', 5, 0, 0, None], [32, 'c', -3, 0, 1, 192], [42, ' a ', 2, 7, 1, None], [52, 'b', None, 7, -1, 12], [62, '', 2, 0, None, 32], [72, 'b', -3, 3, 1, None], [82, 'a', 0, 1, None, 192], [92, 'a', 5, 0, None, 12], [102, '', None, 3, 0, 192]]), [])
elif N == 3:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[13, 'a', None, 8, None, None], [23, 'a', 0, 3, 0, 13], [33, 'a', 2, 1, 1, 23], [43, 'a', 2, 2, 2, 903], [53, 'a', -1, 4, -1, 33], [63, 'a', 3, 1, 1, 43], [73, 'b', -2, 2, 0, 13], [83, 'b', 2, 8, 1, 23], [93, 'b', None, 4, None, None], [103, None, None, 0, 1, 903], [113, None, 0, 5, 0, 13], [123, None, None, 7, None, 23], [133, 'c', None, 6, None, 33], [143, 'd', -1, 1, 0, 43], [153, 'A', 2, 2, 1, 53], [163, ' a ', 2, 8, 1, None], [173, '', None, 2, 0, None], [183, 'a', 2, 8, 1, 13], [193, 'd', 1, 3, 0, 43], [203, 'd', -1, 0, -1, 23]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[13, 'a', None, 0, 1, None], [23, 'a', 2, 2, 0, None], [33, 'a', 2, 3, 2, None], [43, 'a', 3, 4, None, None], [53, 'b', -2, 2, 1, None], [63, 'b', 0, 8, -1, None], [73, None, None, 2, 1, None], [83, None, 0, 5, None, None], [93, 'z', 3, 2, 0, None], [103, 'z', 3, 2, 1, None], [113, 'A', 2, 1, 1, None], [123, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[13, 'a', None, 8, None, None], [23, 'a', 0, 3, 0, 13], [33, 'a', 2, 1, 1, 23], [43, 'a', 2, 2, 2, 903], [53, 'a', -1, 4, -1, 33], [63, 'a', 3, 1, 1, 43], [73, 'b', -2, 2, 0, 13], [83, 'b', 2, 8, 1, 23], [93, 'b', None, 4, None, None], [103, None, None, 0, 1, 903], [113, None, 0, 5, 0, 13], [123, None, None, 7, None, 23], [133, 'c', None, 6, None, 33], [143, 'd', -1, 1, 0, 43], [153, 'A', 2, 2, 1, 53], [163, ' a ', 2, 8, 1, None], [173, '', None, 2, 0, None], [183, 'a', 2, 8, 1, 13], [193, 'd', 1, 3, 0, 43], [203, 'd', -1, 0, -1, 23]], [[13, 'a', None, 0, 1, None], [23, 'a', 2, 2, 0, None], [33, 'a', 2, 3, 2, None], [43, 'a', 3, 4, None, None], [53, 'b', -2, 2, 1, None], [63, 'b', 0, 8, -1, None], [73, None, None, 2, 1, None], [83, None, 0, 5, None, None], [93, 'z', 3, 2, 0, None], [103, 'z', 3, 2, 1, None], [113, 'A', 2, 1, 1, None], [123, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[13, None, None, 3, None, None], [23, None, None, 4, None, None], [33, 'x', None, 5, None, None]], [[13, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[13, 'a', 0, 9, 0, 13]], [[13, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[13, 'n', -2, 4, -1, 13], [23, 'n', None, 2, 0, 23], [33, 'n', -1, 0, 2, None]], [[13, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[13, 'p', 2, 1, 1, 13], [23, 'p', 2, 2, 1, 13], [33, 'p', 3, 0, 1, 13], [43, 'p', None, 1, 0, None]], [[13, 'p', 2, 1, 1, None], [23, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[13, '', 3, 7, 0, 193], [23, 'b', 3, 3, -1, 33], [33, 'c', None, 2, -1, 23], [43, ' a ', 3, 0, 2, 193], [53, ' a ', 1, 3, 2, 23], [63, 'b', None, 2, 0, 13], [73, 'a', -2, 2, -1, None], [83, 'c', None, 0, -1, None], [93, 'a', -1, 1, -1, 33], [103, ' a ', None, 3, 0, 33], [113, 'A', None, 1, 1, 33], [123, 'a', 3, 3, None, None]], [[13, 'c', 0, 2, None, 13], [23, '', 0, 3, 0, 23], [33, 'c', -1, 1, -1, 23], [43, 'a', 2, 2, -1, 193], [53, 'a', -1, 7, -1, 23], [63, ' a ', None, 2, -1, 13], [73, None, 2, 7, 2, 193], [83, 'a', None, 0, -1, 23], [93, None, 2, 1, None, 13], [103, 'b', 3, 2, 1, None], [113, ' a ', 2, 2, 0, 33]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[13, None, -2, 1, 0, 13], [23, 'b', None, 2, 1, 193], [33, None, 2, 7, 2, 193], [43, 'A', 3, 3, -1, 33], [53, ' a ', None, 7, 2, 13], [63, '', 1, 7, 2, None], [73, None, 2, 0, 2, 23], [83, 'A', None, 3, -1, 23], [93, 'a', 2, 7, 2, 193], [103, 'b', 3, 2, 0, None], [113, 'c', None, 3, 2, None], [123, 'A', 5, 2, None, None], [133, ' a ', 0, 1, 1, 23], [143, 'b', 2, 7, 2, None]], [[13, ' a ', -1, 1, 0, 33], [23, 'a', 5, 0, 0, None], [33, 'c', -3, 0, 1, 193], [43, ' a ', 2, 7, 1, None], [53, 'b', None, 7, -1, 13], [63, '', 2, 0, None, 33], [73, 'b', -3, 3, 1, None], [83, 'a', 0, 1, None, 193], [93, 'a', 5, 0, None, 13], [103, '', None, 3, 0, 193]]), [])
elif N == 4:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[14, 'a', None, 8, None, None], [24, 'a', 0, 3, 0, 14], [34, 'a', 2, 1, 1, 24], [44, 'a', 2, 2, 2, 904], [54, 'a', -1, 4, -1, 34], [64, 'a', 3, 1, 1, 44], [74, 'b', -2, 2, 0, 14], [84, 'b', 2, 8, 1, 24], [94, 'b', None, 4, None, None], [104, None, None, 0, 1, 904], [114, None, 0, 5, 0, 14], [124, None, None, 7, None, 24], [134, 'c', None, 6, None, 34], [144, 'd', -1, 1, 0, 44], [154, 'A', 2, 2, 1, 54], [164, ' a ', 2, 8, 1, None], [174, '', None, 2, 0, None], [184, 'a', 2, 8, 1, 14], [194, 'd', 1, 3, 0, 44], [204, 'd', -1, 0, -1, 24]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[14, 'a', None, 0, 1, None], [24, 'a', 2, 2, 0, None], [34, 'a', 2, 3, 2, None], [44, 'a', 3, 4, None, None], [54, 'b', -2, 2, 1, None], [64, 'b', 0, 8, -1, None], [74, None, None, 2, 1, None], [84, None, 0, 5, None, None], [94, 'z', 3, 2, 0, None], [104, 'z', 3, 2, 1, None], [114, 'A', 2, 1, 1, None], [124, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[14, 'a', None, 8, None, None], [24, 'a', 0, 3, 0, 14], [34, 'a', 2, 1, 1, 24], [44, 'a', 2, 2, 2, 904], [54, 'a', -1, 4, -1, 34], [64, 'a', 3, 1, 1, 44], [74, 'b', -2, 2, 0, 14], [84, 'b', 2, 8, 1, 24], [94, 'b', None, 4, None, None], [104, None, None, 0, 1, 904], [114, None, 0, 5, 0, 14], [124, None, None, 7, None, 24], [134, 'c', None, 6, None, 34], [144, 'd', -1, 1, 0, 44], [154, 'A', 2, 2, 1, 54], [164, ' a ', 2, 8, 1, None], [174, '', None, 2, 0, None], [184, 'a', 2, 8, 1, 14], [194, 'd', 1, 3, 0, 44], [204, 'd', -1, 0, -1, 24]], [[14, 'a', None, 0, 1, None], [24, 'a', 2, 2, 0, None], [34, 'a', 2, 3, 2, None], [44, 'a', 3, 4, None, None], [54, 'b', -2, 2, 1, None], [64, 'b', 0, 8, -1, None], [74, None, None, 2, 1, None], [84, None, 0, 5, None, None], [94, 'z', 3, 2, 0, None], [104, 'z', 3, 2, 1, None], [114, 'A', 2, 1, 1, None], [124, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[14, None, None, 3, None, None], [24, None, None, 4, None, None], [34, 'x', None, 5, None, None]], [[14, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[14, 'a', 0, 9, 0, 14]], [[14, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[14, 'n', -2, 4, -1, 14], [24, 'n', None, 2, 0, 24], [34, 'n', -1, 0, 2, None]], [[14, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[14, 'p', 2, 1, 1, 14], [24, 'p', 2, 2, 1, 14], [34, 'p', 3, 0, 1, 14], [44, 'p', None, 1, 0, None]], [[14, 'p', 2, 1, 1, None], [24, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[14, '', 3, 7, 0, 194], [24, 'b', 3, 3, -1, 34], [34, 'c', None, 2, -1, 24], [44, ' a ', 3, 0, 2, 194], [54, ' a ', 1, 3, 2, 24], [64, 'b', None, 2, 0, 14], [74, 'a', -2, 2, -1, None], [84, 'c', None, 0, -1, None], [94, 'a', -1, 1, -1, 34], [104, ' a ', None, 3, 0, 34], [114, 'A', None, 1, 1, 34], [124, 'a', 3, 3, None, None]], [[14, 'c', 0, 2, None, 14], [24, '', 0, 3, 0, 24], [34, 'c', -1, 1, -1, 24], [44, 'a', 2, 2, -1, 194], [54, 'a', -1, 7, -1, 24], [64, ' a ', None, 2, -1, 14], [74, None, 2, 7, 2, 194], [84, 'a', None, 0, -1, 24], [94, None, 2, 1, None, 14], [104, 'b', 3, 2, 1, None], [114, ' a ', 2, 2, 0, 34]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[14, None, -2, 1, 0, 14], [24, 'b', None, 2, 1, 194], [34, None, 2, 7, 2, 194], [44, 'A', 3, 3, -1, 34], [54, ' a ', None, 7, 2, 14], [64, '', 1, 7, 2, None], [74, None, 2, 0, 2, 24], [84, 'A', None, 3, -1, 24], [94, 'a', 2, 7, 2, 194], [104, 'b', 3, 2, 0, None], [114, 'c', None, 3, 2, None], [124, 'A', 5, 2, None, None], [134, ' a ', 0, 1, 1, 24], [144, 'b', 2, 7, 2, None]], [[14, ' a ', -1, 1, 0, 34], [24, 'a', 5, 0, 0, None], [34, 'c', -3, 0, 1, 194], [44, ' a ', 2, 7, 1, None], [54, 'b', None, 7, -1, 14], [64, '', 2, 0, None, 34], [74, 'b', -3, 3, 1, None], [84, 'a', 0, 1, None, 194], [94, 'a', 5, 0, None, 14], [104, '', None, 3, 0, 194]]), [])
elif N == 5:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[15, 'a', None, 8, None, None], [25, 'a', 0, 3, 0, 15], [35, 'a', 2, 1, 1, 25], [45, 'a', 2, 2, 2, 905], [55, 'a', -1, 4, -1, 35], [65, 'a', 3, 1, 1, 45], [75, 'b', -2, 2, 0, 15], [85, 'b', 2, 8, 1, 25], [95, 'b', None, 4, None, None], [105, None, None, 0, 1, 905], [115, None, 0, 5, 0, 15], [125, None, None, 7, None, 25], [135, 'c', None, 6, None, 35], [145, 'd', -1, 1, 0, 45], [155, 'A', 2, 2, 1, 55], [165, ' a ', 2, 8, 1, None], [175, '', None, 2, 0, None], [185, 'a', 2, 8, 1, 15], [195, 'd', 1, 3, 0, 45], [205, 'd', -1, 0, -1, 25]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[15, 'a', None, 0, 1, None], [25, 'a', 2, 2, 0, None], [35, 'a', 2, 3, 2, None], [45, 'a', 3, 4, None, None], [55, 'b', -2, 2, 1, None], [65, 'b', 0, 8, -1, None], [75, None, None, 2, 1, None], [85, None, 0, 5, None, None], [95, 'z', 3, 2, 0, None], [105, 'z', 3, 2, 1, None], [115, 'A', 2, 1, 1, None], [125, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[15, 'a', None, 8, None, None], [25, 'a', 0, 3, 0, 15], [35, 'a', 2, 1, 1, 25], [45, 'a', 2, 2, 2, 905], [55, 'a', -1, 4, -1, 35], [65, 'a', 3, 1, 1, 45], [75, 'b', -2, 2, 0, 15], [85, 'b', 2, 8, 1, 25], [95, 'b', None, 4, None, None], [105, None, None, 0, 1, 905], [115, None, 0, 5, 0, 15], [125, None, None, 7, None, 25], [135, 'c', None, 6, None, 35], [145, 'd', -1, 1, 0, 45], [155, 'A', 2, 2, 1, 55], [165, ' a ', 2, 8, 1, None], [175, '', None, 2, 0, None], [185, 'a', 2, 8, 1, 15], [195, 'd', 1, 3, 0, 45], [205, 'd', -1, 0, -1, 25]], [[15, 'a', None, 0, 1, None], [25, 'a', 2, 2, 0, None], [35, 'a', 2, 3, 2, None], [45, 'a', 3, 4, None, None], [55, 'b', -2, 2, 1, None], [65, 'b', 0, 8, -1, None], [75, None, None, 2, 1, None], [85, None, 0, 5, None, None], [95, 'z', 3, 2, 0, None], [105, 'z', 3, 2, 1, None], [115, 'A', 2, 1, 1, None], [125, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[15, None, None, 3, None, None], [25, None, None, 4, None, None], [35, 'x', None, 5, None, None]], [[15, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[15, 'a', 0, 9, 0, 15]], [[15, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[15, 'n', -2, 4, -1, 15], [25, 'n', None, 2, 0, 25], [35, 'n', -1, 0, 2, None]], [[15, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[15, 'p', 2, 1, 1, 15], [25, 'p', 2, 2, 1, 15], [35, 'p', 3, 0, 1, 15], [45, 'p', None, 1, 0, None]], [[15, 'p', 2, 1, 1, None], [25, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[15, '', 3, 7, 0, 195], [25, 'b', 3, 3, -1, 35], [35, 'c', None, 2, -1, 25], [45, ' a ', 3, 0, 2, 195], [55, ' a ', 1, 3, 2, 25], [65, 'b', None, 2, 0, 15], [75, 'a', -2, 2, -1, None], [85, 'c', None, 0, -1, None], [95, 'a', -1, 1, -1, 35], [105, ' a ', None, 3, 0, 35], [115, 'A', None, 1, 1, 35], [125, 'a', 3, 3, None, None]], [[15, 'c', 0, 2, None, 15], [25, '', 0, 3, 0, 25], [35, 'c', -1, 1, -1, 25], [45, 'a', 2, 2, -1, 195], [55, 'a', -1, 7, -1, 25], [65, ' a ', None, 2, -1, 15], [75, None, 2, 7, 2, 195], [85, 'a', None, 0, -1, 25], [95, None, 2, 1, None, 15], [105, 'b', 3, 2, 1, None], [115, ' a ', 2, 2, 0, 35]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[15, None, -2, 1, 0, 15], [25, 'b', None, 2, 1, 195], [35, None, 2, 7, 2, 195], [45, 'A', 3, 3, -1, 35], [55, ' a ', None, 7, 2, 15], [65, '', 1, 7, 2, None], [75, None, 2, 0, 2, 25], [85, 'A', None, 3, -1, 25], [95, 'a', 2, 7, 2, 195], [105, 'b', 3, 2, 0, None], [115, 'c', None, 3, 2, None], [125, 'A', 5, 2, None, None], [135, ' a ', 0, 1, 1, 25], [145, 'b', 2, 7, 2, None]], [[15, ' a ', -1, 1, 0, 35], [25, 'a', 5, 0, 0, None], [35, 'c', -3, 0, 1, 195], [45, ' a ', 2, 7, 1, None], [55, 'b', None, 7, -1, 15], [65, '', 2, 0, None, 35], [75, 'b', -3, 3, 1, None], [85, 'a', 0, 1, None, 195], [95, 'a', 5, 0, None, 15], [105, '', None, 3, 0, 195]]), [])
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
empty relations	`[]`	`[]`	Passed
left facts without references	`[['a', 2, 3], ['d', -1, 2]]`	`[['a', 2, 3], ['d', -1, 2]]`	Passed
references without candidates	`[]`	`[]`	Passed
mixed nullable groups duplicates ties and truth flags	`[['a', 2, 3], ['d', -1, 2]]`	`[['a', 2, 3], ['d', -1, 2]]`	Passed
unknown-only group with duplicate nullable index keys	`[]`	`[]`	Passed
single known zero and matching reference	`[]`	`[]`	Passed
negative-only group and missing measurement	`[]`	`[]`	Passed
positive-only group with repeated measurements and NULL	`[['p', 2, 2]]`	`[['p', 2, 2]]`	Passed
adversarial key cardinality and NULL placement witness 12	`[]`	`[]`	Passed
adversarial key cardinality and NULL placement witness 9	`[[None, 2, 2]]`	`[]`	Failed

SHA-256 / 5d850a87d22da03f603fefb754b83ae4fda53f3d1184228206bf7df09d08ab69

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import sqlite3
N = 1
observations = []
def solve(rows, refs):
    db = sqlite3.connect(':memory:')
    try:
        for name, records in [('a', rows), ('b', refs)]:
            db.execute('CREATE TABLE ' + name + ' (id INTEGER PRIMARY KEY, k TEXT, v INTEGER, w INTEGER, flag INTEGER, parent INTEGER)')
            db.executemany('INSERT INTO ' + name + ' VALUES (?,?,?,?,?,?)', records)
        return sorted([list(row) for row in db.execute('SELECT k,v,COUNT(*) FROM a GROUP BY k,v HAVING COUNT(*)>1')], key=repr)
    finally:
        db.close()
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[11, 'a', None, 8, None, None], [21, 'a', 0, 3, 0, 11], [31, 'a', 2, 1, 1, 21], [41, 'a', 2, 2, 2, 901], [51, 'a', -1, 4, -1, 31], [61, 'a', 3, 1, 1, 41], [71, 'b', -2, 2, 0, 11], [81, 'b', 2, 8, 1, 21], [91, 'b', None, 4, None, None], [101, None, None, 0, 1, 901], [111, None, 0, 5, 0, 11], [121, None, None, 7, None, 21], [131, 'c', None, 6, None, 31], [141, 'd', -1, 1, 0, 41], [151, 'A', 2, 2, 1, 51], [161, ' a ', 2, 8, 1, None], [171, '', None, 2, 0, None], [181, 'a', 2, 8, 1, 11], [191, 'd', 1, 3, 0, 41], [201, 'd', -1, 0, -1, 21]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[11, 'a', None, 0, 1, None], [21, 'a', 2, 2, 0, None], [31, 'a', 2, 3, 2, None], [41, 'a', 3, 4, None, None], [51, 'b', -2, 2, 1, None], [61, 'b', 0, 8, -1, None], [71, None, None, 2, 1, None], [81, None, 0, 5, None, None], [91, 'z', 3, 2, 0, None], [101, 'z', 3, 2, 1, None], [111, 'A', 2, 1, 1, None], [121, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[11, 'a', None, 8, None, None], [21, 'a', 0, 3, 0, 11], [31, 'a', 2, 1, 1, 21], [41, 'a', 2, 2, 2, 901], [51, 'a', -1, 4, -1, 31], [61, 'a', 3, 1, 1, 41], [71, 'b', -2, 2, 0, 11], [81, 'b', 2, 8, 1, 21], [91, 'b', None, 4, None, None], [101, None, None, 0, 1, 901], [111, None, 0, 5, 0, 11], [121, None, None, 7, None, 21], [131, 'c', None, 6, None, 31], [141, 'd', -1, 1, 0, 41], [151, 'A', 2, 2, 1, 51], [161, ' a ', 2, 8, 1, None], [171, '', None, 2, 0, None], [181, 'a', 2, 8, 1, 11], [191, 'd', 1, 3, 0, 41], [201, 'd', -1, 0, -1, 21]], [[11, 'a', None, 0, 1, None], [21, 'a', 2, 2, 0, None], [31, 'a', 2, 3, 2, None], [41, 'a', 3, 4, None, None], [51, 'b', -2, 2, 1, None], [61, 'b', 0, 8, -1, None], [71, None, None, 2, 1, None], [81, None, 0, 5, None, None], [91, 'z', 3, 2, 0, None], [101, 'z', 3, 2, 1, None], [111, 'A', 2, 1, 1, None], [121, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[11, None, None, 3, None, None], [21, None, None, 4, None, None], [31, 'x', None, 5, None, None]], [[11, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[11, 'a', 0, 9, 0, 11]], [[11, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[11, 'n', -2, 4, -1, 11], [21, 'n', None, 2, 0, 21], [31, 'n', -1, 0, 2, None]], [[11, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[11, 'p', 2, 1, 1, 11], [21, 'p', 2, 2, 1, 11], [31, 'p', 3, 0, 1, 11], [41, 'p', None, 1, 0, None]], [[11, 'p', 2, 1, 1, None], [21, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[11, '', 3, 7, 0, 191], [21, 'b', 3, 3, -1, 31], [31, 'c', None, 2, -1, 21], [41, ' a ', 3, 0, 2, 191], [51, ' a ', 1, 3, 2, 21], [61, 'b', None, 2, 0, 11], [71, 'a', -2, 2, -1, None], [81, 'c', None, 0, -1, None], [91, 'a', -1, 1, -1, 31], [101, ' a ', None, 3, 0, 31], [111, 'A', None, 1, 1, 31], [121, 'a', 3, 3, None, None]], [[11, 'c', 0, 2, None, 11], [21, '', 0, 3, 0, 21], [31, 'c', -1, 1, -1, 21], [41, 'a', 2, 2, -1, 191], [51, 'a', -1, 7, -1, 21], [61, ' a ', None, 2, -1, 11], [71, None, 2, 7, 2, 191], [81, 'a', None, 0, -1, 21], [91, None, 2, 1, None, 11], [101, 'b', 3, 2, 1, None], [111, ' a ', 2, 2, 0, 31]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[11, None, -2, 1, 0, 11], [21, 'b', None, 2, 1, 191], [31, None, 2, 7, 2, 191], [41, 'A', 3, 3, -1, 31], [51, ' a ', None, 7, 2, 11], [61, '', 1, 7, 2, None], [71, None, 2, 0, 2, 21], [81, 'A', None, 3, -1, 21], [91, 'a', 2, 7, 2, 191], [101, 'b', 3, 2, 0, None], [111, 'c', None, 3, 2, None], [121, 'A', 5, 2, None, None], [131, ' a ', 0, 1, 1, 21], [141, 'b', 2, 7, 2, None]], [[11, ' a ', -1, 1, 0, 31], [21, 'a', 5, 0, 0, None], [31, 'c', -3, 0, 1, 191], [41, ' a ', 2, 7, 1, None], [51, 'b', None, 7, -1, 11], [61, '', 2, 0, None, 31], [71, 'b', -3, 3, 1, None], [81, 'a', 0, 1, None, 191], [91, 'a', 5, 0, None, 11], [101, '', None, 3, 0, 191]]), [])
elif N == 2:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[12, 'a', None, 8, None, None], [22, 'a', 0, 3, 0, 12], [32, 'a', 2, 1, 1, 22], [42, 'a', 2, 2, 2, 902], [52, 'a', -1, 4, -1, 32], [62, 'a', 3, 1, 1, 42], [72, 'b', -2, 2, 0, 12], [82, 'b', 2, 8, 1, 22], [92, 'b', None, 4, None, None], [102, None, None, 0, 1, 902], [112, None, 0, 5, 0, 12], [122, None, None, 7, None, 22], [132, 'c', None, 6, None, 32], [142, 'd', -1, 1, 0, 42], [152, 'A', 2, 2, 1, 52], [162, ' a ', 2, 8, 1, None], [172, '', None, 2, 0, None], [182, 'a', 2, 8, 1, 12], [192, 'd', 1, 3, 0, 42], [202, 'd', -1, 0, -1, 22]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[12, 'a', None, 0, 1, None], [22, 'a', 2, 2, 0, None], [32, 'a', 2, 3, 2, None], [42, 'a', 3, 4, None, None], [52, 'b', -2, 2, 1, None], [62, 'b', 0, 8, -1, None], [72, None, None, 2, 1, None], [82, None, 0, 5, None, None], [92, 'z', 3, 2, 0, None], [102, 'z', 3, 2, 1, None], [112, 'A', 2, 1, 1, None], [122, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[12, 'a', None, 8, None, None], [22, 'a', 0, 3, 0, 12], [32, 'a', 2, 1, 1, 22], [42, 'a', 2, 2, 2, 902], [52, 'a', -1, 4, -1, 32], [62, 'a', 3, 1, 1, 42], [72, 'b', -2, 2, 0, 12], [82, 'b', 2, 8, 1, 22], [92, 'b', None, 4, None, None], [102, None, None, 0, 1, 902], [112, None, 0, 5, 0, 12], [122, None, None, 7, None, 22], [132, 'c', None, 6, None, 32], [142, 'd', -1, 1, 0, 42], [152, 'A', 2, 2, 1, 52], [162, ' a ', 2, 8, 1, None], [172, '', None, 2, 0, None], [182, 'a', 2, 8, 1, 12], [192, 'd', 1, 3, 0, 42], [202, 'd', -1, 0, -1, 22]], [[12, 'a', None, 0, 1, None], [22, 'a', 2, 2, 0, None], [32, 'a', 2, 3, 2, None], [42, 'a', 3, 4, None, None], [52, 'b', -2, 2, 1, None], [62, 'b', 0, 8, -1, None], [72, None, None, 2, 1, None], [82, None, 0, 5, None, None], [92, 'z', 3, 2, 0, None], [102, 'z', 3, 2, 1, None], [112, 'A', 2, 1, 1, None], [122, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[12, None, None, 3, None, None], [22, None, None, 4, None, None], [32, 'x', None, 5, None, None]], [[12, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[12, 'a', 0, 9, 0, 12]], [[12, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[12, 'n', -2, 4, -1, 12], [22, 'n', None, 2, 0, 22], [32, 'n', -1, 0, 2, None]], [[12, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[12, 'p', 2, 1, 1, 12], [22, 'p', 2, 2, 1, 12], [32, 'p', 3, 0, 1, 12], [42, 'p', None, 1, 0, None]], [[12, 'p', 2, 1, 1, None], [22, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[12, '', 3, 7, 0, 192], [22, 'b', 3, 3, -1, 32], [32, 'c', None, 2, -1, 22], [42, ' a ', 3, 0, 2, 192], [52, ' a ', 1, 3, 2, 22], [62, 'b', None, 2, 0, 12], [72, 'a', -2, 2, -1, None], [82, 'c', None, 0, -1, None], [92, 'a', -1, 1, -1, 32], [102, ' a ', None, 3, 0, 32], [112, 'A', None, 1, 1, 32], [122, 'a', 3, 3, None, None]], [[12, 'c', 0, 2, None, 12], [22, '', 0, 3, 0, 22], [32, 'c', -1, 1, -1, 22], [42, 'a', 2, 2, -1, 192], [52, 'a', -1, 7, -1, 22], [62, ' a ', None, 2, -1, 12], [72, None, 2, 7, 2, 192], [82, 'a', None, 0, -1, 22], [92, None, 2, 1, None, 12], [102, 'b', 3, 2, 1, None], [112, ' a ', 2, 2, 0, 32]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[12, None, -2, 1, 0, 12], [22, 'b', None, 2, 1, 192], [32, None, 2, 7, 2, 192], [42, 'A', 3, 3, -1, 32], [52, ' a ', None, 7, 2, 12], [62, '', 1, 7, 2, None], [72, None, 2, 0, 2, 22], [82, 'A', None, 3, -1, 22], [92, 'a', 2, 7, 2, 192], [102, 'b', 3, 2, 0, None], [112, 'c', None, 3, 2, None], [122, 'A', 5, 2, None, None], [132, ' a ', 0, 1, 1, 22], [142, 'b', 2, 7, 2, None]], [[12, ' a ', -1, 1, 0, 32], [22, 'a', 5, 0, 0, None], [32, 'c', -3, 0, 1, 192], [42, ' a ', 2, 7, 1, None], [52, 'b', None, 7, -1, 12], [62, '', 2, 0, None, 32], [72, 'b', -3, 3, 1, None], [82, 'a', 0, 1, None, 192], [92, 'a', 5, 0, None, 12], [102, '', None, 3, 0, 192]]), [])
elif N == 3:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[13, 'a', None, 8, None, None], [23, 'a', 0, 3, 0, 13], [33, 'a', 2, 1, 1, 23], [43, 'a', 2, 2, 2, 903], [53, 'a', -1, 4, -1, 33], [63, 'a', 3, 1, 1, 43], [73, 'b', -2, 2, 0, 13], [83, 'b', 2, 8, 1, 23], [93, 'b', None, 4, None, None], [103, None, None, 0, 1, 903], [113, None, 0, 5, 0, 13], [123, None, None, 7, None, 23], [133, 'c', None, 6, None, 33], [143, 'd', -1, 1, 0, 43], [153, 'A', 2, 2, 1, 53], [163, ' a ', 2, 8, 1, None], [173, '', None, 2, 0, None], [183, 'a', 2, 8, 1, 13], [193, 'd', 1, 3, 0, 43], [203, 'd', -1, 0, -1, 23]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[13, 'a', None, 0, 1, None], [23, 'a', 2, 2, 0, None], [33, 'a', 2, 3, 2, None], [43, 'a', 3, 4, None, None], [53, 'b', -2, 2, 1, None], [63, 'b', 0, 8, -1, None], [73, None, None, 2, 1, None], [83, None, 0, 5, None, None], [93, 'z', 3, 2, 0, None], [103, 'z', 3, 2, 1, None], [113, 'A', 2, 1, 1, None], [123, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[13, 'a', None, 8, None, None], [23, 'a', 0, 3, 0, 13], [33, 'a', 2, 1, 1, 23], [43, 'a', 2, 2, 2, 903], [53, 'a', -1, 4, -1, 33], [63, 'a', 3, 1, 1, 43], [73, 'b', -2, 2, 0, 13], [83, 'b', 2, 8, 1, 23], [93, 'b', None, 4, None, None], [103, None, None, 0, 1, 903], [113, None, 0, 5, 0, 13], [123, None, None, 7, None, 23], [133, 'c', None, 6, None, 33], [143, 'd', -1, 1, 0, 43], [153, 'A', 2, 2, 1, 53], [163, ' a ', 2, 8, 1, None], [173, '', None, 2, 0, None], [183, 'a', 2, 8, 1, 13], [193, 'd', 1, 3, 0, 43], [203, 'd', -1, 0, -1, 23]], [[13, 'a', None, 0, 1, None], [23, 'a', 2, 2, 0, None], [33, 'a', 2, 3, 2, None], [43, 'a', 3, 4, None, None], [53, 'b', -2, 2, 1, None], [63, 'b', 0, 8, -1, None], [73, None, None, 2, 1, None], [83, None, 0, 5, None, None], [93, 'z', 3, 2, 0, None], [103, 'z', 3, 2, 1, None], [113, 'A', 2, 1, 1, None], [123, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[13, None, None, 3, None, None], [23, None, None, 4, None, None], [33, 'x', None, 5, None, None]], [[13, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[13, 'a', 0, 9, 0, 13]], [[13, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[13, 'n', -2, 4, -1, 13], [23, 'n', None, 2, 0, 23], [33, 'n', -1, 0, 2, None]], [[13, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[13, 'p', 2, 1, 1, 13], [23, 'p', 2, 2, 1, 13], [33, 'p', 3, 0, 1, 13], [43, 'p', None, 1, 0, None]], [[13, 'p', 2, 1, 1, None], [23, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[13, '', 3, 7, 0, 193], [23, 'b', 3, 3, -1, 33], [33, 'c', None, 2, -1, 23], [43, ' a ', 3, 0, 2, 193], [53, ' a ', 1, 3, 2, 23], [63, 'b', None, 2, 0, 13], [73, 'a', -2, 2, -1, None], [83, 'c', None, 0, -1, None], [93, 'a', -1, 1, -1, 33], [103, ' a ', None, 3, 0, 33], [113, 'A', None, 1, 1, 33], [123, 'a', 3, 3, None, None]], [[13, 'c', 0, 2, None, 13], [23, '', 0, 3, 0, 23], [33, 'c', -1, 1, -1, 23], [43, 'a', 2, 2, -1, 193], [53, 'a', -1, 7, -1, 23], [63, ' a ', None, 2, -1, 13], [73, None, 2, 7, 2, 193], [83, 'a', None, 0, -1, 23], [93, None, 2, 1, None, 13], [103, 'b', 3, 2, 1, None], [113, ' a ', 2, 2, 0, 33]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[13, None, -2, 1, 0, 13], [23, 'b', None, 2, 1, 193], [33, None, 2, 7, 2, 193], [43, 'A', 3, 3, -1, 33], [53, ' a ', None, 7, 2, 13], [63, '', 1, 7, 2, None], [73, None, 2, 0, 2, 23], [83, 'A', None, 3, -1, 23], [93, 'a', 2, 7, 2, 193], [103, 'b', 3, 2, 0, None], [113, 'c', None, 3, 2, None], [123, 'A', 5, 2, None, None], [133, ' a ', 0, 1, 1, 23], [143, 'b', 2, 7, 2, None]], [[13, ' a ', -1, 1, 0, 33], [23, 'a', 5, 0, 0, None], [33, 'c', -3, 0, 1, 193], [43, ' a ', 2, 7, 1, None], [53, 'b', None, 7, -1, 13], [63, '', 2, 0, None, 33], [73, 'b', -3, 3, 1, None], [83, 'a', 0, 1, None, 193], [93, 'a', 5, 0, None, 13], [103, '', None, 3, 0, 193]]), [])
elif N == 4:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[14, 'a', None, 8, None, None], [24, 'a', 0, 3, 0, 14], [34, 'a', 2, 1, 1, 24], [44, 'a', 2, 2, 2, 904], [54, 'a', -1, 4, -1, 34], [64, 'a', 3, 1, 1, 44], [74, 'b', -2, 2, 0, 14], [84, 'b', 2, 8, 1, 24], [94, 'b', None, 4, None, None], [104, None, None, 0, 1, 904], [114, None, 0, 5, 0, 14], [124, None, None, 7, None, 24], [134, 'c', None, 6, None, 34], [144, 'd', -1, 1, 0, 44], [154, 'A', 2, 2, 1, 54], [164, ' a ', 2, 8, 1, None], [174, '', None, 2, 0, None], [184, 'a', 2, 8, 1, 14], [194, 'd', 1, 3, 0, 44], [204, 'd', -1, 0, -1, 24]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[14, 'a', None, 0, 1, None], [24, 'a', 2, 2, 0, None], [34, 'a', 2, 3, 2, None], [44, 'a', 3, 4, None, None], [54, 'b', -2, 2, 1, None], [64, 'b', 0, 8, -1, None], [74, None, None, 2, 1, None], [84, None, 0, 5, None, None], [94, 'z', 3, 2, 0, None], [104, 'z', 3, 2, 1, None], [114, 'A', 2, 1, 1, None], [124, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[14, 'a', None, 8, None, None], [24, 'a', 0, 3, 0, 14], [34, 'a', 2, 1, 1, 24], [44, 'a', 2, 2, 2, 904], [54, 'a', -1, 4, -1, 34], [64, 'a', 3, 1, 1, 44], [74, 'b', -2, 2, 0, 14], [84, 'b', 2, 8, 1, 24], [94, 'b', None, 4, None, None], [104, None, None, 0, 1, 904], [114, None, 0, 5, 0, 14], [124, None, None, 7, None, 24], [134, 'c', None, 6, None, 34], [144, 'd', -1, 1, 0, 44], [154, 'A', 2, 2, 1, 54], [164, ' a ', 2, 8, 1, None], [174, '', None, 2, 0, None], [184, 'a', 2, 8, 1, 14], [194, 'd', 1, 3, 0, 44], [204, 'd', -1, 0, -1, 24]], [[14, 'a', None, 0, 1, None], [24, 'a', 2, 2, 0, None], [34, 'a', 2, 3, 2, None], [44, 'a', 3, 4, None, None], [54, 'b', -2, 2, 1, None], [64, 'b', 0, 8, -1, None], [74, None, None, 2, 1, None], [84, None, 0, 5, None, None], [94, 'z', 3, 2, 0, None], [104, 'z', 3, 2, 1, None], [114, 'A', 2, 1, 1, None], [124, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[14, None, None, 3, None, None], [24, None, None, 4, None, None], [34, 'x', None, 5, None, None]], [[14, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[14, 'a', 0, 9, 0, 14]], [[14, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[14, 'n', -2, 4, -1, 14], [24, 'n', None, 2, 0, 24], [34, 'n', -1, 0, 2, None]], [[14, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[14, 'p', 2, 1, 1, 14], [24, 'p', 2, 2, 1, 14], [34, 'p', 3, 0, 1, 14], [44, 'p', None, 1, 0, None]], [[14, 'p', 2, 1, 1, None], [24, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[14, '', 3, 7, 0, 194], [24, 'b', 3, 3, -1, 34], [34, 'c', None, 2, -1, 24], [44, ' a ', 3, 0, 2, 194], [54, ' a ', 1, 3, 2, 24], [64, 'b', None, 2, 0, 14], [74, 'a', -2, 2, -1, None], [84, 'c', None, 0, -1, None], [94, 'a', -1, 1, -1, 34], [104, ' a ', None, 3, 0, 34], [114, 'A', None, 1, 1, 34], [124, 'a', 3, 3, None, None]], [[14, 'c', 0, 2, None, 14], [24, '', 0, 3, 0, 24], [34, 'c', -1, 1, -1, 24], [44, 'a', 2, 2, -1, 194], [54, 'a', -1, 7, -1, 24], [64, ' a ', None, 2, -1, 14], [74, None, 2, 7, 2, 194], [84, 'a', None, 0, -1, 24], [94, None, 2, 1, None, 14], [104, 'b', 3, 2, 1, None], [114, ' a ', 2, 2, 0, 34]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[14, None, -2, 1, 0, 14], [24, 'b', None, 2, 1, 194], [34, None, 2, 7, 2, 194], [44, 'A', 3, 3, -1, 34], [54, ' a ', None, 7, 2, 14], [64, '', 1, 7, 2, None], [74, None, 2, 0, 2, 24], [84, 'A', None, 3, -1, 24], [94, 'a', 2, 7, 2, 194], [104, 'b', 3, 2, 0, None], [114, 'c', None, 3, 2, None], [124, 'A', 5, 2, None, None], [134, ' a ', 0, 1, 1, 24], [144, 'b', 2, 7, 2, None]], [[14, ' a ', -1, 1, 0, 34], [24, 'a', 5, 0, 0, None], [34, 'c', -3, 0, 1, 194], [44, ' a ', 2, 7, 1, None], [54, 'b', None, 7, -1, 14], [64, '', 2, 0, None, 34], [74, 'b', -3, 3, 1, None], [84, 'a', 0, 1, None, 194], [94, 'a', 5, 0, None, 14], [104, '', None, 3, 0, 194]]), [])
elif N == 5:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[15, 'a', None, 8, None, None], [25, 'a', 0, 3, 0, 15], [35, 'a', 2, 1, 1, 25], [45, 'a', 2, 2, 2, 905], [55, 'a', -1, 4, -1, 35], [65, 'a', 3, 1, 1, 45], [75, 'b', -2, 2, 0, 15], [85, 'b', 2, 8, 1, 25], [95, 'b', None, 4, None, None], [105, None, None, 0, 1, 905], [115, None, 0, 5, 0, 15], [125, None, None, 7, None, 25], [135, 'c', None, 6, None, 35], [145, 'd', -1, 1, 0, 45], [155, 'A', 2, 2, 1, 55], [165, ' a ', 2, 8, 1, None], [175, '', None, 2, 0, None], [185, 'a', 2, 8, 1, 15], [195, 'd', 1, 3, 0, 45], [205, 'd', -1, 0, -1, 25]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[15, 'a', None, 0, 1, None], [25, 'a', 2, 2, 0, None], [35, 'a', 2, 3, 2, None], [45, 'a', 3, 4, None, None], [55, 'b', -2, 2, 1, None], [65, 'b', 0, 8, -1, None], [75, None, None, 2, 1, None], [85, None, 0, 5, None, None], [95, 'z', 3, 2, 0, None], [105, 'z', 3, 2, 1, None], [115, 'A', 2, 1, 1, None], [125, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[15, 'a', None, 8, None, None], [25, 'a', 0, 3, 0, 15], [35, 'a', 2, 1, 1, 25], [45, 'a', 2, 2, 2, 905], [55, 'a', -1, 4, -1, 35], [65, 'a', 3, 1, 1, 45], [75, 'b', -2, 2, 0, 15], [85, 'b', 2, 8, 1, 25], [95, 'b', None, 4, None, None], [105, None, None, 0, 1, 905], [115, None, 0, 5, 0, 15], [125, None, None, 7, None, 25], [135, 'c', None, 6, None, 35], [145, 'd', -1, 1, 0, 45], [155, 'A', 2, 2, 1, 55], [165, ' a ', 2, 8, 1, None], [175, '', None, 2, 0, None], [185, 'a', 2, 8, 1, 15], [195, 'd', 1, 3, 0, 45], [205, 'd', -1, 0, -1, 25]], [[15, 'a', None, 0, 1, None], [25, 'a', 2, 2, 0, None], [35, 'a', 2, 3, 2, None], [45, 'a', 3, 4, None, None], [55, 'b', -2, 2, 1, None], [65, 'b', 0, 8, -1, None], [75, None, None, 2, 1, None], [85, None, 0, 5, None, None], [95, 'z', 3, 2, 0, None], [105, 'z', 3, 2, 1, None], [115, 'A', 2, 1, 1, None], [125, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[15, None, None, 3, None, None], [25, None, None, 4, None, None], [35, 'x', None, 5, None, None]], [[15, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[15, 'a', 0, 9, 0, 15]], [[15, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[15, 'n', -2, 4, -1, 15], [25, 'n', None, 2, 0, 25], [35, 'n', -1, 0, 2, None]], [[15, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[15, 'p', 2, 1, 1, 15], [25, 'p', 2, 2, 1, 15], [35, 'p', 3, 0, 1, 15], [45, 'p', None, 1, 0, None]], [[15, 'p', 2, 1, 1, None], [25, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[15, '', 3, 7, 0, 195], [25, 'b', 3, 3, -1, 35], [35, 'c', None, 2, -1, 25], [45, ' a ', 3, 0, 2, 195], [55, ' a ', 1, 3, 2, 25], [65, 'b', None, 2, 0, 15], [75, 'a', -2, 2, -1, None], [85, 'c', None, 0, -1, None], [95, 'a', -1, 1, -1, 35], [105, ' a ', None, 3, 0, 35], [115, 'A', None, 1, 1, 35], [125, 'a', 3, 3, None, None]], [[15, 'c', 0, 2, None, 15], [25, '', 0, 3, 0, 25], [35, 'c', -1, 1, -1, 25], [45, 'a', 2, 2, -1, 195], [55, 'a', -1, 7, -1, 25], [65, ' a ', None, 2, -1, 15], [75, None, 2, 7, 2, 195], [85, 'a', None, 0, -1, 25], [95, None, 2, 1, None, 15], [105, 'b', 3, 2, 1, None], [115, ' a ', 2, 2, 0, 35]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[15, None, -2, 1, 0, 15], [25, 'b', None, 2, 1, 195], [35, None, 2, 7, 2, 195], [45, 'A', 3, 3, -1, 35], [55, ' a ', None, 7, 2, 15], [65, '', 1, 7, 2, None], [75, None, 2, 0, 2, 25], [85, 'A', None, 3, -1, 25], [95, 'a', 2, 7, 2, 195], [105, 'b', 3, 2, 0, None], [115, 'c', None, 3, 2, None], [125, 'A', 5, 2, None, None], [135, ' a ', 0, 1, 1, 25], [145, 'b', 2, 7, 2, None]], [[15, ' a ', -1, 1, 0, 35], [25, 'a', 5, 0, 0, None], [35, 'c', -3, 0, 1, 195], [45, ' a ', 2, 7, 1, None], [55, 'b', None, 7, -1, 15], [65, '', 2, 0, None, 35], [75, 'b', -3, 3, 1, None], [85, 'a', 0, 1, None, 195], [95, 'a', 5, 0, None, 15], [105, '', None, 3, 0, 195]]), [])
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
empty relations	`[]`	`[]`	Passed
left facts without references	`[['a', 2, 3], ['d', -1, 2], [None, None, 2]]`	`[['a', 2, 3], ['d', -1, 2]]`	Failed
references without candidates	`[]`	`[]`	Passed
mixed nullable groups duplicates ties and truth flags	`[['a', 2, 3], ['d', -1, 2], [None, None, 2]]`	`[['a', 2, 3], ['d', -1, 2]]`	Failed
unknown-only group with duplicate nullable index keys	`[[None, None, 2]]`	`[]`	Failed
single known zero and matching reference	`[]`	`[]`	Passed
negative-only group and missing measurement	`[]`	`[]`	Passed
positive-only group with repeated measurements and NULL	`[['p', 2, 2]]`	`[['p', 2, 2]]`	Passed
adversarial key cardinality and NULL placement witness 12	`[['c', None, 2]]`	`[]`	Failed
adversarial key cardinality and NULL placement witness 9	`[[None, 2, 2]]`	`[]`	Failed

SHA-256 / 810fd6ea20957eca54bba16d57fca5a392ac1fc3930167ca1372f766fa4c926e

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import sqlite3
N = 1
observations = []
def solve(rows, refs):
    db = sqlite3.connect(':memory:')
    try:
        for name, records in [('a', rows), ('b', refs)]:
            db.execute('CREATE TABLE ' + name + ' (id INTEGER PRIMARY KEY, k TEXT, v INTEGER, w INTEGER, flag INTEGER, parent INTEGER)')
            db.executemany('INSERT INTO ' + name + ' VALUES (?,?,?,?,?,?)', records)
        return sorted([list(row) for row in db.execute('SELECT k,v,COUNT(*) FROM a WHERE k IS NOT NULL AND v IS NOT NULL GROUP BY k,v HAVING COUNT(*)>1')], key=repr)
    finally:
        db.close()
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[11, 'a', None, 8, None, None], [21, 'a', 0, 3, 0, 11], [31, 'a', 2, 1, 1, 21], [41, 'a', 2, 2, 2, 901], [51, 'a', -1, 4, -1, 31], [61, 'a', 3, 1, 1, 41], [71, 'b', -2, 2, 0, 11], [81, 'b', 2, 8, 1, 21], [91, 'b', None, 4, None, None], [101, None, None, 0, 1, 901], [111, None, 0, 5, 0, 11], [121, None, None, 7, None, 21], [131, 'c', None, 6, None, 31], [141, 'd', -1, 1, 0, 41], [151, 'A', 2, 2, 1, 51], [161, ' a ', 2, 8, 1, None], [171, '', None, 2, 0, None], [181, 'a', 2, 8, 1, 11], [191, 'd', 1, 3, 0, 41], [201, 'd', -1, 0, -1, 21]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[11, 'a', None, 0, 1, None], [21, 'a', 2, 2, 0, None], [31, 'a', 2, 3, 2, None], [41, 'a', 3, 4, None, None], [51, 'b', -2, 2, 1, None], [61, 'b', 0, 8, -1, None], [71, None, None, 2, 1, None], [81, None, 0, 5, None, None], [91, 'z', 3, 2, 0, None], [101, 'z', 3, 2, 1, None], [111, 'A', 2, 1, 1, None], [121, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[11, 'a', None, 8, None, None], [21, 'a', 0, 3, 0, 11], [31, 'a', 2, 1, 1, 21], [41, 'a', 2, 2, 2, 901], [51, 'a', -1, 4, -1, 31], [61, 'a', 3, 1, 1, 41], [71, 'b', -2, 2, 0, 11], [81, 'b', 2, 8, 1, 21], [91, 'b', None, 4, None, None], [101, None, None, 0, 1, 901], [111, None, 0, 5, 0, 11], [121, None, None, 7, None, 21], [131, 'c', None, 6, None, 31], [141, 'd', -1, 1, 0, 41], [151, 'A', 2, 2, 1, 51], [161, ' a ', 2, 8, 1, None], [171, '', None, 2, 0, None], [181, 'a', 2, 8, 1, 11], [191, 'd', 1, 3, 0, 41], [201, 'd', -1, 0, -1, 21]], [[11, 'a', None, 0, 1, None], [21, 'a', 2, 2, 0, None], [31, 'a', 2, 3, 2, None], [41, 'a', 3, 4, None, None], [51, 'b', -2, 2, 1, None], [61, 'b', 0, 8, -1, None], [71, None, None, 2, 1, None], [81, None, 0, 5, None, None], [91, 'z', 3, 2, 0, None], [101, 'z', 3, 2, 1, None], [111, 'A', 2, 1, 1, None], [121, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[11, None, None, 3, None, None], [21, None, None, 4, None, None], [31, 'x', None, 5, None, None]], [[11, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[11, 'a', 0, 9, 0, 11]], [[11, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[11, 'n', -2, 4, -1, 11], [21, 'n', None, 2, 0, 21], [31, 'n', -1, 0, 2, None]], [[11, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[11, 'p', 2, 1, 1, 11], [21, 'p', 2, 2, 1, 11], [31, 'p', 3, 0, 1, 11], [41, 'p', None, 1, 0, None]], [[11, 'p', 2, 1, 1, None], [21, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[11, '', 3, 7, 0, 191], [21, 'b', 3, 3, -1, 31], [31, 'c', None, 2, -1, 21], [41, ' a ', 3, 0, 2, 191], [51, ' a ', 1, 3, 2, 21], [61, 'b', None, 2, 0, 11], [71, 'a', -2, 2, -1, None], [81, 'c', None, 0, -1, None], [91, 'a', -1, 1, -1, 31], [101, ' a ', None, 3, 0, 31], [111, 'A', None, 1, 1, 31], [121, 'a', 3, 3, None, None]], [[11, 'c', 0, 2, None, 11], [21, '', 0, 3, 0, 21], [31, 'c', -1, 1, -1, 21], [41, 'a', 2, 2, -1, 191], [51, 'a', -1, 7, -1, 21], [61, ' a ', None, 2, -1, 11], [71, None, 2, 7, 2, 191], [81, 'a', None, 0, -1, 21], [91, None, 2, 1, None, 11], [101, 'b', 3, 2, 1, None], [111, ' a ', 2, 2, 0, 31]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[11, None, -2, 1, 0, 11], [21, 'b', None, 2, 1, 191], [31, None, 2, 7, 2, 191], [41, 'A', 3, 3, -1, 31], [51, ' a ', None, 7, 2, 11], [61, '', 1, 7, 2, None], [71, None, 2, 0, 2, 21], [81, 'A', None, 3, -1, 21], [91, 'a', 2, 7, 2, 191], [101, 'b', 3, 2, 0, None], [111, 'c', None, 3, 2, None], [121, 'A', 5, 2, None, None], [131, ' a ', 0, 1, 1, 21], [141, 'b', 2, 7, 2, None]], [[11, ' a ', -1, 1, 0, 31], [21, 'a', 5, 0, 0, None], [31, 'c', -3, 0, 1, 191], [41, ' a ', 2, 7, 1, None], [51, 'b', None, 7, -1, 11], [61, '', 2, 0, None, 31], [71, 'b', -3, 3, 1, None], [81, 'a', 0, 1, None, 191], [91, 'a', 5, 0, None, 11], [101, '', None, 3, 0, 191]]), [])
elif N == 2:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[12, 'a', None, 8, None, None], [22, 'a', 0, 3, 0, 12], [32, 'a', 2, 1, 1, 22], [42, 'a', 2, 2, 2, 902], [52, 'a', -1, 4, -1, 32], [62, 'a', 3, 1, 1, 42], [72, 'b', -2, 2, 0, 12], [82, 'b', 2, 8, 1, 22], [92, 'b', None, 4, None, None], [102, None, None, 0, 1, 902], [112, None, 0, 5, 0, 12], [122, None, None, 7, None, 22], [132, 'c', None, 6, None, 32], [142, 'd', -1, 1, 0, 42], [152, 'A', 2, 2, 1, 52], [162, ' a ', 2, 8, 1, None], [172, '', None, 2, 0, None], [182, 'a', 2, 8, 1, 12], [192, 'd', 1, 3, 0, 42], [202, 'd', -1, 0, -1, 22]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[12, 'a', None, 0, 1, None], [22, 'a', 2, 2, 0, None], [32, 'a', 2, 3, 2, None], [42, 'a', 3, 4, None, None], [52, 'b', -2, 2, 1, None], [62, 'b', 0, 8, -1, None], [72, None, None, 2, 1, None], [82, None, 0, 5, None, None], [92, 'z', 3, 2, 0, None], [102, 'z', 3, 2, 1, None], [112, 'A', 2, 1, 1, None], [122, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[12, 'a', None, 8, None, None], [22, 'a', 0, 3, 0, 12], [32, 'a', 2, 1, 1, 22], [42, 'a', 2, 2, 2, 902], [52, 'a', -1, 4, -1, 32], [62, 'a', 3, 1, 1, 42], [72, 'b', -2, 2, 0, 12], [82, 'b', 2, 8, 1, 22], [92, 'b', None, 4, None, None], [102, None, None, 0, 1, 902], [112, None, 0, 5, 0, 12], [122, None, None, 7, None, 22], [132, 'c', None, 6, None, 32], [142, 'd', -1, 1, 0, 42], [152, 'A', 2, 2, 1, 52], [162, ' a ', 2, 8, 1, None], [172, '', None, 2, 0, None], [182, 'a', 2, 8, 1, 12], [192, 'd', 1, 3, 0, 42], [202, 'd', -1, 0, -1, 22]], [[12, 'a', None, 0, 1, None], [22, 'a', 2, 2, 0, None], [32, 'a', 2, 3, 2, None], [42, 'a', 3, 4, None, None], [52, 'b', -2, 2, 1, None], [62, 'b', 0, 8, -1, None], [72, None, None, 2, 1, None], [82, None, 0, 5, None, None], [92, 'z', 3, 2, 0, None], [102, 'z', 3, 2, 1, None], [112, 'A', 2, 1, 1, None], [122, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[12, None, None, 3, None, None], [22, None, None, 4, None, None], [32, 'x', None, 5, None, None]], [[12, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[12, 'a', 0, 9, 0, 12]], [[12, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[12, 'n', -2, 4, -1, 12], [22, 'n', None, 2, 0, 22], [32, 'n', -1, 0, 2, None]], [[12, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[12, 'p', 2, 1, 1, 12], [22, 'p', 2, 2, 1, 12], [32, 'p', 3, 0, 1, 12], [42, 'p', None, 1, 0, None]], [[12, 'p', 2, 1, 1, None], [22, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[12, '', 3, 7, 0, 192], [22, 'b', 3, 3, -1, 32], [32, 'c', None, 2, -1, 22], [42, ' a ', 3, 0, 2, 192], [52, ' a ', 1, 3, 2, 22], [62, 'b', None, 2, 0, 12], [72, 'a', -2, 2, -1, None], [82, 'c', None, 0, -1, None], [92, 'a', -1, 1, -1, 32], [102, ' a ', None, 3, 0, 32], [112, 'A', None, 1, 1, 32], [122, 'a', 3, 3, None, None]], [[12, 'c', 0, 2, None, 12], [22, '', 0, 3, 0, 22], [32, 'c', -1, 1, -1, 22], [42, 'a', 2, 2, -1, 192], [52, 'a', -1, 7, -1, 22], [62, ' a ', None, 2, -1, 12], [72, None, 2, 7, 2, 192], [82, 'a', None, 0, -1, 22], [92, None, 2, 1, None, 12], [102, 'b', 3, 2, 1, None], [112, ' a ', 2, 2, 0, 32]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[12, None, -2, 1, 0, 12], [22, 'b', None, 2, 1, 192], [32, None, 2, 7, 2, 192], [42, 'A', 3, 3, -1, 32], [52, ' a ', None, 7, 2, 12], [62, '', 1, 7, 2, None], [72, None, 2, 0, 2, 22], [82, 'A', None, 3, -1, 22], [92, 'a', 2, 7, 2, 192], [102, 'b', 3, 2, 0, None], [112, 'c', None, 3, 2, None], [122, 'A', 5, 2, None, None], [132, ' a ', 0, 1, 1, 22], [142, 'b', 2, 7, 2, None]], [[12, ' a ', -1, 1, 0, 32], [22, 'a', 5, 0, 0, None], [32, 'c', -3, 0, 1, 192], [42, ' a ', 2, 7, 1, None], [52, 'b', None, 7, -1, 12], [62, '', 2, 0, None, 32], [72, 'b', -3, 3, 1, None], [82, 'a', 0, 1, None, 192], [92, 'a', 5, 0, None, 12], [102, '', None, 3, 0, 192]]), [])
elif N == 3:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[13, 'a', None, 8, None, None], [23, 'a', 0, 3, 0, 13], [33, 'a', 2, 1, 1, 23], [43, 'a', 2, 2, 2, 903], [53, 'a', -1, 4, -1, 33], [63, 'a', 3, 1, 1, 43], [73, 'b', -2, 2, 0, 13], [83, 'b', 2, 8, 1, 23], [93, 'b', None, 4, None, None], [103, None, None, 0, 1, 903], [113, None, 0, 5, 0, 13], [123, None, None, 7, None, 23], [133, 'c', None, 6, None, 33], [143, 'd', -1, 1, 0, 43], [153, 'A', 2, 2, 1, 53], [163, ' a ', 2, 8, 1, None], [173, '', None, 2, 0, None], [183, 'a', 2, 8, 1, 13], [193, 'd', 1, 3, 0, 43], [203, 'd', -1, 0, -1, 23]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[13, 'a', None, 0, 1, None], [23, 'a', 2, 2, 0, None], [33, 'a', 2, 3, 2, None], [43, 'a', 3, 4, None, None], [53, 'b', -2, 2, 1, None], [63, 'b', 0, 8, -1, None], [73, None, None, 2, 1, None], [83, None, 0, 5, None, None], [93, 'z', 3, 2, 0, None], [103, 'z', 3, 2, 1, None], [113, 'A', 2, 1, 1, None], [123, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[13, 'a', None, 8, None, None], [23, 'a', 0, 3, 0, 13], [33, 'a', 2, 1, 1, 23], [43, 'a', 2, 2, 2, 903], [53, 'a', -1, 4, -1, 33], [63, 'a', 3, 1, 1, 43], [73, 'b', -2, 2, 0, 13], [83, 'b', 2, 8, 1, 23], [93, 'b', None, 4, None, None], [103, None, None, 0, 1, 903], [113, None, 0, 5, 0, 13], [123, None, None, 7, None, 23], [133, 'c', None, 6, None, 33], [143, 'd', -1, 1, 0, 43], [153, 'A', 2, 2, 1, 53], [163, ' a ', 2, 8, 1, None], [173, '', None, 2, 0, None], [183, 'a', 2, 8, 1, 13], [193, 'd', 1, 3, 0, 43], [203, 'd', -1, 0, -1, 23]], [[13, 'a', None, 0, 1, None], [23, 'a', 2, 2, 0, None], [33, 'a', 2, 3, 2, None], [43, 'a', 3, 4, None, None], [53, 'b', -2, 2, 1, None], [63, 'b', 0, 8, -1, None], [73, None, None, 2, 1, None], [83, None, 0, 5, None, None], [93, 'z', 3, 2, 0, None], [103, 'z', 3, 2, 1, None], [113, 'A', 2, 1, 1, None], [123, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[13, None, None, 3, None, None], [23, None, None, 4, None, None], [33, 'x', None, 5, None, None]], [[13, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[13, 'a', 0, 9, 0, 13]], [[13, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[13, 'n', -2, 4, -1, 13], [23, 'n', None, 2, 0, 23], [33, 'n', -1, 0, 2, None]], [[13, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[13, 'p', 2, 1, 1, 13], [23, 'p', 2, 2, 1, 13], [33, 'p', 3, 0, 1, 13], [43, 'p', None, 1, 0, None]], [[13, 'p', 2, 1, 1, None], [23, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[13, '', 3, 7, 0, 193], [23, 'b', 3, 3, -1, 33], [33, 'c', None, 2, -1, 23], [43, ' a ', 3, 0, 2, 193], [53, ' a ', 1, 3, 2, 23], [63, 'b', None, 2, 0, 13], [73, 'a', -2, 2, -1, None], [83, 'c', None, 0, -1, None], [93, 'a', -1, 1, -1, 33], [103, ' a ', None, 3, 0, 33], [113, 'A', None, 1, 1, 33], [123, 'a', 3, 3, None, None]], [[13, 'c', 0, 2, None, 13], [23, '', 0, 3, 0, 23], [33, 'c', -1, 1, -1, 23], [43, 'a', 2, 2, -1, 193], [53, 'a', -1, 7, -1, 23], [63, ' a ', None, 2, -1, 13], [73, None, 2, 7, 2, 193], [83, 'a', None, 0, -1, 23], [93, None, 2, 1, None, 13], [103, 'b', 3, 2, 1, None], [113, ' a ', 2, 2, 0, 33]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[13, None, -2, 1, 0, 13], [23, 'b', None, 2, 1, 193], [33, None, 2, 7, 2, 193], [43, 'A', 3, 3, -1, 33], [53, ' a ', None, 7, 2, 13], [63, '', 1, 7, 2, None], [73, None, 2, 0, 2, 23], [83, 'A', None, 3, -1, 23], [93, 'a', 2, 7, 2, 193], [103, 'b', 3, 2, 0, None], [113, 'c', None, 3, 2, None], [123, 'A', 5, 2, None, None], [133, ' a ', 0, 1, 1, 23], [143, 'b', 2, 7, 2, None]], [[13, ' a ', -1, 1, 0, 33], [23, 'a', 5, 0, 0, None], [33, 'c', -3, 0, 1, 193], [43, ' a ', 2, 7, 1, None], [53, 'b', None, 7, -1, 13], [63, '', 2, 0, None, 33], [73, 'b', -3, 3, 1, None], [83, 'a', 0, 1, None, 193], [93, 'a', 5, 0, None, 13], [103, '', None, 3, 0, 193]]), [])
elif N == 4:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[14, 'a', None, 8, None, None], [24, 'a', 0, 3, 0, 14], [34, 'a', 2, 1, 1, 24], [44, 'a', 2, 2, 2, 904], [54, 'a', -1, 4, -1, 34], [64, 'a', 3, 1, 1, 44], [74, 'b', -2, 2, 0, 14], [84, 'b', 2, 8, 1, 24], [94, 'b', None, 4, None, None], [104, None, None, 0, 1, 904], [114, None, 0, 5, 0, 14], [124, None, None, 7, None, 24], [134, 'c', None, 6, None, 34], [144, 'd', -1, 1, 0, 44], [154, 'A', 2, 2, 1, 54], [164, ' a ', 2, 8, 1, None], [174, '', None, 2, 0, None], [184, 'a', 2, 8, 1, 14], [194, 'd', 1, 3, 0, 44], [204, 'd', -1, 0, -1, 24]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[14, 'a', None, 0, 1, None], [24, 'a', 2, 2, 0, None], [34, 'a', 2, 3, 2, None], [44, 'a', 3, 4, None, None], [54, 'b', -2, 2, 1, None], [64, 'b', 0, 8, -1, None], [74, None, None, 2, 1, None], [84, None, 0, 5, None, None], [94, 'z', 3, 2, 0, None], [104, 'z', 3, 2, 1, None], [114, 'A', 2, 1, 1, None], [124, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[14, 'a', None, 8, None, None], [24, 'a', 0, 3, 0, 14], [34, 'a', 2, 1, 1, 24], [44, 'a', 2, 2, 2, 904], [54, 'a', -1, 4, -1, 34], [64, 'a', 3, 1, 1, 44], [74, 'b', -2, 2, 0, 14], [84, 'b', 2, 8, 1, 24], [94, 'b', None, 4, None, None], [104, None, None, 0, 1, 904], [114, None, 0, 5, 0, 14], [124, None, None, 7, None, 24], [134, 'c', None, 6, None, 34], [144, 'd', -1, 1, 0, 44], [154, 'A', 2, 2, 1, 54], [164, ' a ', 2, 8, 1, None], [174, '', None, 2, 0, None], [184, 'a', 2, 8, 1, 14], [194, 'd', 1, 3, 0, 44], [204, 'd', -1, 0, -1, 24]], [[14, 'a', None, 0, 1, None], [24, 'a', 2, 2, 0, None], [34, 'a', 2, 3, 2, None], [44, 'a', 3, 4, None, None], [54, 'b', -2, 2, 1, None], [64, 'b', 0, 8, -1, None], [74, None, None, 2, 1, None], [84, None, 0, 5, None, None], [94, 'z', 3, 2, 0, None], [104, 'z', 3, 2, 1, None], [114, 'A', 2, 1, 1, None], [124, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[14, None, None, 3, None, None], [24, None, None, 4, None, None], [34, 'x', None, 5, None, None]], [[14, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[14, 'a', 0, 9, 0, 14]], [[14, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[14, 'n', -2, 4, -1, 14], [24, 'n', None, 2, 0, 24], [34, 'n', -1, 0, 2, None]], [[14, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[14, 'p', 2, 1, 1, 14], [24, 'p', 2, 2, 1, 14], [34, 'p', 3, 0, 1, 14], [44, 'p', None, 1, 0, None]], [[14, 'p', 2, 1, 1, None], [24, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[14, '', 3, 7, 0, 194], [24, 'b', 3, 3, -1, 34], [34, 'c', None, 2, -1, 24], [44, ' a ', 3, 0, 2, 194], [54, ' a ', 1, 3, 2, 24], [64, 'b', None, 2, 0, 14], [74, 'a', -2, 2, -1, None], [84, 'c', None, 0, -1, None], [94, 'a', -1, 1, -1, 34], [104, ' a ', None, 3, 0, 34], [114, 'A', None, 1, 1, 34], [124, 'a', 3, 3, None, None]], [[14, 'c', 0, 2, None, 14], [24, '', 0, 3, 0, 24], [34, 'c', -1, 1, -1, 24], [44, 'a', 2, 2, -1, 194], [54, 'a', -1, 7, -1, 24], [64, ' a ', None, 2, -1, 14], [74, None, 2, 7, 2, 194], [84, 'a', None, 0, -1, 24], [94, None, 2, 1, None, 14], [104, 'b', 3, 2, 1, None], [114, ' a ', 2, 2, 0, 34]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[14, None, -2, 1, 0, 14], [24, 'b', None, 2, 1, 194], [34, None, 2, 7, 2, 194], [44, 'A', 3, 3, -1, 34], [54, ' a ', None, 7, 2, 14], [64, '', 1, 7, 2, None], [74, None, 2, 0, 2, 24], [84, 'A', None, 3, -1, 24], [94, 'a', 2, 7, 2, 194], [104, 'b', 3, 2, 0, None], [114, 'c', None, 3, 2, None], [124, 'A', 5, 2, None, None], [134, ' a ', 0, 1, 1, 24], [144, 'b', 2, 7, 2, None]], [[14, ' a ', -1, 1, 0, 34], [24, 'a', 5, 0, 0, None], [34, 'c', -3, 0, 1, 194], [44, ' a ', 2, 7, 1, None], [54, 'b', None, 7, -1, 14], [64, '', 2, 0, None, 34], [74, 'b', -3, 3, 1, None], [84, 'a', 0, 1, None, 194], [94, 'a', 5, 0, None, 14], [104, '', None, 3, 0, 194]]), [])
elif N == 5:
    check('empty relations', solve([], []), [])
    check('left facts without references', solve([[15, 'a', None, 8, None, None], [25, 'a', 0, 3, 0, 15], [35, 'a', 2, 1, 1, 25], [45, 'a', 2, 2, 2, 905], [55, 'a', -1, 4, -1, 35], [65, 'a', 3, 1, 1, 45], [75, 'b', -2, 2, 0, 15], [85, 'b', 2, 8, 1, 25], [95, 'b', None, 4, None, None], [105, None, None, 0, 1, 905], [115, None, 0, 5, 0, 15], [125, None, None, 7, None, 25], [135, 'c', None, 6, None, 35], [145, 'd', -1, 1, 0, 45], [155, 'A', 2, 2, 1, 55], [165, ' a ', 2, 8, 1, None], [175, '', None, 2, 0, None], [185, 'a', 2, 8, 1, 15], [195, 'd', 1, 3, 0, 45], [205, 'd', -1, 0, -1, 25]], []), [['a', 2, 3], ['d', -1, 2]])
    check('references without candidates', solve([], [[15, 'a', None, 0, 1, None], [25, 'a', 2, 2, 0, None], [35, 'a', 2, 3, 2, None], [45, 'a', 3, 4, None, None], [55, 'b', -2, 2, 1, None], [65, 'b', 0, 8, -1, None], [75, None, None, 2, 1, None], [85, None, 0, 5, None, None], [95, 'z', 3, 2, 0, None], [105, 'z', 3, 2, 1, None], [115, 'A', 2, 1, 1, None], [125, 'c', None, 2, 0, None]]), [])
    check('mixed nullable groups duplicates ties and truth flags', solve([[15, 'a', None, 8, None, None], [25, 'a', 0, 3, 0, 15], [35, 'a', 2, 1, 1, 25], [45, 'a', 2, 2, 2, 905], [55, 'a', -1, 4, -1, 35], [65, 'a', 3, 1, 1, 45], [75, 'b', -2, 2, 0, 15], [85, 'b', 2, 8, 1, 25], [95, 'b', None, 4, None, None], [105, None, None, 0, 1, 905], [115, None, 0, 5, 0, 15], [125, None, None, 7, None, 25], [135, 'c', None, 6, None, 35], [145, 'd', -1, 1, 0, 45], [155, 'A', 2, 2, 1, 55], [165, ' a ', 2, 8, 1, None], [175, '', None, 2, 0, None], [185, 'a', 2, 8, 1, 15], [195, 'd', 1, 3, 0, 45], [205, 'd', -1, 0, -1, 25]], [[15, 'a', None, 0, 1, None], [25, 'a', 2, 2, 0, None], [35, 'a', 2, 3, 2, None], [45, 'a', 3, 4, None, None], [55, 'b', -2, 2, 1, None], [65, 'b', 0, 8, -1, None], [75, None, None, 2, 1, None], [85, None, 0, 5, None, None], [95, 'z', 3, 2, 0, None], [105, 'z', 3, 2, 1, None], [115, 'A', 2, 1, 1, None], [125, 'c', None, 2, 0, None]]), [['a', 2, 3], ['d', -1, 2]])
    check('unknown-only group with duplicate nullable index keys', solve([[15, None, None, 3, None, None], [25, None, None, 4, None, None], [35, 'x', None, 5, None, None]], [[15, None, None, 2, None, None]]), [])
    check('single known zero and matching reference', solve([[15, 'a', 0, 9, 0, 15]], [[15, 'a', 0, 3, 1, None]]), [])
    check('negative-only group and missing measurement', solve([[15, 'n', -2, 4, -1, 15], [25, 'n', None, 2, 0, 25], [35, 'n', -1, 0, 2, None]], [[15, 'n', -2, 1, 1, None]]), [])
    check('positive-only group with repeated measurements and NULL', solve([[15, 'p', 2, 1, 1, 15], [25, 'p', 2, 2, 1, 15], [35, 'p', 3, 0, 1, 15], [45, 'p', None, 1, 0, None]], [[15, 'p', 2, 1, 1, None], [25, 'p', 2, 1, 1, None]]), [['p', 2, 2]])
    check('adversarial key cardinality and NULL placement witness 12', solve([[15, '', 3, 7, 0, 195], [25, 'b', 3, 3, -1, 35], [35, 'c', None, 2, -1, 25], [45, ' a ', 3, 0, 2, 195], [55, ' a ', 1, 3, 2, 25], [65, 'b', None, 2, 0, 15], [75, 'a', -2, 2, -1, None], [85, 'c', None, 0, -1, None], [95, 'a', -1, 1, -1, 35], [105, ' a ', None, 3, 0, 35], [115, 'A', None, 1, 1, 35], [125, 'a', 3, 3, None, None]], [[15, 'c', 0, 2, None, 15], [25, '', 0, 3, 0, 25], [35, 'c', -1, 1, -1, 25], [45, 'a', 2, 2, -1, 195], [55, 'a', -1, 7, -1, 25], [65, ' a ', None, 2, -1, 15], [75, None, 2, 7, 2, 195], [85, 'a', None, 0, -1, 25], [95, None, 2, 1, None, 15], [105, 'b', 3, 2, 1, None], [115, ' a ', 2, 2, 0, 35]]), [])
    check('adversarial key cardinality and NULL placement witness 9', solve([[15, None, -2, 1, 0, 15], [25, 'b', None, 2, 1, 195], [35, None, 2, 7, 2, 195], [45, 'A', 3, 3, -1, 35], [55, ' a ', None, 7, 2, 15], [65, '', 1, 7, 2, None], [75, None, 2, 0, 2, 25], [85, 'A', None, 3, -1, 25], [95, 'a', 2, 7, 2, 195], [105, 'b', 3, 2, 0, None], [115, 'c', None, 3, 2, None], [125, 'A', 5, 2, None, None], [135, ' a ', 0, 1, 1, 25], [145, 'b', 2, 7, 2, None]], [[15, ' a ', -1, 1, 0, 35], [25, 'a', 5, 0, 0, None], [35, 'c', -3, 0, 1, 195], [45, ' a ', 2, 7, 1, None], [55, 'b', None, 7, -1, 15], [65, '', 2, 0, None, 35], [75, 'b', -3, 3, 1, None], [85, 'a', 0, 1, None, 195], [95, 'a', 5, 0, None, 15], [105, '', None, 3, 0, 195]]), [])
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
empty relations	`[]`	`[]`	Passed
left facts without references	`[['a', 2, 3], ['d', -1, 2]]`	`[['a', 2, 3], ['d', -1, 2]]`	Passed
references without candidates	`[]`	`[]`	Passed
mixed nullable groups duplicates ties and truth flags	`[['a', 2, 3], ['d', -1, 2]]`	`[['a', 2, 3], ['d', -1, 2]]`	Passed
unknown-only group with duplicate nullable index keys	`[]`	`[]`	Passed
single known zero and matching reference	`[]`	`[]`	Passed
negative-only group and missing measurement	`[]`	`[]`	Passed
positive-only group with repeated measurements and NULL	`[['p', 2, 2]]`	`[['p', 2, 2]]`	Passed
adversarial key cardinality and NULL placement witness 12	`[]`	`[]`	Passed
adversarial key cardinality and NULL placement witness 9	`[]`	`[]`	Passed

SHA-256 / e312384e496508c1521839eb6db768c968837dbea28d847077252eb4e9c7632b

Verification & scope

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 2026-09-29T14:37:15.344495+00:00.

Case digest / 9ff08d0b3fced7d45dbd91d0e614977ad2a74a5281795d9e3b1e8e1d7d33a66c