FA-1796 / Relational algebra / Open access

Semi join: Uses NULL-safe equality for membership · case 01

The query violates its result contract: uses null-safe equality for membership.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Uses NULL-safe equality for membership. The faulty SQL is: SELECT a.id FROM a WHERE EXISTS(SELECT 1 FROM b WHERE b.k IS a.k)

THE FAILURE

Uses NULL-safe equality for membership. The faulty SQL is: SELECT a.id FROM a WHERE EXISTS(SELECT 1 FROM b WHERE b.k IS a.k)

Unsuccessful approach: The alternative query still fails because it emits one left ID per matching right occurrence. Attempted SQL: SELECT a.id FROM a JOIN b ON a.k=b.k

Case contract

Return each a ID once if any b has the same known k. 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 a.id FROM a WHERE EXISTS(SELECT 1 FROM b WHERE b.k IS a.k)')], 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]], []), [])
    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]]), [[11], [131], [151], [181], [21], [31], [41], [51], [61], [71], [81], [91]])
    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]]), [[11]])
    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]]), [[11], [21], [31]])
    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]]), [[11], [21], [31], [41]])
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]], []), [])
    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]]), [[12], [132], [152], [182], [22], [32], [42], [52], [62], [72], [82], [92]])
    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]]), [[12]])
    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]]), [[12], [22], [32]])
    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]]), [[12], [22], [32], [42]])
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]], []), [])
    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]]), [[133], [13], [153], [183], [23], [33], [43], [53], [63], [73], [83], [93]])
    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]]), [[13]])
    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]]), [[13], [23], [33]])
    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]]), [[13], [23], [33], [43]])
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]], []), [])
    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]]), [[134], [14], [154], [184], [24], [34], [44], [54], [64], [74], [84], [94]])
    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]]), [[14]])
    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]]), [[14], [24], [34]])
    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]]), [[14], [24], [34], [44]])
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]], []), [])
    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]]), [[135], [155], [15], [185], [25], [35], [45], [55], [65], [75], [85], [95]])
    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]]), [[15]])
    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]]), [[15], [25], [35]])
    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]]), [[15], [25], [35], [45]])
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	`[]`	`[]`	Passed
references without candidates	`[]`	`[]`	Passed
mixed nullable groups duplicates ties and truth flags	`[[101], [111], [11], [121], [131], [151], [181], [21], [31], [41], [51], [61], [71], [81], [91]]`	`[[11], [131], [151], [181], [21], [31], [41], [51], [61], [71], [81], [91]]`	Failed
unknown-only group with duplicate nullable index keys	`[[11], [21]]`	`[]`	Failed
single known zero and matching reference	`[[11]]`	`[[11]]`	Passed
negative-only group and missing measurement	`[[11], [21], [31]]`	`[[11], [21], [31]]`	Passed
positive-only group with repeated measurements and NULL	`[[11], [21], [31], [41]]`	`[[11], [21], [31], [41]]`	Passed

SHA-256 / 6c8df180bef5e20f499a898fb3e46dbb18d7b950e10d29b388ac58e701ce6afe

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 a.id FROM a JOIN b ON a.k=b.k')], 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]], []), [])
    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]]), [[11], [131], [151], [181], [21], [31], [41], [51], [61], [71], [81], [91]])
    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]]), [[11]])
    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]]), [[11], [21], [31]])
    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]]), [[11], [21], [31], [41]])
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]], []), [])
    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]]), [[12], [132], [152], [182], [22], [32], [42], [52], [62], [72], [82], [92]])
    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]]), [[12]])
    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]]), [[12], [22], [32]])
    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]]), [[12], [22], [32], [42]])
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]], []), [])
    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]]), [[133], [13], [153], [183], [23], [33], [43], [53], [63], [73], [83], [93]])
    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]]), [[13]])
    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]]), [[13], [23], [33]])
    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]]), [[13], [23], [33], [43]])
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]], []), [])
    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]]), [[134], [14], [154], [184], [24], [34], [44], [54], [64], [74], [84], [94]])
    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]]), [[14]])
    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]]), [[14], [24], [34]])
    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]]), [[14], [24], [34], [44]])
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]], []), [])
    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]]), [[135], [155], [15], [185], [25], [35], [45], [55], [65], [75], [85], [95]])
    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]]), [[15]])
    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]]), [[15], [25], [35]])
    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]]), [[15], [25], [35], [45]])
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	`[]`	`[]`	Passed
references without candidates	`[]`	`[]`	Passed
mixed nullable groups duplicates ties and truth flags	`[[11], [11], [11], [11], [131], [151], [181], [181], [181], [181], [21], [21], [21], [21], [31], [31], [31], [31], [41], [41], [41], [41], [51], [51], [51], [51], [61], [61], [61], [61], [71], [71], [81], [81], [91], [91]]`	`[[11], [131], [151], [181], [21], [31], [41], [51], [61], [71], [81], [91]]`	Failed
unknown-only group with duplicate nullable index keys	`[]`	`[]`	Passed
single known zero and matching reference	`[[11]]`	`[[11]]`	Passed
negative-only group and missing measurement	`[[11], [21], [31]]`	`[[11], [21], [31]]`	Passed
positive-only group with repeated measurements and NULL	`[[11], [11], [21], [21], [31], [31], [41], [41]]`	`[[11], [21], [31], [41]]`	Failed

SHA-256 / 85a8546cb61bc7223225ebefe81bf77f276e417bd71634e7a6c2b402ec77fd4e

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

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

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:37:05.905420+00:00.

Case digest / 1b07d2a5c9c7392f5b29372bafa527c9528eb53364b026bf7198da739ee6041e