FAILURE MAP
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FA-2056 / Analytical processing / Open access

Group minimum: Defaults unknown-only minima to zero · case 01

The query violates its result contract: defaults unknown-only minima to zero.

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

ROOT CAUSE

Defaults unknown-only minima to zero. The faulty SQL is: SELECT k,COALESCE(MIN(v),0) FROM a GROUP BY k

THE FAILURE

Defaults unknown-only minima to zero. The faulty SQL is: SELECT k,COALESCE(MIN(v),0) FROM a GROUP BY k

Unsuccessful approach: The alternative query still fails because it finds the minimum only among eligible rows. Attempted SQL: SELECT k,MIN(v) FROM a WHERE flag GROUP BY k

Case contract

Return the minimum known v for each k, or NULL when every value is unknown. 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,COALESCE(MIN(v),0) FROM a GROUP BY 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]], []), [[' a ', 2], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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]]), [['x', None], [None, None]])
    check('single known zero and matching reference', solve([[11, 'a', 0, 9, 0, 11]], [[11, 'a', 0, 3, 1, None]]), [['a', 0]])
    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]]), [['n', -2]])
    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]])
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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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]]), [['x', None], [None, None]])
    check('single known zero and matching reference', solve([[12, 'a', 0, 9, 0, 12]], [[12, 'a', 0, 3, 1, None]]), [['a', 0]])
    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]]), [['n', -2]])
    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]])
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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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]]), [['x', None], [None, None]])
    check('single known zero and matching reference', solve([[13, 'a', 0, 9, 0, 13]], [[13, 'a', 0, 3, 1, None]]), [['a', 0]])
    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]]), [['n', -2]])
    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]])
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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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]]), [['x', None], [None, None]])
    check('single known zero and matching reference', solve([[14, 'a', 0, 9, 0, 14]], [[14, 'a', 0, 3, 1, None]]), [['a', 0]])
    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]]), [['n', -2]])
    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]])
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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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]]), [['x', None], [None, None]])
    check('single known zero and matching reference', solve([[15, 'a', 0, 9, 0, 15]], [[15, 'a', 0, 3, 1, None]]), [['a', 0]])
    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]]), [['n', -2]])
    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]])
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
empty relations[][]Passed
left facts without references[[' a ', 2], ['', 0], ['A', 2], ['a', -1], ['b', -2], ['c', 0], ['d', -1], [None, 0]][[' a ', 2], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]]Failed
references without candidates[][]Passed
mixed nullable groups duplicates ties and truth flags[[' a ', 2], ['', 0], ['A', 2], ['a', -1], ['b', -2], ['c', 0], ['d', -1], [None, 0]][[' a ', 2], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]]Failed
unknown-only group with duplicate nullable index keys[['x', 0], [None, 0]][['x', None], [None, None]]Failed
single known zero and matching reference[['a', 0]][['a', 0]]Passed
negative-only group and missing measurement[['n', -2]][['n', -2]]Passed
positive-only group with repeated measurements and NULL[['p', 2]][['p', 2]]Passed

SHA-256 / c5cbd7660cb91b753648ec79375675c370ffb8173504e8f6338a4f16065fc000

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,MIN(v) FROM a WHERE flag GROUP BY 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]], []), [[' a ', 2], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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]]), [['x', None], [None, None]])
    check('single known zero and matching reference', solve([[11, 'a', 0, 9, 0, 11]], [[11, 'a', 0, 3, 1, None]]), [['a', 0]])
    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]]), [['n', -2]])
    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]])
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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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]]), [['x', None], [None, None]])
    check('single known zero and matching reference', solve([[12, 'a', 0, 9, 0, 12]], [[12, 'a', 0, 3, 1, None]]), [['a', 0]])
    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]]), [['n', -2]])
    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]])
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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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]]), [['x', None], [None, None]])
    check('single known zero and matching reference', solve([[13, 'a', 0, 9, 0, 13]], [[13, 'a', 0, 3, 1, None]]), [['a', 0]])
    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]]), [['n', -2]])
    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]])
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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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]]), [['x', None], [None, None]])
    check('single known zero and matching reference', solve([[14, 'a', 0, 9, 0, 14]], [[14, 'a', 0, 3, 1, None]]), [['a', 0]])
    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]]), [['n', -2]])
    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]])
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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]])
    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]]), [['x', None], [None, None]])
    check('single known zero and matching reference', solve([[15, 'a', 0, 9, 0, 15]], [[15, 'a', 0, 3, 1, None]]), [['a', 0]])
    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]]), [['n', -2]])
    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]])
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
empty relations[][]Passed
left facts without references[[' a ', 2], ['A', 2], ['a', -1], ['b', 2], ['d', -1], [None, None]][[' a ', 2], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]]Failed
references without candidates[][]Passed
mixed nullable groups duplicates ties and truth flags[[' a ', 2], ['A', 2], ['a', -1], ['b', 2], ['d', -1], [None, None]][[' a ', 2], ['', None], ['A', 2], ['a', -1], ['b', -2], ['c', None], ['d', -1], [None, 0]]Failed
unknown-only group with duplicate nullable index keys[][['x', None], [None, None]]Failed
single known zero and matching reference[][['a', 0]]Failed
negative-only group and missing measurement[['n', -2]][['n', -2]]Passed
positive-only group with repeated measurements and NULL[['p', 2]][['p', 2]]Passed

SHA-256 / 968c5b6dd91af84894342133f3dbd4b663922c2d1babd88741c1d59b714a0d49

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.

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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 2026-09-29T14:37:08.917826+00:00.

Case digest / 3fd876c8557f45e19226d9b6da24e6502a7c5a57ab4bf6fde8548a48cbd4e3ef