FA-4266 / Collection algebra / Open access

Cartesian product order · case 01

The operation returns a result or retained state that violates this contract: Emit all ordered pairs in left-major, right-minor order, retaining duplicates.

Verified by executionVariant 1 · 4 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Loop nesting changes the required left-major product order.

VERIFIED REPAIR

Emit all ordered pairs in left-major, right-minor order, retaining duplicates.

Unsuccessful approach: Position-wise zipping does not enumerate every pair.

Case contract

Emit all ordered pairs in left-major, right-minor order, retaining duplicates. Inputs are the finite Python values shown by the executable fixtures; no concurrent execution is assumed.

Why this case matters

A controlled local-runtime regression for collection APIs, language semantics, or ownership wrappers. Fixtures include boundary and interaction cases.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(x, y=None):
    return [[a,b] for b in y for a in x]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('both empty', solve([], []), [])
check('empty right operand', solve(['a'], []), [])
check('empty left operand', solve([], ['b']), [])
check('overlap and multiplicity', solve(['b', 'a', 'b'], ['b', 'c', 'c']), [['b', 'b'], ['b', 'c'], ['b', 'c'], ['a', 'b'], ['a', 'c'], ['a', 'c'], ['b', 'b'], ['b', 'c'], ['b', 'c']])
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
both empty	`[]`	`[]`	Passed
empty right operand	`[]`	`[]`	Passed
empty left operand	`[]`	`[]`	Passed
overlap and multiplicity	`[['b', 'b'], ['a', 'b'], ['b', 'b'], ['b', 'c'], ['a', 'c'], ['b', 'c'], ['b', 'c'], ['a', 'c'], ['b', 'c']]`	`[['b', 'b'], ['b', 'c'], ['b', 'c'], ['a', 'b'], ['a', 'c'], ['a', 'c'], ['b', 'b'], ['b', 'c'], ['b', 'c']]`	Failed

SHA-256 / e604369870e63bd6b23f66d8b6ca4af0fb08ee223ec9aeb8456600d7cab630bf

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(x, y=None):
    return [[a,b] for a,b in zip(x,y)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('both empty', solve([], []), [])
check('empty right operand', solve(['a'], []), [])
check('empty left operand', solve([], ['b']), [])
check('overlap and multiplicity', solve(['b', 'a', 'b'], ['b', 'c', 'c']), [['b', 'b'], ['b', 'c'], ['b', 'c'], ['a', 'b'], ['a', 'c'], ['a', 'c'], ['b', 'b'], ['b', 'c'], ['b', 'c']])
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
both empty	`[]`	`[]`	Passed
empty right operand	`[]`	`[]`	Passed
empty left operand	`[]`	`[]`	Passed
overlap and multiplicity	`[['b', 'b'], ['a', 'c'], ['b', 'c']]`	`[['b', 'b'], ['b', 'c'], ['b', 'c'], ['a', 'b'], ['a', 'c'], ['a', 'c'], ['b', 'b'], ['b', 'c'], ['b', 'c']]`	Failed

SHA-256 / c0fb05cc033ed0c1d47fddbf8688898cac1248d74d82a13001d43eb16d658fcf

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(x, y=None):
    return [[a,b] for a in x for b in y]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('both empty', solve([], []), [])
check('empty right operand', solve(['a'], []), [])
check('empty left operand', solve([], ['b']), [])
check('overlap and multiplicity', solve(['b', 'a', 'b'], ['b', 'c', 'c']), [['b', 'b'], ['b', 'c'], ['b', 'c'], ['a', 'b'], ['a', 'c'], ['a', 'c'], ['b', 'b'], ['b', 'c'], ['b', 'c']])
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
both empty	`[]`	`[]`	Passed
empty right operand	`[]`	`[]`	Passed
empty left operand	`[]`	`[]`	Passed
overlap and multiplicity	`[['b', 'b'], ['b', 'c'], ['b', 'c'], ['a', 'b'], ['a', 'c'], ['a', 'c'], ['b', 'b'], ['b', 'c'], ['b', 'c']]`	`[['b', 'b'], ['b', 'c'], ['b', 'c'], ['a', 'b'], ['a', 'c'], ['a', 'c'], ['b', 'b'], ['b', 'c'], ['b', 'c']]`	Passed

SHA-256 / 8a4b75dbb5d4e54fd94bf5a86d0eb5768093670239bc192cc4c1bfe73ceb5f31

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 2026-09-29T14:37:37.379418+00:00.

Case digest / 0412e4d60d07b03530b1ec3730df9146e042f90073cc225d1540b06a414db9f2