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FA-45436 / Data systems / Open access

UNION pagination reverses branch traversal · case 01

UNION pagination reverses branch traversal.

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

ROOT CAUSE

union-global-pagination: UNION pagination reverses branch traversal.

THE FAILURE

union-global-pagination: UNION pagination reverses branch traversal.

Unsuccessful approach: Sorting branches by size changes the deterministic union stream.

Case contract

Concatenate ordered input branches with bag semantics, then apply one global nonnegative offset and limit. Branch-local boundaries, empty branches, and repeated rows do not reset pagination counters. Output order is branch order then row order.

Why this case matters

A bounded deterministic data engine model makes representation and changelog faults reproducible.

1 / The failure

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

N = 1
observations = []
def solve(d):
    try:
        branches,offset,limit=d
        remaining=offset; out=[]
        for branch in reversed(branches):
            for row in branch:
                if remaining: remaining-=1; continue
                if len(out)>=limit: return out
                out.append(row)
        return out
    except (IndexError, KeyError, ValueError, StopIteration) as exc:
        return {"representation_error": type(exc).__name__}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('offset crosses branches', solve([[[1], [2, 3], [4]], 2, 2]), [3, 4])
    check('global limit', solve([[[1, 2], [3, 4]], 0, 3]), [1, 2, 3])
    check('empty middle', solve([[[1], [], [2, 3]], 1, 2]), [2, 3])
    check('duplicates', solve([[[1, 1], [2]], 0, 3]), [1, 1, 2])
    check('zero limit', solve([[[1]], 0, 0]), [])
    check('large offset', solve([[[1], [2]], 4, 2]), [])
    check('no branches', solve([[], 0, 3]), [])
elif N == 2:
    check('offset crosses branches', solve([[[2], [3, 4], [5]], 2, 2]), [4, 5])
    check('global limit', solve([[[2, 3], [4, 5]], 0, 3]), [2, 3, 4])
    check('empty middle', solve([[[2], [], [3, 4]], 1, 2]), [3, 4])
    check('duplicates', solve([[[2, 2], [3]], 0, 3]), [2, 2, 3])
    check('zero limit', solve([[[2]], 0, 0]), [])
    check('large offset', solve([[[2], [3]], 4, 2]), [])
    check('no branches', solve([[], 0, 3]), [])
elif N == 3:
    check('offset crosses branches', solve([[[3], [4, 5], [6]], 2, 2]), [5, 6])
    check('global limit', solve([[[3, 4], [5, 6]], 0, 3]), [3, 4, 5])
    check('empty middle', solve([[[3], [], [4, 5]], 1, 2]), [4, 5])
    check('duplicates', solve([[[3, 3], [4]], 0, 3]), [3, 3, 4])
    check('zero limit', solve([[[3]], 0, 0]), [])
    check('large offset', solve([[[3], [4]], 4, 2]), [])
    check('no branches', solve([[], 0, 3]), [])
elif N == 4:
    check('offset crosses branches', solve([[[4], [5, 6], [7]], 2, 2]), [6, 7])
    check('global limit', solve([[[4, 5], [6, 7]], 0, 3]), [4, 5, 6])
    check('empty middle', solve([[[4], [], [5, 6]], 1, 2]), [5, 6])
    check('duplicates', solve([[[4, 4], [5]], 0, 3]), [4, 4, 5])
    check('zero limit', solve([[[4]], 0, 0]), [])
    check('large offset', solve([[[4], [5]], 4, 2]), [])
    check('no branches', solve([[], 0, 3]), [])
elif N == 5:
    check('offset crosses branches', solve([[[5], [6, 7], [8]], 2, 2]), [7, 8])
    check('global limit', solve([[[5, 6], [7, 8]], 0, 3]), [5, 6, 7])
    check('empty middle', solve([[[5], [], [6, 7]], 1, 2]), [6, 7])
    check('duplicates', solve([[[5, 5], [6]], 0, 3]), [5, 5, 6])
    check('zero limit', solve([[[5]], 0, 0]), [])
    check('large offset', solve([[[5], [6]], 4, 2]), [])
    check('no branches', solve([[], 0, 3]), [])
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
offset crosses branches[3, 1][3, 4]Failed
global limit[3, 4, 1][1, 2, 3]Failed
empty middle[3, 1][2, 3]Failed
duplicates[2, 1, 1][1, 1, 2]Failed
zero limit[][]Passed
large offset[][]Passed
no branches[][]Passed

SHA-256 / c7e34b28cad066d12e8eb026b7ca8e5d031d49815a86ec3a4d512baf24556fb5

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(d):
    try:
        branches,offset,limit=d
        remaining=offset; out=[]
        for branch in sorted(branches,key=len):
            for row in branch:
                if remaining: remaining-=1; continue
                if len(out)>=limit: return out
                out.append(row)
        return out
    except (IndexError, KeyError, ValueError, StopIteration) as exc:
        return {"representation_error": type(exc).__name__}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('offset crosses branches', solve([[[1], [2, 3], [4]], 2, 2]), [3, 4])
    check('global limit', solve([[[1, 2], [3, 4]], 0, 3]), [1, 2, 3])
    check('empty middle', solve([[[1], [], [2, 3]], 1, 2]), [2, 3])
    check('duplicates', solve([[[1, 1], [2]], 0, 3]), [1, 1, 2])
    check('zero limit', solve([[[1]], 0, 0]), [])
    check('large offset', solve([[[1], [2]], 4, 2]), [])
    check('no branches', solve([[], 0, 3]), [])
elif N == 2:
    check('offset crosses branches', solve([[[2], [3, 4], [5]], 2, 2]), [4, 5])
    check('global limit', solve([[[2, 3], [4, 5]], 0, 3]), [2, 3, 4])
    check('empty middle', solve([[[2], [], [3, 4]], 1, 2]), [3, 4])
    check('duplicates', solve([[[2, 2], [3]], 0, 3]), [2, 2, 3])
    check('zero limit', solve([[[2]], 0, 0]), [])
    check('large offset', solve([[[2], [3]], 4, 2]), [])
    check('no branches', solve([[], 0, 3]), [])
elif N == 3:
    check('offset crosses branches', solve([[[3], [4, 5], [6]], 2, 2]), [5, 6])
    check('global limit', solve([[[3, 4], [5, 6]], 0, 3]), [3, 4, 5])
    check('empty middle', solve([[[3], [], [4, 5]], 1, 2]), [4, 5])
    check('duplicates', solve([[[3, 3], [4]], 0, 3]), [3, 3, 4])
    check('zero limit', solve([[[3]], 0, 0]), [])
    check('large offset', solve([[[3], [4]], 4, 2]), [])
    check('no branches', solve([[], 0, 3]), [])
elif N == 4:
    check('offset crosses branches', solve([[[4], [5, 6], [7]], 2, 2]), [6, 7])
    check('global limit', solve([[[4, 5], [6, 7]], 0, 3]), [4, 5, 6])
    check('empty middle', solve([[[4], [], [5, 6]], 1, 2]), [5, 6])
    check('duplicates', solve([[[4, 4], [5]], 0, 3]), [4, 4, 5])
    check('zero limit', solve([[[4]], 0, 0]), [])
    check('large offset', solve([[[4], [5]], 4, 2]), [])
    check('no branches', solve([[], 0, 3]), [])
elif N == 5:
    check('offset crosses branches', solve([[[5], [6, 7], [8]], 2, 2]), [7, 8])
    check('global limit', solve([[[5, 6], [7, 8]], 0, 3]), [5, 6, 7])
    check('empty middle', solve([[[5], [], [6, 7]], 1, 2]), [6, 7])
    check('duplicates', solve([[[5, 5], [6]], 0, 3]), [5, 5, 6])
    check('zero limit', solve([[[5]], 0, 0]), [])
    check('large offset', solve([[[5], [6]], 4, 2]), [])
    check('no branches', solve([[], 0, 3]), [])
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
offset crosses branches[2, 3][3, 4]Failed
global limit[1, 2, 3][1, 2, 3]Passed
empty middle[2, 3][2, 3]Passed
duplicates[2, 1, 1][1, 1, 2]Failed
zero limit[][]Passed
large offset[][]Passed
no branches[][]Passed

SHA-256 / 320fda52389a6f02eb12da73686bd273aaac149e37acb9b4000873b7af663b6f

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 7 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.

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Verification & scope

Offline stipulated semantics over valid small inputs; no performance, concurrency, or production-engine conformance claim. 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 2026-09-29T14:44:22.302884+00:00.

Case digest / ed6bb82784dbf8e6f3d034a4bee9cb6011654ed69a1294936990994e975e7f4d