FA-12936 / Numerical aggregation / Open access
Capped prefix balance: An overflowing balance resets instead of saturating. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
An overflowing balance resets instead of saturating.
THE FAILURE
An overflowing balance resets instead of saturating.
Unsuccessful approach: Reflecting an overflow back into range models a different boundary.
Case contract
Starting at zero, apply each signed delta and clamp the running balance into [0,cap] after every event. cap is positive.
Why this case matters
Exact bounded examples isolate a reduction defect without floating-point or external-service effects.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(xs, cap):
b=0
for x in xs:
b=b+x
b=0 if b<0 or b>cap else b
return b
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([8, -3], 5)), 2)
check('regression 2', solve(*([-4, 3], 5)), 3)
check('regression 3', solve(*([], 5)), 0)
check('regression 4', solve(*([2, 2], 5)), 4)
check('regression 5', solve(*([8, -9, 2], 5)), 2)
check("variable path",solve([N+4,-2],N+1),N-1)
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 |
|---|---|---|---|
| regression 1 | 0 | 2 | Failed |
| regression 2 | 3 | 3 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 4 | 4 | Passed |
| regression 5 | 2 | 2 | Passed |
| variable path | 0 | 0 | Passed |
SHA-256 / f22f072c6396599afedd9156d424237af6fbeae0896443b933dc435521c7dfde
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(xs, cap):
b=0
for x in xs: b=abs(b+x) if b+x<0 else (2*cap-b-x if b+x>cap else b+x)
return b
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([8, -3], 5)), 2)
check('regression 2', solve(*([-4, 3], 5)), 3)
check('regression 3', solve(*([], 5)), 0)
check('regression 4', solve(*([2, 2], 5)), 4)
check('regression 5', solve(*([8, -9, 2], 5)), 2)
check("variable path",solve([N+4,-2],N+1),N-1)
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 |
|---|---|---|---|
| regression 1 | 1 | 2 | Failed |
| regression 2 | 3 | 3 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 4 | 4 | Passed |
| regression 5 | 1 | 2 | Failed |
| variable path | 3 | 0 | Failed |
SHA-256 / e99cf7161d7c6d4b25cac10daf21e2376ffe3255b1105d099a680e2e0979911d
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 6 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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Sign in to the archive ↗Verification & scope
Small offline integer/rational inputs only; no performance, statistical inference, or production-library 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 2026-09-29T14:39:01.647309+00:00.
Case digest / cd72d6b03a7edfa830c1645b52a6948d531a272bfa877e813d46951b0b2fed35