FA-12921 / Numerical aggregation / Open access
Capped prefix balance: Negative intermediate debt survives the lower saturation bound. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Negative intermediate debt survives the lower saturation bound.
VERIFIED REPAIR
Preserve the capped prefix balance contract at the identified reduction decision.
Unsuccessful approach: Clamping debt only at the end leaves later credits consumed by discarded debt.
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=min(cap,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 | 2 | 2 | Passed |
| regression 2 | -1 | 3 | Failed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 4 | 4 | Passed |
| regression 5 | -2 | 2 | Failed |
| variable path | 0 | 0 | Passed |
SHA-256 / 83ac3e7ce89fad03294fb88f09238c3538f8c44530f96eb12db853c2648a24af
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=min(cap,b+x)
return max(0,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 | 2 | 2 | Passed |
| regression 2 | 0 | 3 | Failed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 4 | 4 | Passed |
| regression 5 | 0 | 2 | Failed |
| variable path | 0 | 0 | Passed |
SHA-256 / 4fb018b619b154eee5c86d41c025d56952922323bb9ca71b352616c54c07a946
3 / The verified repair
Exit 0"""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):
balance=0
for x in xs:
balance=max(0,min(cap,balance+x))
return balance
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 | 2 | 2 | Passed |
| 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 / 67d2a02cda1a3ed2cde9738695bf60f9bb77734d47397183af3752d8ab110627
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 2026-09-29T14:39:01.616970+00:00.
Case digest / b218b3526eb2c6b4311b2686408c0fe6037e1228ea503323fdf7595e425229c5