FA-13511 / Numerical aggregation / Open access
Recursive exponential level: The initial level is zero instead of the first observation. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
The initial level is zero instead of the first observation.
VERIFIED REPAIR
Preserve the recursive exponential level contract at the identified reduction decision.
Unsuccessful approach: Attenuating the initial value also changes the first-observation initialization contract.
Case contract
For 0<=p<=q and q>0, initialise the recursive level to the first observation and update y=(p/q)*x+(1-p/q)*y for each later observation. Empty input returns None; return exact Fraction string.
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, p, q):
if not xs: return None
alpha=Fraction(p,q)
y=Fraction(0)
for x in xs[1:]:
y=alpha*x+(1-alpha)*y
return str(y)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([2, 8, 4], 1, 2)), '9/2')
check('regression 2', solve(*([], 1, 2)), None)
check('regression 3', solve(*([7], 1, 3)), '7')
check('regression 4', solve(*([2, 9], 0, 1)), '2')
check('regression 5', solve(*([3, 8, 1], 1, 1)), '1')
check('regression 6', solve(*([-3, 5, -2], 2, 3)), '-5/9')
check('regression 7', solve(*([0, 0, 8], 1, 4)), '2')
check("variable impulse",solve([0,N,0],1,2),str(Fraction(N,4)))
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 | 4 | 9/2 | Failed |
| regression 2 | None | None | Passed |
| regression 3 | 0 | 7 | Failed |
| regression 4 | 0 | 2 | Failed |
| regression 5 | 1 | 1 | Passed |
| regression 6 | -2/9 | -5/9 | Failed |
| regression 7 | 2 | 2 | Passed |
| variable impulse | 1/4 | 1/4 | Passed |
SHA-256 / fa25cf84c711085b6712412ea300463e076c04391d32af43c14228bd4331f4c9
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, p, q):
if not xs: return None
alpha=Fraction(p,q)
y=alpha*xs[0]
for x in xs[1:]:
y=alpha*x+(1-alpha)*y
return str(y)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([2, 8, 4], 1, 2)), '9/2')
check('regression 2', solve(*([], 1, 2)), None)
check('regression 3', solve(*([7], 1, 3)), '7')
check('regression 4', solve(*([2, 9], 0, 1)), '2')
check('regression 5', solve(*([3, 8, 1], 1, 1)), '1')
check('regression 6', solve(*([-3, 5, -2], 2, 3)), '-5/9')
check('regression 7', solve(*([0, 0, 8], 1, 4)), '2')
check("variable impulse",solve([0,N,0],1,2),str(Fraction(N,4)))
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 | 17/4 | 9/2 | Failed |
| regression 2 | None | None | Passed |
| regression 3 | 7/3 | 7 | Failed |
| regression 4 | 0 | 2 | Failed |
| regression 5 | 1 | 1 | Passed |
| regression 6 | -4/9 | -5/9 | Failed |
| regression 7 | 2 | 2 | Passed |
| variable impulse | 1/4 | 1/4 | Passed |
SHA-256 / f869b4ef782ed1d5248f5668f11f8332cfae2c06372310c3e7ff3ee7e114bfb4
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, p, q):
if not xs: return None
alpha=Fraction(p,q)
y=Fraction(xs[0])
for x in xs[1:]:
y=alpha*x+(1-alpha)*y
return str(y)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([2, 8, 4], 1, 2)), '9/2')
check('regression 2', solve(*([], 1, 2)), None)
check('regression 3', solve(*([7], 1, 3)), '7')
check('regression 4', solve(*([2, 9], 0, 1)), '2')
check('regression 5', solve(*([3, 8, 1], 1, 1)), '1')
check('regression 6', solve(*([-3, 5, -2], 2, 3)), '-5/9')
check('regression 7', solve(*([0, 0, 8], 1, 4)), '2')
check("variable impulse",solve([0,N,0],1,2),str(Fraction(N,4)))
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 | 9/2 | 9/2 | Passed |
| regression 2 | None | None | Passed |
| regression 3 | 7 | 7 | Passed |
| regression 4 | 2 | 2 | Passed |
| regression 5 | 1 | 1 | Passed |
| regression 6 | -5/9 | -5/9 | Passed |
| regression 7 | 2 | 2 | Passed |
| variable impulse | 1/4 | 1/4 | Passed |
SHA-256 / 8ace4ea471d2912374f7d4005a5287324b160218f1e1701a2b16830f1b43c189
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 2026-09-29T14:39:07.827363+00:00.
Case digest / 04d99b41123ba7d53fbcb65a8fc259fb881546a6a93d27fa2e4fc3bb4758cf27