FA-13556 / Numerical aggregation / Open access
Recursive exponential level: Recursive initialization is replaced by a normalized zero-origin exponential average. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Recursive initialization is replaced by a normalized zero-origin exponential average.
VERIFIED REPAIR
Preserve the recursive exponential level contract at the identified reduction decision.
Unsuccessful approach: An ordinary arithmetic average also ignores the stipulated recursive initialization and decay.
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(xs[0])
for x in xs[1:]:
y=alpha*x+(1-alpha)*y
return str(sum(alpha*(1-alpha)**(len(xs)-1-i)*x for i,x in enumerate(xs))/(1-(1-alpha)**len(xs))) if alpha else str(Fraction(sum(xs),len(xs)))
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 | 34/7 | 9/2 | Failed |
| regression 2 | None | None | Passed |
| regression 3 | 7 | 7 | Passed |
| regression 4 | 11/2 | 2 | Failed |
| regression 5 | 1 | 1 | Passed |
| regression 6 | -6/13 | -5/9 | Failed |
| regression 7 | 128/37 | 2 | Failed |
| variable impulse | 2/7 | 1/4 | Failed |
SHA-256 / 693068ab7ae6145b70825dd78cf15da1889283ef80186a996b349f7488d3093a
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=Fraction(xs[0])
for x in xs[1:]:
y=alpha*x+(1-alpha)*y
return str(Fraction(sum(xs),len(xs)))
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 | 14/3 | 9/2 | Failed |
| regression 2 | None | None | Passed |
| regression 3 | 7 | 7 | Passed |
| regression 4 | 11/2 | 2 | Failed |
| regression 5 | 4 | 1 | Failed |
| regression 6 | 0 | -5/9 | Failed |
| regression 7 | 8/3 | 2 | Failed |
| variable impulse | 1/3 | 1/4 | Failed |
SHA-256 / ede795ca6bee9ca561b7044bd77b31d3ddb8b514cf57351c787278e11498a62e
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 2026-09-29T14:39:08.211376+00:00.
Case digest / 7a878f2f1261ae0f457ca44cd6b794292e139675a36541f70577f7feba372392