FA-13526 / Numerical aggregation / Open access

Recursive exponential level: Every update uses the first observation instead of the recursive level. · case 01

The reduction disagrees with its explicit aggregation oracle.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Every update uses the first observation instead of the recursive level.

THE FAILURE

Every update uses the first observation instead of the recursive level.

Unsuccessful approach: Using the final observation leaks future data into earlier updates.

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)*xs[0]
    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	`3`	`9/2`	Failed
regression 2	`None`	`None`	Passed
regression 3	`7`	`7`	Passed
regression 4	`2`	`2`	Passed
regression 5	`1`	`1`	Passed
regression 6	`-7/3`	`-5/9`	Failed
regression 7	`2`	`2`	Passed
variable impulse	`0`	`1/4`	Failed

SHA-256 / a134aad17f60de8ec76a9ff9e7f48ec8d786020d148350d4e8ae01c607646735

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)*xs[-1]
    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	`7`	`7`	Passed
regression 4	`9`	`2`	Failed
regression 5	`1`	`1`	Passed
regression 6	`-2`	`-5/9`	Failed
regression 7	`8`	`2`	Failed
variable impulse	`0`	`1/4`	Failed

SHA-256 / 49d0d1a3d65b49091e8102b1bc996b966094d093b7e62489d45ebe11996f6f35

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 8 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

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 / 5d3e71bbb834500fd0e0ebf41fdd5f4201d260690603f61eb75988acf89319b2