FA-13541 / Numerical aggregation / Open access
Recursive exponential level: The mixing fraction is truncated before use. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
The mixing fraction is truncated before use.
THE FAILURE
The mixing fraction is truncated before use.
Unsuccessful approach: Rounding selects only extreme memory policies for many fractions.
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=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 | 2 | 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 | -3 | -5/9 | Failed |
| regression 7 | 0 | 2 | Failed |
| variable impulse | 0 | 1/4 | Failed |
SHA-256 / 0fad0b42d11704eefd4966d4c040ba614f40ac6ae70dbd61e41c4f35fa9bdaf2
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=round(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 | 2 | 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 | -2 | -5/9 | Failed |
| regression 7 | 0 | 2 | Failed |
| variable impulse | 0 | 1/4 | Failed |
SHA-256 / b840ac6133f001ac6f0697553c5aa1ca99e8aed3fa538144673e794a12835d7e
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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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 2026-09-29T14:39:08.211376+00:00.
Case digest / 1942ad65b74b75a692b0718a985928670a429005504af2972f2b32435aeca9f9