FA-13566 / Numerical aggregation / Open access
Timestamp half decayed mass: The exponential kernel amplifies historical contributions. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
The exponential kernel amplifies historical contributions.
THE FAILURE
The exponential kernel amplifies historical contributions.
Unsuccessful approach: A reciprocal age kernel does not implement half-life decay.
Case contract
Each [integer timestamp, integer contribution] independently contributes value/2**age at integer query now; exclude future events. Same-time events are independent additive contributions. 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(events, now):
out=Fraction(0)
for t,value in events:
if t>now: continue
out+=Fraction(value*2**(now-t))
return str(out)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(0, 8), (2, 4)], 3)), '3')
check('regression 2', solve(*([], 4)), '0')
check('regression 3', solve(*([(5, 3)], 4)), '0')
check('regression 4', solve(*([(3, -4), (3, 8)], 3)), '4')
check('regression 5', solve(*([(0, 3), (1, 2), (1, 2)], 2)), '11/4')
check('regression 6', solve(*([(-2, 8), (0, -1)], 1)), '1/2')
check('regression 7', solve(*([(4, 9), (0, 16)], 4)), '10')
check("variable age",solve([(0,2**N)],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 | 72 | 3 | Failed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 4 | 4 | Passed |
| regression 5 | 20 | 11/4 | Failed |
| regression 6 | 62 | 1/2 | Failed |
| regression 7 | 265 | 10 | Failed |
| variable age | 4 | 1 | Failed |
SHA-256 / a852cf992de572b05f523e704c2fa47ef99c1076c130b0d66ccb01e5b52e3d0c
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(events, now):
out=Fraction(0)
for t,value in events:
if t>now: continue
out+=Fraction(value,now-t+1)
return str(out)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(0, 8), (2, 4)], 3)), '3')
check('regression 2', solve(*([], 4)), '0')
check('regression 3', solve(*([(5, 3)], 4)), '0')
check('regression 4', solve(*([(3, -4), (3, 8)], 3)), '4')
check('regression 5', solve(*([(0, 3), (1, 2), (1, 2)], 2)), '11/4')
check('regression 6', solve(*([(-2, 8), (0, -1)], 1)), '1/2')
check('regression 7', solve(*([(4, 9), (0, 16)], 4)), '10')
check("variable age",solve([(0,2**N)],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 | 4 | 3 | Failed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 4 | 4 | Passed |
| regression 5 | 3 | 11/4 | Failed |
| regression 6 | 3/2 | 1/2 | Failed |
| regression 7 | 61/5 | 10 | Failed |
| variable age | 1 | 1 | Passed |
SHA-256 / 231ee7a2c0c20888765b498ffe038500e43934cdb281f216e0ed9b63c23d7f87
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 2026-09-29T14:39:08.845578+00:00.
Case digest / 68783efb1347b975e945412e1cfbc9af1b498fa59b2982d2131102b789b8840f