FA-13561 / Numerical aggregation / Open access
Timestamp half decayed mass: Decay age is the event arrival index rather than elapsed timestamp distance. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Decay age is the event arrival index rather than elapsed timestamp distance.
VERIFIED REPAIR
Preserve the timestamp half decayed mass contract at the identified reduction decision.
Unsuccessful approach: Discarding all event ages also treats old mass as current.
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 enumerate(v for t,v 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 | 2 | 3 | Failed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 3/16 | 0 | Failed |
| regression 4 | 3/2 | 4 | Failed |
| regression 5 | 15/4 | 11/4 | Failed |
| regression 6 | 3 | 1/2 | Failed |
| regression 7 | 41/16 | 10 | Failed |
| variable age | 1 | 1 | Passed |
SHA-256 / 420a38658fa62c2c929750a7532b91d546f5184c465ec1e00266ffcdf3ba2d3d
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 sorted(events,reverse=True):
t=now
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 | 12 | 3 | Failed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 3 | 0 | Failed |
| regression 4 | 4 | 4 | Passed |
| regression 5 | 7 | 11/4 | Failed |
| regression 6 | 7 | 1/2 | Failed |
| regression 7 | 25 | 10 | Failed |
| variable age | 2 | 1 | Failed |
SHA-256 / e9be5e9ae75bdf5c3959b05bafbbe91a7820bb9e1f7fc60298c9d30e8e0966bc
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(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 | 3 | 3 | Passed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 0 | 0 | Passed |
| regression 4 | 4 | 4 | Passed |
| regression 5 | 11/4 | 11/4 | Passed |
| regression 6 | 1/2 | 1/2 | Passed |
| regression 7 | 10 | 10 | Passed |
| variable age | 1 | 1 | Passed |
SHA-256 / 1e2dbd9dc2732119fd3166906d82ac3d8c75f01596f3ed96e684181e9366e44f
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 2026-09-29T14:39:08.211760+00:00.
Case digest / 5e9c8ad678976b3257b009d9740e59f4230d45bc9ccdb1a64db04a544f9aa7e6