FA-13621 / Numerical aggregation / Open access
Time weighted step level: A change is not active at its exact timestamp. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
A change is not active at its exact timestamp.
VERIFIED REPAIR
Preserve the time weighted step level contract at the identified reduction decision.
Unsuccessful approach: Subtracting one timestamp repeats the strict-boundary mistake for integer changes.
Case contract
Events set a right-continuous integer-timestamp level; later-listed events win timestamp ties. Initial level before any event is zero. Return exact average over [start,end), including level carried from earlier history, or None if interval has no duration.
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, start, end):
if end<=start: return None
changes={}
for t,value in events:
changes[t]=value
points=sorted(set([start,end]+[t for t in changes if start<t<end]))
area=0
for left,right in zip(points,points[1:]):
earlier=[t for t in changes if t<left]
value=changes[max(earlier)] if earlier else 0
area+=value*(right-left)
return str(Fraction(area,end-start))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(0, 2), (3, 8)], 1, 5)), '5')
check('regression 2', solve(*([], 0, 4)), '0')
check('regression 3', solve(*([(3, 5)], 0, 5)), '2')
check('regression 4', solve(*([(0, 4), (0, 7), (4, 9)], 0, 4)), '7')
check('regression 5', solve(*([(2, -3), (-2, 8), (5, 1)], 0, 7)), '9/7')
check('regression 6', solve(*([(0, 2)], 3, 3)), None)
check('regression 7', solve(*([(0, 1), (1, 10), (2, 2)], 0, 5)), '17/5')
check("variable duration weighting",solve([(0,0),(N,6)],0,N+2),str(Fraction(12,N+2)))
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 | 5 | Failed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 0 | 2 | Failed |
| regression 4 | 0 | 7 | Failed |
| regression 5 | 34/7 | 9/7 | Failed |
| regression 6 | None | None | Passed |
| regression 7 | 31/5 | 17/5 | Failed |
| variable duration weighting | 0 | 4 | Failed |
SHA-256 / ad363b165068d7808e9a727d3860f4de639201952bfb33be6849d82ba15f1861
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, start, end):
if end<=start: return None
changes={}
for t,value in events:
changes[t]=value
points=sorted(set([start,end]+[t for t in changes if start<t<end]))
area=0
for left,right in zip(points,points[1:]):
earlier=[t for t in changes if t<=left-1]
value=changes[max(earlier)] if earlier else 0
area+=value*(right-left)
return str(Fraction(area,end-start))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(0, 2), (3, 8)], 1, 5)), '5')
check('regression 2', solve(*([], 0, 4)), '0')
check('regression 3', solve(*([(3, 5)], 0, 5)), '2')
check('regression 4', solve(*([(0, 4), (0, 7), (4, 9)], 0, 4)), '7')
check('regression 5', solve(*([(2, -3), (-2, 8), (5, 1)], 0, 7)), '9/7')
check('regression 6', solve(*([(0, 2)], 3, 3)), None)
check('regression 7', solve(*([(0, 1), (1, 10), (2, 2)], 0, 5)), '17/5')
check("variable duration weighting",solve([(0,0),(N,6)],0,N+2),str(Fraction(12,N+2)))
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 | 5 | Failed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 0 | 2 | Failed |
| regression 4 | 0 | 7 | Failed |
| regression 5 | 34/7 | 9/7 | Failed |
| regression 6 | None | None | Passed |
| regression 7 | 31/5 | 17/5 | Failed |
| variable duration weighting | 0 | 4 | Failed |
SHA-256 / 7e0e467133ec69ac7dbb8e3de58e4b8780af4a1de576824b2dcfc7e56e17ceff
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, start, end):
if end<=start: return None
changes={}
for t,value in events:
changes[t]=value
points=sorted(set([start,end]+[t for t in changes if start<t<end]))
area=0
for left,right in zip(points,points[1:]):
earlier=[t for t in changes if t<=left]
value=changes[max(earlier)] if earlier else 0
area+=value*(right-left)
return str(Fraction(area,end-start))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([(0, 2), (3, 8)], 1, 5)), '5')
check('regression 2', solve(*([], 0, 4)), '0')
check('regression 3', solve(*([(3, 5)], 0, 5)), '2')
check('regression 4', solve(*([(0, 4), (0, 7), (4, 9)], 0, 4)), '7')
check('regression 5', solve(*([(2, -3), (-2, 8), (5, 1)], 0, 7)), '9/7')
check('regression 6', solve(*([(0, 2)], 3, 3)), None)
check('regression 7', solve(*([(0, 1), (1, 10), (2, 2)], 0, 5)), '17/5')
check("variable duration weighting",solve([(0,0),(N,6)],0,N+2),str(Fraction(12,N+2)))
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 | 5 | 5 | Passed |
| regression 2 | 0 | 0 | Passed |
| regression 3 | 2 | 2 | Passed |
| regression 4 | 7 | 7 | Passed |
| regression 5 | 9/7 | 9/7 | Passed |
| regression 6 | None | None | Passed |
| regression 7 | 17/5 | 17/5 | Passed |
| variable duration weighting | 4 | 4 | Passed |
SHA-256 / ec56b09168128a2cff596d10d65fb53579b28d586988114cb3e4e6f00788e2c7
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 2026-09-29T14:39:08.966637+00:00.
Case digest / a79b291e24d57f7140851b87b2f4eac79f2181dad16a1380468d261061995bb8