FA-13031 / Numerical aggregation / Open access
Histogram interval mass: The query left edge is ignored when truncating bins. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
The query left edge is ignored when truncating bins.
THE FAILURE
The query left edge is ignored when truncating bins.
Unsuccessful approach: Using only the query left edge extends bins backward into gaps.
Case contract
Bins [left,right,mass] have positive widths and nonnegative integer masses. Treat each bin as uniform density. Return exact mass in query [a,b] as a Fraction string; reversed/empty queries have zero mass.
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(bins, a, b):
return str(sum((Fraction(m*max(0,min(r,b)-l),r-l) for l,r,m in bins),Fraction(0))) if a<b else "0"
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([[0, 4, 8], [4, 10, 3]], 2, 7)), '11/2')
check('regression 2', solve(*([[0, 4, 8]], 1, 2)), '2')
check('regression 3', solve(*([[0, 4, 8]], -3, 8)), '8')
check('regression 4', solve(*([[0, 4, 8]], 4, 9)), '0')
check('regression 5', solve(*([[0, 4, 8]], 7, 9)), '0')
check('regression 6', solve(*([], 0, 1)), '0')
check('regression 7', solve(*([[0, 4, 8]], 3, 1)), '0')
check('regression 8', solve(*([[2, 7, 10], [10, 12, 8]], 0, 11)), '14')
check("variable density mass",solve([[0,N+2,2*(N+2)]],1,N+1),str(2*N))
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 | 19/2 | 11/2 | Failed |
| regression 2 | 4 | 2 | Failed |
| regression 3 | 8 | 8 | Passed |
| regression 4 | 8 | 0 | Failed |
| regression 5 | 8 | 0 | Failed |
| regression 6 | 0 | 0 | Passed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 14 | 14 | Passed |
| variable density mass | 4 | 2 | Failed |
SHA-256 / 026a5a7cd70e4701be80758b2a09d3c66dec4cd219c37e56ffbf5afb5d1f29a7
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(bins, a, b):
return str(sum((Fraction(m*max(0,min(r,b)-a),r-l) for l,r,m in bins),Fraction(0))) if a<b else "0"
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([[0, 4, 8], [4, 10, 3]], 2, 7)), '11/2')
check('regression 2', solve(*([[0, 4, 8]], 1, 2)), '2')
check('regression 3', solve(*([[0, 4, 8]], -3, 8)), '8')
check('regression 4', solve(*([[0, 4, 8]], 4, 9)), '0')
check('regression 5', solve(*([[0, 4, 8]], 7, 9)), '0')
check('regression 6', solve(*([], 0, 1)), '0')
check('regression 7', solve(*([[0, 4, 8]], 3, 1)), '0')
check('regression 8', solve(*([[2, 7, 10], [10, 12, 8]], 0, 11)), '14')
check("variable density mass",solve([[0,N+2,2*(N+2)]],1,N+1),str(2*N))
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 | 13/2 | 11/2 | Failed |
| regression 2 | 2 | 2 | Passed |
| regression 3 | 14 | 8 | Failed |
| regression 4 | 0 | 0 | Passed |
| regression 5 | 0 | 0 | Passed |
| regression 6 | 0 | 0 | Passed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 58 | 14 | Failed |
| variable density mass | 2 | 2 | Passed |
SHA-256 / 030e7c53a3b9904f24e3d067a3a21e1f0326b30058b6488ba99083e04b367c58
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 9 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 2026-09-29T14:39:03.075051+00:00.
Case digest / 230f2bb2ab4376041744cc0c61afa0dd6525e56fcf55df1075585f2a89cd8df2