FA-13026 / Numerical aggregation / Open access
Histogram interval mass: Disjoint bins contribute negative signed overlap. · case 01
The reduction disagrees with its explicit aggregation oracle.
ROOT CAUSE
Disjoint bins contribute negative signed overlap.
THE FAILURE
Disjoint bins contribute negative signed overlap.
Unsuccessful approach: Absolute overlap turns gaps into positive mass.
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*(min(r,b)-max(l,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 | 11/2 | 11/2 | Passed |
| regression 2 | 2 | 2 | Passed |
| regression 3 | 8 | 8 | Passed |
| regression 4 | 0 | 0 | Passed |
| regression 5 | -6 | 0 | Failed |
| regression 6 | 0 | 0 | Passed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 14 | 14 | Passed |
| variable density mass | 2 | 2 | Passed |
SHA-256 / 32efef394924eb6459c8791afb428f0a726d5e18739a27efe2a8bb2a14862766
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*abs(min(r,b)-max(l,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 | 11/2 | 11/2 | Passed |
| regression 2 | 2 | 2 | Passed |
| regression 3 | 8 | 8 | Passed |
| regression 4 | 0 | 0 | Passed |
| regression 5 | 6 | 0 | Failed |
| regression 6 | 0 | 0 | Passed |
| regression 7 | 0 | 0 | Passed |
| regression 8 | 14 | 14 | Passed |
| variable density mass | 2 | 2 | Passed |
SHA-256 / 967d99a1baf9aa318eae41321d4223d9ad317a0465d1f65b32172fc8a6cb00db
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 / fe923fc46e5cfa3f71f53b425ceafdd956bc1a4a247f616b209df38899de5531