FA-6421 / Discrete calculus / Open access
Valid cross correlation · case 01
Kernel reversal changes correlation into convolution.
ROOT CAUSE
Kernel reversal changes correlation into convolution.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return [sum(signal[i+j]*kernel[j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel)+1)]
Unsuccessful approach: The last fully overlapping window is omitted.
Case contract
Integer sample values and compatible sample-array lengths. Rational results are reduced Fraction strings; spacing is positive unless explicitly stated otherwise. kernel is nonempty; return only full-overlap windows, retaining kernel order. Exact operational definition: [sum(signal[i+j]*kernel[j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel)+1)]
Why this case matters
Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Discrete calculus results depend on the stated convention.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(signal, kernel):
return [sum(signal[i+j]*kernel[-1-j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel)+1)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 3], [1, 2])', solve(*([1, 2, 3], [1, 2])), [5, 8])
check('fixture 2: ([1, 0, 1], [1, -1])', solve(*([1, 0, 1], [1, -1])), [1, -1])
check('fixture 3: ([2], [3])', solve(*([2], [3])), [6])
check('fixture 4: ([1], [1, 2])', solve(*([1], [1, 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 |
|---|---|---|---|
| fixture 1: ([1, 2, 3], [1, 2]) | [4, 7] | [5, 8] | Failed |
| fixture 2: ([1, 0, 1], [1, -1]) | [-1, 1] | [1, -1] | Failed |
| fixture 3: ([2], [3]) | [6] | [6] | Passed |
| fixture 4: ([1], [1, 2]) | [] | [] | Passed |
SHA-256 / 63749c90d062f4afa18d752b5d916107737c68658418044dfd7f000dc1d5df71
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(signal, kernel):
return [sum(signal[i+j]*kernel[j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel))]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 3], [1, 2])', solve(*([1, 2, 3], [1, 2])), [5, 8])
check('fixture 2: ([1, 0, 1], [1, -1])', solve(*([1, 0, 1], [1, -1])), [1, -1])
check('fixture 3: ([2], [3])', solve(*([2], [3])), [6])
check('fixture 4: ([1], [1, 2])', solve(*([1], [1, 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 |
|---|---|---|---|
| fixture 1: ([1, 2, 3], [1, 2]) | [5] | [5, 8] | Failed |
| fixture 2: ([1, 0, 1], [1, -1]) | [1] | [1, -1] | Failed |
| fixture 3: ([2], [3]) | [] | [6] | Failed |
| fixture 4: ([1], [1, 2]) | [] | [] | Passed |
SHA-256 / c777d649e1a6be102b64fe7d972189c75999f584157700b7b0100c7abfa2e537
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
import calendar
import statistics
import itertools
from fractions import Fraction
from datetime import date, datetime, timedelta, timezone
from decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR
N = 1
observations = []
def solve(signal, kernel):
return [sum(signal[i+j]*kernel[j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel)+1)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 2, 3], [1, 2])', solve(*([1, 2, 3], [1, 2])), [5, 8])
check('fixture 2: ([1, 0, 1], [1, -1])', solve(*([1, 0, 1], [1, -1])), [1, -1])
check('fixture 3: ([2], [3])', solve(*([2], [3])), [6])
check('fixture 4: ([1], [1, 2])', solve(*([1], [1, 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 |
|---|---|---|---|
| fixture 1: ([1, 2, 3], [1, 2]) | [5, 8] | [5, 8] | Passed |
| fixture 2: ([1, 0, 1], [1, -1]) | [1, -1] | [1, -1] | Passed |
| fixture 3: ([2], [3]) | [6] | [6] | Passed |
| fixture 4: ([1], [1, 2]) | [] | [] | Passed |
SHA-256 / 26dfc8b336ee61faf367c507554543793deb4d1d744f05dd61457cc88f512bf9
Verification & scope
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 2026-09-29T14:38:01.610450+00:00.
Case digest / 14758fdb6863b9b8af5b17e1442da57e69fcda6ea468476e9fc360891d8d586b