FA-6426 / Discrete calculus / Open access
Discrete total variation · case 01
Net displacement cancels intermediate variation.
ROOT CAUSE
Net displacement cancels intermediate variation.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return sum(abs(b-a) for a,b in zip(values,values[1:]))
Unsuccessful approach: Squared differences implement a different roughness measure.
Case contract
Integer sample values and compatible sample-array lengths. Rational results are reduced Fraction strings; spacing is positive unless explicitly stated otherwise. Discrete total variation. Exact operational definition: sum(abs(b-a) for a,b in zip(values,values[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(values):
return abs(values[-1]-values[0]) if values else 0
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([0, 2, 0],)', solve(*([0, 2, 0],)), 4)
check('fixture 2: ([1, 4, 9],)', solve(*([1, 4, 9],)), 8)
check('fixture 3: ([5],)', solve(*([5],)), 0)
check('fixture 4: ([],)', solve(*([],)), 0)
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: ([0, 2, 0],) | 0 | 4 | Failed |
| fixture 2: ([1, 4, 9],) | 8 | 8 | Passed |
| fixture 3: ([5],) | 0 | 0 | Passed |
| fixture 4: ([],) | 0 | 0 | Passed |
SHA-256 / 546e51c26adf1ab18403dd384b3c49aeebb13027efa2cb13e196751257e1137a
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(values):
return sum((b-a)**2 for a,b in zip(values,values[1:]))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([0, 2, 0],)', solve(*([0, 2, 0],)), 4)
check('fixture 2: ([1, 4, 9],)', solve(*([1, 4, 9],)), 8)
check('fixture 3: ([5],)', solve(*([5],)), 0)
check('fixture 4: ([],)', solve(*([],)), 0)
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: ([0, 2, 0],) | 8 | 4 | Failed |
| fixture 2: ([1, 4, 9],) | 34 | 8 | Failed |
| fixture 3: ([5],) | 0 | 0 | Passed |
| fixture 4: ([],) | 0 | 0 | Passed |
SHA-256 / 064f1ab7b45c8598ffef3cf4c212ef27bac1d1c3856e674a6a3e1d05860b9663
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(values):
return sum(abs(b-a) for a,b in zip(values,values[1:]))
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([0, 2, 0],)', solve(*([0, 2, 0],)), 4)
check('fixture 2: ([1, 4, 9],)', solve(*([1, 4, 9],)), 8)
check('fixture 3: ([5],)', solve(*([5],)), 0)
check('fixture 4: ([],)', solve(*([],)), 0)
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: ([0, 2, 0],) | 4 | 4 | Passed |
| fixture 2: ([1, 4, 9],) | 8 | 8 | Passed |
| fixture 3: ([5],) | 0 | 0 | Passed |
| fixture 4: ([],) | 0 | 0 | Passed |
SHA-256 / 4d9e4233547e53dd4591670ac938201538df267bc2f6fbe05996374c2c4ada91
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 2026-09-29T14:38:01.616540+00:00.
Case digest / 52dd9e13b8bc4774ba476e8dd51e76bf4896c2be6efa2499113d7795ed5c9744