FA-6406 / Discrete calculus / Open access
Linear extrapolation last slope · case 01
Last-value persistence discards the final slope.
ROOT CAUSE
Last-value persistence discards the final slope.
VERIFIED REPAIR
Apply the specified mathematical contract directly, preserving all terms and boundary cases: return 2*values[-1]-values[-2] if len(values)>1 else None
Unsuccessful approach: The previous value is added instead of subtracting it in the slope.
Case contract
Integer sample values and compatible sample-array lengths. Rational results are reduced Fraction strings; spacing is positive unless explicitly stated otherwise. Linear extrapolation last slope. Exact operational definition: 2*values[-1]-values[-2] if len(values)>1 else None
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 values[-1] if values else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 3, 5],)', solve(*([1, 3, 5],)), 7)
check('fixture 2: ([5, 3, 1],)', solve(*([5, 3, 1],)), -1)
check('fixture 3: ([4, 4],)', solve(*([4, 4],)), 4)
check('fixture 4: ([2],)', solve(*([2],)), None)
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, 3, 5],) | 5 | 7 | Failed |
| fixture 2: ([5, 3, 1],) | 1 | -1 | Failed |
| fixture 3: ([4, 4],) | 4 | 4 | Passed |
| fixture 4: ([2],) | 2 | None | Failed |
SHA-256 / 708a68f0201c1bbd04a21d128cef75efd12ff054caaefc728f3745b7118072a9
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 values[-1]+values[-2] if len(values)>1 else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 3, 5],)', solve(*([1, 3, 5],)), 7)
check('fixture 2: ([5, 3, 1],)', solve(*([5, 3, 1],)), -1)
check('fixture 3: ([4, 4],)', solve(*([4, 4],)), 4)
check('fixture 4: ([2],)', solve(*([2],)), None)
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, 3, 5],) | 8 | 7 | Failed |
| fixture 2: ([5, 3, 1],) | 4 | -1 | Failed |
| fixture 3: ([4, 4],) | 8 | 4 | Failed |
| fixture 4: ([2],) | None | None | Passed |
SHA-256 / 8fe621d742f6c31e1daf21f4f75d3530ccfe134a7bcf05f27cdd36c4f6ee85e4
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 2*values[-1]-values[-2] if len(values)>1 else None
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 3, 5],)', solve(*([1, 3, 5],)), 7)
check('fixture 2: ([5, 3, 1],)', solve(*([5, 3, 1],)), -1)
check('fixture 3: ([4, 4],)', solve(*([4, 4],)), 4)
check('fixture 4: ([2],)', solve(*([2],)), None)
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, 3, 5],) | 7 | 7 | Passed |
| fixture 2: ([5, 3, 1],) | -1 | -1 | Passed |
| fixture 3: ([4, 4],) | 4 | 4 | Passed |
| fixture 4: ([2],) | None | None | Passed |
SHA-256 / d837faae0800ae829ba5156783e2a13233a79a417f6318f93614b4d2e1c60309
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 2026-09-29T14:38:01.558012+00:00.
Case digest / 436fa1a3dc01e3ae674c902d37904a86141cbff07e5f97b33820d6161693bf73