FAILURE MAP
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FA-6396 / Discrete calculus / Open access

Linear interpolation rational · case 01

The start value is scaled rather than retained as the intercept.

Verified by executionVariant 1 · 4 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The start value is scaled rather than retained as the intercept.

VERIFIED REPAIR

Apply the specified mathematical contract directly, preserving all terms and boundary cases: return str(Fraction(a)+(Fraction(b)-Fraction(a))*Fraction(t))

Unsuccessful approach: Endpoint weights are reversed.

Case contract

Integer sample values and compatible sample-array lengths. Rational results are reduced Fraction strings; spacing is positive unless explicitly stated otherwise. a,b are integers and t is a rational string; extrapolation outside [0,1] is allowed. Exact operational definition: str(Fraction(a)+(Fraction(b)-Fraction(a))*Fraction(t))

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(a, b, t):
    return str((Fraction(a)+Fraction(b))*Fraction(t))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check("fixture 1: (2, 10, '1/4')", solve(*(2, 10, '1/4')), '4')
check("fixture 2: (3, 7, '0')", solve(*(3, 7, '0')), '3')
check("fixture 3: (3, 7, '1')", solve(*(3, 7, '1')), '7')
check("fixture 4: (2, 2, '1/3')", solve(*(2, 2, '1/3')), '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 fixtureActualExpectedOutcome
fixture 1: (2, 10, '1/4')34Failed
fixture 2: (3, 7, '0')03Failed
fixture 3: (3, 7, '1')107Failed
fixture 4: (2, 2, '1/3')4/32Failed

SHA-256 / a252bc5b3a4baf0e5b5925f5ddfd160a498a4475ced2cafa3b49f81c698fa613

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(a, b, t):
    return str(Fraction(a)*Fraction(t)+Fraction(b)*(1-Fraction(t)))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check("fixture 1: (2, 10, '1/4')", solve(*(2, 10, '1/4')), '4')
check("fixture 2: (3, 7, '0')", solve(*(3, 7, '0')), '3')
check("fixture 3: (3, 7, '1')", solve(*(3, 7, '1')), '7')
check("fixture 4: (2, 2, '1/3')", solve(*(2, 2, '1/3')), '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 fixtureActualExpectedOutcome
fixture 1: (2, 10, '1/4')84Failed
fixture 2: (3, 7, '0')73Failed
fixture 3: (3, 7, '1')37Failed
fixture 4: (2, 2, '1/3')22Passed

SHA-256 / 37cbc05b938e74864ff25f6c7e247e6782b538967c19e48cc6be6d0b7e86379b

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(a, b, t):
    return str(Fraction(a)+(Fraction(b)-Fraction(a))*Fraction(t))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check("fixture 1: (2, 10, '1/4')", solve(*(2, 10, '1/4')), '4')
check("fixture 2: (3, 7, '0')", solve(*(3, 7, '0')), '3')
check("fixture 3: (3, 7, '1')", solve(*(3, 7, '1')), '7')
check("fixture 4: (2, 2, '1/3')", solve(*(2, 2, '1/3')), '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 fixtureActualExpectedOutcome
fixture 1: (2, 10, '1/4')44Passed
fixture 2: (3, 7, '0')33Passed
fixture 3: (3, 7, '1')77Passed
fixture 4: (2, 2, '1/3')22Passed

SHA-256 / 5aaf296c50a486222171f8ba70127d8de9148b72fa06b96f26b1e083595aae76

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 2026-09-29T14:38:01.453112+00:00.

Case digest / bcb34ae194d26d45dd4b1112627e4deed7140a3bca2fab5777142e56e6cdecc6