FAILURE MAP
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FA-6306 / Statistics / Open access

Survival function strict · case 01

Including equal observations mismatches the strict survival convention.

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

ROOT CAUSE

Including equal observations mismatches the strict survival convention.

VERIFIED REPAIR

Apply the specified mathematical contract directly, preserving all terms and boundary cases: return str(Fraction(sum(v>x for v in values),len(values))) if values else None

Unsuccessful approach: The lower tail is selected instead of the upper tail.

Case contract

Integer finite observations and equal lengths for paired samples. Counts and weights are nonnegative. Rational results use reduced Fraction strings. Empty or undefined statistics return None where shown. Survival function strict. Exact operational definition: str(Fraction(sum(v>x for v in values),len(values))) if values else None

Why this case matters

Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Statistical estimators 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, x):
    return str(Fraction(sum(v>=x for v in values),len(values))) if values else None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 1, 2], 1)', solve(*([1, 1, 2], 1)), '1/3')
check('fixture 2: ([1, 2, 3], 0)', solve(*([1, 2, 3], 0)), '1')
check('fixture 3: ([1, 2, 3], 3)', solve(*([1, 2, 3], 3)), '0')
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 fixtureActualExpectedOutcome
fixture 1: ([1, 1, 2], 1)11/3Failed
fixture 2: ([1, 2, 3], 0)11Passed
fixture 3: ([1, 2, 3], 3)1/30Failed
fixture 4: ([], 2)NoneNonePassed

SHA-256 / cf20b8ef7dc1cfe1e0808bef9b22e99a4cadac6f7147bcddf98b0837e008c562

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, x):
    return str(Fraction(sum(v<x for v in values),len(values))) if values else None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 1, 2], 1)', solve(*([1, 1, 2], 1)), '1/3')
check('fixture 2: ([1, 2, 3], 0)', solve(*([1, 2, 3], 0)), '1')
check('fixture 3: ([1, 2, 3], 3)', solve(*([1, 2, 3], 3)), '0')
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 fixtureActualExpectedOutcome
fixture 1: ([1, 1, 2], 1)01/3Failed
fixture 2: ([1, 2, 3], 0)01Failed
fixture 3: ([1, 2, 3], 3)2/30Failed
fixture 4: ([], 2)NoneNonePassed

SHA-256 / 156e52d95682230fef2cc0905d91898a1c5ae259580fad2b5d8ea15ed44bb988

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, x):
    return str(Fraction(sum(v>x for v in values),len(values))) if values else None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([1, 1, 2], 1)', solve(*([1, 1, 2], 1)), '1/3')
check('fixture 2: ([1, 2, 3], 0)', solve(*([1, 2, 3], 0)), '1')
check('fixture 3: ([1, 2, 3], 3)', solve(*([1, 2, 3], 3)), '0')
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 fixtureActualExpectedOutcome
fixture 1: ([1, 1, 2], 1)1/31/3Passed
fixture 2: ([1, 2, 3], 0)11Passed
fixture 3: ([1, 2, 3], 3)00Passed
fixture 4: ([], 2)NoneNonePassed

SHA-256 / b7656237f589fa26d3ad8b77f0c8ea9366d1b59305de73a99c7477df115907fe

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 2026-09-29T14:37:59.989149+00:00.

Case digest / 4507303bdf0281e513112341f3055b499e5bdbed2deab4d839867ec17c8f3f75