FA-6216 / Statistics / Open access

Root mean square squared · case 01

Squaring the mean allows opposite-sign observations to cancel.

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

ROOT CAUSE

Squaring the mean allows opposite-sign observations to cancel.

VERIFIED REPAIR

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

Unsuccessful approach: The sum of squares omits the mean normalization.

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. Root mean square squared. Exact operational definition: str(Fraction(sum(v*v 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):
    return str(Fraction(sum(values),len(values))**2) if values else None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([-3, 3],)', solve(*([-3, 3],)), '9')
check('fixture 2: ([1, 2, 3],)', solve(*([1, 2, 3],)), '14/3')
check('fixture 3: ([0],)', solve(*([0],)), '0')
check('fixture 4: ([],)', solve(*([],)), 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: ([-3, 3],)	`0`	`9`	Failed
fixture 2: ([1, 2, 3],)	`4`	`14/3`	Failed
fixture 3: ([0],)	`0`	`0`	Passed
fixture 4: ([],)	`None`	`None`	Passed

SHA-256 / 464a2457f8773df41af55fb1ff7d285cb48e6d94c9814f584575b17825203f00

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 str(sum(v*v for v in values)) if values else None
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('fixture 1: ([-3, 3],)', solve(*([-3, 3],)), '9')
check('fixture 2: ([1, 2, 3],)', solve(*([1, 2, 3],)), '14/3')
check('fixture 3: ([0],)', solve(*([0],)), '0')
check('fixture 4: ([],)', solve(*([],)), 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: ([-3, 3],)	`18`	`9`	Failed
fixture 2: ([1, 2, 3],)	`14`	`14/3`	Failed
fixture 3: ([0],)	`0`	`0`	Passed
fixture 4: ([],)	`None`	`None`	Passed

SHA-256 / d38eabf42d23ac1f815193e2b7c83a8bf89c195e2e69687eecffca1f71189173

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 str(Fraction(sum(v*v 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: ([-3, 3],)', solve(*([-3, 3],)), '9')
check('fixture 2: ([1, 2, 3],)', solve(*([1, 2, 3],)), '14/3')
check('fixture 3: ([0],)', solve(*([0],)), '0')
check('fixture 4: ([],)', solve(*([],)), 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: ([-3, 3],)	`9`	`9`	Passed
fixture 2: ([1, 2, 3],)	`14/3`	`14/3`	Passed
fixture 3: ([0],)	`0`	`0`	Passed
fixture 4: ([],)	`None`	`None`	Passed

SHA-256 / aa7c8d44053744eacf8af52d3ef28810a766997211ad315cb05822c8dd4c47fb

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 2026-09-29T14:37:58.872391+00:00.

Case digest / 73eb34d563b6ff37abe93f696a6f2af38bd9dc30a91a175e1f9973a4a2f0c513