FA-14216 / Numerical aggregation / Open access

Group balanced squared loss: Each group retains only its latest residual. · case 01

The reduction disagrees with its explicit aggregation oracle.

Verified by executionVariant 1 · 9 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Each group retains only its latest residual.

THE FAILURE

Each group retains only its latest residual.

Unsuccessful approach: Keeping only the first residual is equally order-dependent.

Case contract

Rows [group label, integer residual or None] are reduced into mean squared residual per group, then arithmetic mean across observed groups. Missing residuals contribute neither count nor group presence; group labels are case-sensitive. Empty observed population returns None. Exact Fraction string.

Why this case matters

Exact bounded examples isolate a reduction defect without floating-point or external-service effects.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(rows):
    groups={}
    for label,error in rows:
        if error is None: continue
        groups[label]=[error]
    if not groups: return None
    means=[Fraction(sum(e*e for e in values),len(values)) for values in groups.values()]
    return str(sum(means)/len(means))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([('a', 1), ('a', 2), ('b', 4)],)), '37/4')
check('regression 2', solve(*([('a', 1), ('a', 3), ('b', 4)],)), '21/2')
check('regression 3', solve(*([],)), None)
check('regression 4', solve(*([('a', None), ('b', None)],)), None)
check('regression 5', solve(*([('a', 0), ('a', 2), ('b', -3), ('b', 1)],)), '7/2')
check('regression 6', solve(*([('a', 1), ('b', 2), ('b', 2), ('b', 2)],)), '5/2')
check('regression 7', solve(*([('a', None), ('a', 2), ('b', 4)],)), '10')
check('regression 8', solve(*([('A', 1), ('a', 4), ('B', 2)],)), '7')
check("variable group balance",solve([("a",N),("a",-N),("b",2*N)]),str(Fraction(5*N*N,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 fixture	Actual	Expected	Outcome
regression 1	`10`	`37/4`	Failed
regression 2	`25/2`	`21/2`	Failed
regression 3	`None`	`None`	Passed
regression 4	`None`	`None`	Passed
regression 5	`5/2`	`7/2`	Failed
regression 6	`5/2`	`5/2`	Passed
regression 7	`10`	`10`	Passed
regression 8	`7`	`7`	Passed
variable group balance	`5/2`	`5/2`	Passed

SHA-256 / 86e30ea822c6753edad81c1aad902e703c1d7206a032a7aa13b9481f59383eb4

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
from collections import Counter, defaultdict
import math
import itertools
N = 1
observations = []
def solve(rows):
    groups={}
    for label,error in rows:
        if error is None: continue
        groups.setdefault(label,[error])
    if not groups: return None
    means=[Fraction(sum(e*e for e in values),len(values)) for values in groups.values()]
    return str(sum(means)/len(means))
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([('a', 1), ('a', 2), ('b', 4)],)), '37/4')
check('regression 2', solve(*([('a', 1), ('a', 3), ('b', 4)],)), '21/2')
check('regression 3', solve(*([],)), None)
check('regression 4', solve(*([('a', None), ('b', None)],)), None)
check('regression 5', solve(*([('a', 0), ('a', 2), ('b', -3), ('b', 1)],)), '7/2')
check('regression 6', solve(*([('a', 1), ('b', 2), ('b', 2), ('b', 2)],)), '5/2')
check('regression 7', solve(*([('a', None), ('a', 2), ('b', 4)],)), '10')
check('regression 8', solve(*([('A', 1), ('a', 4), ('B', 2)],)), '7')
check("variable group balance",solve([("a",N),("a",-N),("b",2*N)]),str(Fraction(5*N*N,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 fixture	Actual	Expected	Outcome
regression 1	`17/2`	`37/4`	Failed
regression 2	`17/2`	`21/2`	Failed
regression 3	`None`	`None`	Passed
regression 4	`None`	`None`	Passed
regression 5	`9/2`	`7/2`	Failed
regression 6	`5/2`	`5/2`	Passed
regression 7	`10`	`10`	Passed
regression 8	`7`	`7`	Passed
variable group balance	`5/2`	`5/2`	Passed

SHA-256 / 1cf807ed65bfe80754f77301f235589b209c910256ce65e3c6a66ac692ede555

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 9 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

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Verification & scope

Small offline integer/rational inputs only; no performance, statistical inference, or production-library conformance claim. 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 2026-09-29T14:39:14.981710+00:00.

Case digest / c773940cd09a86bf385c9a7148ad43b1fd7ce83fee0eec7baa5f51bd3c40b14b