FA-13896 / Numerical aggregation / Open access

Retractable zero aware product: The multiplicative accumulator starts at zero. · case 01

The reduction disagrees with its explicit aggregation oracle.

Verified by executionVariant 1 · 11 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The multiplicative accumulator starts at zero.

THE FAILURE

The multiplicative accumulator starts at zero.

Unsuccessful approach: Negative one changes every empty and even-negative product sign.

Case contract

Process add/remove integer factors; each removal removes one currently present equal factor. Return the exact product of active factors with empty product one. Preserve zero multiplicity and signed parity while zero factors temporarily hide the nonzero product.

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(events):
    magnitude=0
    negative=zero=0
    for op,x in events:
        if op=="add":
            if x==0: zero+=1
            else:
                magnitude*=abs(x)
                negative+=int(x<0)
        else:
            if x==0: zero-=1
            else:
                magnitude//=abs(x)
                negative-=int(x<0)
    return 0 if zero else (-magnitude if negative%2 else magnitude)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([('add', 0), ('add', 0)],)), 0)
check('regression 2', solve(*([('add', 0), ('add', -3)],)), 0)
check('regression 3', solve(*([('add', -1), ('add', -2), ('add', -3)],)), -6)
check('regression 4', solve(*([('add', 2), ('add', 0), ('add', -3), ('remove', 0)],)), -6)
check('regression 5', solve(*([('add', 0), ('add', 0), ('remove', 0)],)), 0)
check('regression 6', solve(*([],)), 1)
check('regression 7', solve(*([('add', -2), ('add', -3), ('remove', -2)],)), -3)
check('regression 8', solve(*([('add', 3), ('add', 3), ('remove', 3)],)), 3)
check('regression 9', solve(*([('add', -1), ('remove', -1)],)), 1)
check('regression 10', solve(*([('add', -2), ('add', 5), ('add', -3)],)), 30)
check("variable zero removal",solve([("add",N),("add",0),("add",-2),("remove",0)]),-2*N)
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	`0`	`0`	Passed
regression 2	`0`	`0`	Passed
regression 3	`0`	`-6`	Failed
regression 4	`0`	`-6`	Failed
regression 5	`0`	`0`	Passed
regression 6	`0`	`1`	Failed
regression 7	`0`	`-3`	Failed
regression 8	`0`	`3`	Failed
regression 9	`0`	`1`	Failed
regression 10	`0`	`30`	Failed
variable zero removal	`0`	`-2`	Failed

SHA-256 / 5ac84bb564f61c1ab881096bd36b7b3a6a618b321734b9cf2e30cf63d015f6cf

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(events):
    magnitude=-1
    negative=zero=0
    for op,x in events:
        if op=="add":
            if x==0: zero+=1
            else:
                magnitude*=abs(x)
                negative+=int(x<0)
        else:
            if x==0: zero-=1
            else:
                magnitude//=abs(x)
                negative-=int(x<0)
    return 0 if zero else (-magnitude if negative%2 else magnitude)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('regression 1', solve(*([('add', 0), ('add', 0)],)), 0)
check('regression 2', solve(*([('add', 0), ('add', -3)],)), 0)
check('regression 3', solve(*([('add', -1), ('add', -2), ('add', -3)],)), -6)
check('regression 4', solve(*([('add', 2), ('add', 0), ('add', -3), ('remove', 0)],)), -6)
check('regression 5', solve(*([('add', 0), ('add', 0), ('remove', 0)],)), 0)
check('regression 6', solve(*([],)), 1)
check('regression 7', solve(*([('add', -2), ('add', -3), ('remove', -2)],)), -3)
check('regression 8', solve(*([('add', 3), ('add', 3), ('remove', 3)],)), 3)
check('regression 9', solve(*([('add', -1), ('remove', -1)],)), 1)
check('regression 10', solve(*([('add', -2), ('add', 5), ('add', -3)],)), 30)
check("variable zero removal",solve([("add",N),("add",0),("add",-2),("remove",0)]),-2*N)
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	`0`	`0`	Passed
regression 2	`0`	`0`	Passed
regression 3	`6`	`-6`	Failed
regression 4	`6`	`-6`	Failed
regression 5	`0`	`0`	Passed
regression 6	`-1`	`1`	Failed
regression 7	`3`	`-3`	Failed
regression 8	`-3`	`3`	Failed
regression 9	`-1`	`1`	Failed
regression 10	`-30`	`30`	Failed
variable zero removal	`2`	`-2`	Failed

SHA-256 / ceb856c38668e1028f1220849e7a8a236ee5536eac5946c2845f0d2aafe897c6

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 11 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.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:39:11.638773+00:00.

Case digest / a1f6b5b9d212c879fef966e64b79df6da10ea79806d4dfcd8ba47eaa5171d665