FA-99341 / Embedding vector normalization / Open access

L2 normalization uses the squared magnitude as divisor · case 01

L2 normalization uses the squared magnitude as divisor.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The squared norm is used directly rather than its square root.

THE FAILURE

The squared norm is used directly rather than its square root.

Unsuccessful approach: Dividing by the L1 length still produces a vector with the wrong Euclidean unit length.

Case contract

For a finite nonzero vector, return its Euclidean unit vector; an empty or zero vector returns an empty list.

Why this case matters

A small embedding preparation contract can be checked without a model or retrieval system.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(v):
    return [x/sum(y*y for y in v) for x in v] if v and any(v) else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('3-4 length', solve([3,4]), [0.6,0.8])
check('scaled diagonal', solve([N,N]), [N/(2*N*N)**0.5,N/(2*N*N)**0.5])
check('negative coordinate', solve([-3,4]), [-0.6,0.8])
check('zero', solve([0,0]), [])
check('empty', solve([]), [])
check('single coordinate', solve([N]), [1.0])
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
3-4 length	`[0.12, 0.16]`	`[0.6, 0.8]`	Failed
scaled diagonal	`[0.5, 0.5]`	`[0.7071067811865475, 0.7071067811865475]`	Failed
negative coordinate	`[-0.12, 0.16]`	`[-0.6, 0.8]`	Failed
zero	`[]`	`[]`	Passed
empty	`[]`	`[]`	Passed
single coordinate	`[1.0]`	`[1.0]`	Passed

SHA-256 / c7fc63dabecce2f16b2619cf1564166b0e9bee0c5a57e6e6dc6e8063cd2c607f

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(v):
    return [x/sum(abs(y) for y in v) for x in v] if v and any(v) else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('3-4 length', solve([3,4]), [0.6,0.8])
check('scaled diagonal', solve([N,N]), [N/(2*N*N)**0.5,N/(2*N*N)**0.5])
check('negative coordinate', solve([-3,4]), [-0.6,0.8])
check('zero', solve([0,0]), [])
check('empty', solve([]), [])
check('single coordinate', solve([N]), [1.0])
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
3-4 length	`[0.42857142857142855, 0.5714285714285714]`	`[0.6, 0.8]`	Failed
scaled diagonal	`[0.5, 0.5]`	`[0.7071067811865475, 0.7071067811865475]`	Failed
negative coordinate	`[-0.42857142857142855, 0.5714285714285714]`	`[-0.6, 0.8]`	Failed
zero	`[]`	`[]`	Passed
empty	`[]`	`[]`	Passed
single coordinate	`[1.0]`	`[1.0]`	Passed

SHA-256 / 811c07bd6330b606625ceb71f1c33021cc6fba28087e146d356e27535352e08e

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 6 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

Inputs are finite toy vectors or token rows; this contract makes no claim about model quality or production embedding behavior. 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 2026-09-30T16:48:23.079300+00:00.

Case digest / 2be253de7c752468ffb75ce988d1c263f33f94f9aefd0074cbacb9be63ff8c2d