FA-99351 / Embedding vector normalization / Open access

Infinity normalization divides by total magnitude · case 01

Infinity normalization divides by total magnitude.

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

ROOT CAUSE

The sum of coordinate magnitudes is used instead of the largest magnitude.

THE FAILURE

The sum of coordinate magnitudes is used instead of the largest magnitude.

Unsuccessful approach: Adding a constant to the total magnitude still leaves the largest coordinate below one.

Case contract

Scale a finite vector so its largest absolute coordinate is one; zero or empty input returns empty.

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(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('dominant coordinate', solve([N,3*N]), [1/3,1.0])
check('negative maximum', solve([-N,2]), [-N/max(N,2),2/max(N,2)])
check('single value', solve([-(N+1)]), [-1.0])
check('zero', solve([0,0]), [])
check('empty', solve([]), [])
check('ties', solve([N,-N]), [1.0,-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
dominant coordinate	`[0.25, 0.75]`	`[0.3333333333333333, 1.0]`	Failed
negative maximum	`[-0.3333333333333333, 0.6666666666666666]`	`[-0.5, 1.0]`	Failed
single value	`[-1.0]`	`[-1.0]`	Passed
zero	`[]`	`[]`	Passed
empty	`[]`	`[]`	Passed
ties	`[0.5, -0.5]`	`[1.0, -1.0]`	Failed

SHA-256 / a95304168c5017e1abbd3d371ec683c372ae9599ca35f20cb173b19efef21cbf

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)+1) 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('dominant coordinate', solve([N,3*N]), [1/3,1.0])
check('negative maximum', solve([-N,2]), [-N/max(N,2),2/max(N,2)])
check('single value', solve([-(N+1)]), [-1.0])
check('zero', solve([0,0]), [])
check('empty', solve([]), [])
check('ties', solve([N,-N]), [1.0,-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
dominant coordinate	`[0.2, 0.6]`	`[0.3333333333333333, 1.0]`	Failed
negative maximum	`[-0.25, 0.5]`	`[-0.5, 1.0]`	Failed
single value	`[-0.6666666666666666]`	`[-1.0]`	Failed
zero	`[]`	`[]`	Passed
empty	`[]`	`[]`	Passed
ties	`[0.3333333333333333, -0.3333333333333333]`	`[1.0, -1.0]`	Failed

SHA-256 / df3929122fb300aece883b8e501761a9ba89421e5ef917984e5c0044c221cb0f

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-30T16:48:23.079377+00:00.

Case digest / eb80727a03d0dfd92224816aee29c5e3f900d8d0cf2ce3eb81929d213759cccd