FA-99361 / Embedding vector normalization / Open access

Vector centering divides by the signed coordinate sum · case 01

Vector centering divides by the signed coordinate sum.

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

ROOT CAUSE

The vector is divided by its signed coordinate sum without removing its coordinate mean.

THE FAILURE

The vector is divided by its signed coordinate sum without removing its coordinate mean.

Unsuccessful approach: Subtracting the first coordinate instead of the mean only works for select symmetric fixtures.

Case contract

Return the L2-unit vector of v minus its scalar coordinate mean; a constant or empty vector 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):
    length=sum(x*x for x in v)**0.5
    u=[x/length for x in v] if length else []
    return [x-sum(u)/len(u) for x in u] if u else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('asymmetric centered', solve([0,0,3]), [-1/(6**0.5),-1/(6**0.5),2/(6**0.5)])
check('offset invariant', solve([N,N+1,N+2]), [-1/(2**0.5),0.0,1/(2**0.5)])
check('constant', solve([N,N,N]), [])
check('empty', solve([]), [])
check('two coordinates', solve([0,2]), [-0.7071067811865475,0.7071067811865475])
check('negative shift', solve([-3,-3,0]), [-1/(6**0.5),-1/(6**0.5),2/(6**0.5)])
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
asymmetric centered	`[-0.3333333333333333, -0.3333333333333333, 0.6666666666666667]`	`[-0.4082482904638631, -0.4082482904638631, 0.8164965809277261]`	Failed
offset invariant	`[-0.2672612419124244, 0.0, 0.2672612419124244]`	`[-0.7071067811865475, 0.0, 0.7071067811865475]`	Failed
constant	`[0.0, 0.0, 0.0]`	`[]`	Failed
empty	`[]`	`[]`	Passed
two coordinates	`[-0.5, 0.5]`	`[-0.7071067811865475, 0.7071067811865475]`	Failed
negative shift	`[-0.23570226039551584, -0.23570226039551584, 0.47140452079103173]`	`[-0.4082482904638631, -0.4082482904638631, 0.8164965809277261]`	Failed

SHA-256 / 4a7262f5cb156ed19a8e853b6a5dd88bce6b7609633b4b411279097f10a9aaa9

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(v):
    r=[x-v[0] for x in v] if len(v)>1 else []
    length=sum(y*y for y in r)**0.5
    return [x/length for x in r] if length else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('asymmetric centered', solve([0,0,3]), [-1/(6**0.5),-1/(6**0.5),2/(6**0.5)])
check('offset invariant', solve([N,N+1,N+2]), [-1/(2**0.5),0.0,1/(2**0.5)])
check('constant', solve([N,N,N]), [])
check('empty', solve([]), [])
check('two coordinates', solve([0,2]), [-0.7071067811865475,0.7071067811865475])
check('negative shift', solve([-3,-3,0]), [-1/(6**0.5),-1/(6**0.5),2/(6**0.5)])
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
asymmetric centered	`[0.0, 0.0, 1.0]`	`[-0.4082482904638631, -0.4082482904638631, 0.8164965809277261]`	Failed
offset invariant	`[0.0, 0.4472135954999579, 0.8944271909999159]`	`[-0.7071067811865475, 0.0, 0.7071067811865475]`	Failed
constant	`[]`	`[]`	Passed
empty	`[]`	`[]`	Passed
two coordinates	`[0.0, 1.0]`	`[-0.7071067811865475, 0.7071067811865475]`	Failed
negative shift	`[0.0, 0.0, 1.0]`	`[-0.4082482904638631, -0.4082482904638631, 0.8164965809277261]`	Failed

SHA-256 / 7868bfd8918fe897a6489c6f2c7bd5bd8d53381739fef440dd5ca8c323ab6895

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 2026-09-30T16:48:23.555236+00:00.

Case digest / 00b3e2d51faa1153115cfa5027612e06fa0f8b6826ab5b3a0bdc2563a0799ae4