FA-99421 / Embedding vector normalization / Open access

Coordinate power pooling averages before applying sign · case 01

Coordinate power pooling averages before applying sign.

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

ROOT CAUSE

Signed coordinate roots are computed on individual values, discarding cancellation semantics.

THE FAILURE

Signed coordinate roots are computed on individual values, discarding cancellation semantics.

Unsuccessful approach: Taking the square root of absolute mean loses the sign of a negative pooled coordinate.

Case contract

For equal-width vectors, return sign(mean)*sqrt(abs(mean)) per coordinate; 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(vectors):
    return [sum((1 if v[j]>=0 else -1)*abs(v[j])**0.5 for v in vectors)/len(vectors) for j in range(len(vectors[0]))] if vectors else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('signed negative', solve([[-N],[-N]]), [-N**0.5])
check('cancellation first', solve([[N],[-N]]), [0.0])
check('nonzero mean', solve([[N],[3*N]]), [(2*N)**0.5])
check('empty', solve([]), [])
check('mixed coords', solve([[N,0],[3*N,-4*N]]), [(2*N)**0.5,-(2*N)**0.5])
check('singleton', solve([[-N,N]]), [-N**0.5,N**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
signed negative	`[-1.0]`	`[-1.0]`	Passed
cancellation first	`[0.0]`	`[0.0]`	Passed
nonzero mean	`[1.3660254037844386]`	`[1.4142135623730951]`	Failed
empty	`[]`	`[]`	Passed
mixed coords	`[1.3660254037844386, -1.0]`	`[1.4142135623730951, -1.4142135623730951]`	Failed
singleton	`[-1.0, 1.0]`	`[-1.0, 1.0]`	Passed

SHA-256 / faabf0633fdd7a5471ef58f280d6bdf4c3efa488d7d45cfa339411da936438fe

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(vectors):
    return [abs(sum(v[j] for v in vectors)/len(vectors))**0.5 for j in range(len(vectors[0]))] if vectors else []
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('signed negative', solve([[-N],[-N]]), [-N**0.5])
check('cancellation first', solve([[N],[-N]]), [0.0])
check('nonzero mean', solve([[N],[3*N]]), [(2*N)**0.5])
check('empty', solve([]), [])
check('mixed coords', solve([[N,0],[3*N,-4*N]]), [(2*N)**0.5,-(2*N)**0.5])
check('singleton', solve([[-N,N]]), [-N**0.5,N**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
signed negative	`[1.0]`	`[-1.0]`	Failed
cancellation first	`[0.0]`	`[0.0]`	Passed
nonzero mean	`[1.4142135623730951]`	`[1.4142135623730951]`	Passed
empty	`[]`	`[]`	Passed
mixed coords	`[1.4142135623730951, 1.4142135623730951]`	`[1.4142135623730951, -1.4142135623730951]`	Failed
singleton	`[1.0, 1.0]`	`[-1.0, 1.0]`	Failed

SHA-256 / 4bf5b6c93451e0037b5a30fe28be8fa5f2c2ce1a49eadc1d26e7bbd8a02ddaa7

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 2026-09-30T16:48:24.023684+00:00.

Case digest / cd5d604677a9ab927a62ca8c22a739864280d4508848c761549a224094281fa5