# LIB2-043 — Unshifted quadratic Kempf–Ness potentials fail the selector-rank test

- class: CLAIM · review_state: PUBLISHED · house_tier: not yet assigned
- labels as printed: math_status NOT_PRINTED · attachment NOT_PRINTED · scorecard tier word none (PDF p.167)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

In the declared unshifted zero-level quadratic-carrier Kempf–Ness class, rank Hess0∥µK∥² ≤ dim K ≤ 63 < 69 = rank QT, so this class cannot reproduce the selector Hessian.

## Caution

Central shifts on proper subgroups or departure from the declared carrier/potential class are not excluded by this bound.

## Primary source

Appendix E, §6(vii), Unshifted Kempf–Ness rank bound, PDF p.174: "rank Hess0 ∥µK ∥2 ≤ dim K ≤ 63 < 69 = rank QT (the rank no-go)"

## Machine

- url: /library-v2/LIB2-043/
- content_sha256: aaf434e33d4198b90c2d62901d11f78c9252c172d75b205a614feee63ab8cd3a
- candidate_ids: C2-108

## Freshness

- BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02
- Declared volatile fields (R36): BUILD_STAMP