# LIB2-042 — A norm-only action leaves the regular norm-level directions flat

- 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

For a twice-differentiable norm-only action S = F(α,N(X)), ambient stationarity in X at a regular norm-one point forces Hess S to vanish on ker dN, leaving at least 26 flats.

## Caution

The source check is on a generic symmetric cubic, not a dedicated full-Jordan computation, and the conclusion is limited to norm-only actions.

## Primary source

Appendix E, §6(vi), Norm-only Hessian obstruction, PDF p.174: "for any C 2 action S = F (α, N (X)), ambient stationarity in X at a regular norm-one point forces FN = 0 and hence Hess S ≡ 0 on ker dN , giving at least 26 flats structurally."

## Machine

- url: /library-v2/LIB2-042/
- content_sha256: 0d50f5d03f3ab8dd4ec4e8ce1a2c210b81cf23aff57ce42a38b9a93816e4408a
- candidate_ids: C2-102

## Freshness

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