# LIB2-027 — The declared action-completion class retains nonlinear-shape freedom

- 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.297)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

In the declared rank-normalized character-completion class, actions with a critical point at the base and positive-semidefinite Hessian form, modulo equivalence, a four-dimensional moduli space: three Hessian-weight ratios and one nonlinear modulus invisible to the complete two-jet.

## Caution

This obstruction is class-relative; enlarging the class changes its moduli count, and matching a Hessian alone does not select an action.

## Primary source

Appendix S, §9.4, Theorem 9.4: moduli space, PDF p.314: "the solution set of “critical point at the base + positive-semidefinite Hessian” modulo equivalence is a four-dimensional moduli space,"

## Machine

- url: /library-v2/LIB2-027/
- content_sha256: 5ba75a403cc9ab5f826fd19ca3c8bee4731163dc8bc8756398cc983b5a1c8fa5
- candidate_ids: C2-108

## Freshness

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