# LIB2-021 — The finite loaded-profile parent action has its stated stable minimum

- 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.170)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

Within the frozen split-real 56-frame and declared finite/internal loaded-profile class, Vtotal attains its stated global minimum at M* = I and the displayed source-aligned pair (j*,q*), with combined Hessian positive for every ρ,u0,κd > 0 on the directions transverse to the exact projective soft ray [W0] at zero inserted dark amplitude, along which it vanishes.

## Caution

This finite configuration-space closure is not a continuum Hamiltonian or an interacting pole/LSZ construction.

## Primary source

Appendix E, §7, Closure declaration: minimum and Hessian, PDF p.177: "the selector parent action Vtotal has its global minimum at (j ∗ , q ∗ = 32 j ∗ , M ∗ = I) with combined Hessian positive for all ρ, u0 , κd > 0 on the directions transverse to [W0 ], the exact projective soft ray at zero inserted dark amplitude, along which it vanishes (scope stated Rev32.9, A1632)."

## Machine

- url: /library-v2/LIB2-021/
- content_sha256: ded57726ab8a0d82c2cb7e4449fb531e4f1726d205f11f1630594cf9e382dff9
- candidate_ids: C2-105

## Freshness

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