# LIB2-170 — A reflection-positive Cartan state exists at finite regulator

- 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.305)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

The registered heat-kernel × Haar product on Spin(5) edges gives a normalized reflection-positive state, an OS Hilbert space and a positive transfer operator at finite regulator.

## Caution

Finite-regulator existence does not establish the continuum limit, Einstein universality or a selected coherent boundary state.

## Primary source

Appendix T, §7, Named datum 7.1: finite state, PDF p.321: "A normalized reflection-positive state exists at the finite Cartan regulator tier: a heat-kernel × Haar product on Spin(5) edges,"

## Machine

- url: /library-v2/LIB2-170/
- content_sha256: ac55344f3cc1cf8beb5682b46536fc148025bb9beec04402f6915b2d03206195
- candidate_ids: C2-094

## Freshness

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