# LIB2-189 — The anisotropic heat-kernel family has nonlinear OS positivity in its cone

- 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.307)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

In the declared anisotropic heat-kernel family with α > |β|, the positive elliptic invariant generates a positive Markov convolution whose reflected-kernel factorization gives OS positivity.

## Caution

This family-specific reflection positivity does not establish a general gravitational measure or a continuum Einstein limit.

## Primary source

Appendix T, §8, Proposition 8.5: nonlinear reflection positivity, PDF p.324: "Lα,β is a positive elliptic invariant on the whole cone α > |β|, the heat semigroup is a positive Markov convolution, and the reflected-kernel factorization gives OS positivity."

## Machine

- url: /library-v2/LIB2-189/
- content_sha256: f968f54fc4ff5d174e5127863e36a508991ef0abb0b91972aa76b48d82237996
- candidate_ids: C2-094

## Freshness

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