# LIB2-172 — The positive completion cone has a strict coefficient domain

- 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 quadratic completion Bα,β = αBC + βBMM is positive definite exactly when α > 0 and |β| < α; its nonzero boundary α = |β| > 0 is chiral-null, and the apex α = β = 0 is the zero form.

## Caution

Positive quadratic completion does not establish Einstein universality, a continuum limit or generic nonlinear reflection positivity.

## Primary source

Appendix T, §7, Proposition 7.4: positive completion cone, PDF p.322: "Bα,β = αBC + βBMM > 0 ⇐⇒ α > 0, |β| < α,"

## Machine

- url: /library-v2/LIB2-172/
- content_sha256: 91828e8945db9d78f87ad5e225f26c3868ea1fa19e51eef5088bc8129f2a9579
- candidate_ids: C2-095

## Freshness

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