# LIB2-171 — The pure MacDowell–Mansouri quadratic form is not a positive covariance

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

## Statement

On the registered 16-representation, BMM = tr(ΓTI TJ) has inertia (3,3,4), so the pure MM/EH weight cannot be a positive coercive covariance.

## Caution

This finite-algebraic obstruction does not exclude the positive completion family or prove that a finite Cartan state is Einstein gravity.

## Primary source

Appendix T, §7, Theorem 7.3: representation and quadratic form, PDF p.322: "On the 16-representation, BC = −tr(TI TJ ) = 4I10 exactly, inertia (10, 0); BMM = tr(ΓTI TJ ) has characteristic polynomial"

## Machine

- url: /library-v2/LIB2-171/
- content_sha256: 2313fcbd2ca764d9b3189c4415bac3c4a55b69620258cc98289d42853b6070f3
- candidate_ids: C2-095

## Freshness

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