# LIB2-077 — The unitary matter-colour class has no image-compatible adjoint

- 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.176)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

For the registered unitary matter-colour class, the invariant embedding-tensor space has dimension 140, and the union of its rowspaces has rank 125, its eight missing directions being exactly the su(3) adjoint.

## Caution

This embedding-class result does not identify a physical colour action elsewhere or supply a derivation of the compact Standard-Model boundary.

## Primary source

Appendix F, §3, Leg A: invariant-space dimension and rowspace rank, PDF p.182: "dimension 140, matching the character prediction 140 = 2·15 (36⊕36)+2·55 (420⊕420) exactly (singular-value gap 8.9 × 1013 ). The union of the rowspaces of all invariant Θ has rank 125,"

## Machine

- url: /library-v2/LIB2-077/
- content_sha256: b99eb22b4883307896b8e25a1799f9c3b86038bb8c1456719589fcb0c982ed95
- candidate_ids: C2-038

## Freshness

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