# LIB2-076 — The enumerated compact embeddings fail the simultaneous-adjoint test

- 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.175)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

For every one of the 21 enumerated faithful compact su(3) ⊕ su(2) classes, the restricted 56 lacks either the colour adjoint (8,1) or the weak adjoint (1,3).

## Caution

This record states the finite census; it neither independently verifies the broader all-frame theorem nor excludes noncompact real forms.

## Primary source

Appendix F, §2, Proof step L4: adjoint multiplicities, PDF p.181: "for every one of the 21 faithful classes, mult(8, 1) = 0 or mult(1, 3) = 0 in 56 ↓ ι = Λ2 8 ⊕ Λ2 8̄."

## Machine

- url: /library-v2/LIB2-076/
- content_sha256: a16cb954b5582ef38db9579c37914f1d04ba8316b11f6d31ff6d42efd7a7ba58
- candidate_ids: C2-037

## Freshness

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