# LIB2-088 — Generic cross-block Yukawa loops are not yet covered by an Artin generator census

- 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.147)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

Artin’s theorem establishes associativity when a diagram’s internal labels lie in a two-generated subalgebra; that containment is not established for generic cross-block Yukawa trilinears with three independent split-octonion entries.

## Caution

Lack of established two-generator containment is not a proof that a particular loop correction is non-associative or nonzero.

## Primary source

Appendix A, §A.7.8(ii), Conditional Artin application, PDF p.153: "Where a diagram’s internal algebra labels lie in a subalgebra generated by two elements, associativity follows by Artin;"

## Machine

- url: /library-v2/LIB2-088/
- content_sha256: 548f99fae7157b44f8e55dd8d9d8a9dc7f83bc9e6d227d44f0f7fdc21c310116
- candidate_ids: C2-114

## Freshness

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