# LIB2-082 — The extra compact Cartan is the B−L charge direction

- 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.177)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

For the registered completion filters, the Yukawa-neutrality and anomaly equations have, modulo the hypercharge direction, a one-dimensional extra-Cartan solution space, whose Higgs-doublet-neutral representative is (1,−1,−1,−3,3,3) = 3(B−L).

## Caution

The unique extra charge direction does not establish that its gauge boson exists or remove the empirical premise used to exclude it.

## Primary source

Appendix F, §4, Theorem 4.1(2): extra Cartan, PDF p.183: "the extra compact Cartan is unique: modulo the existing hypercharge direction the extra solution space of the Yukawa- neutrality + anomaly system is one-dimensional, and in the Higgs-doublet-neutral representative it is spanned by (1, −1, −1, −3, 3, 3) = 3(B−L)"

## Machine

- url: /library-v2/LIB2-082/
- content_sha256: be2416cf706a627c2f05ee5a39e5613b922994a92a1c9d03b4f6645203a3b9df
- candidate_ids: C2-043

## Freshness

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