# LIB2-161 — The registered up–down operation is a parity, not a derived isospin action

- 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.133)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

The registered u ↔ d operation is the split-octonion sign map e7 → −e7, exchanging Hu and Hd as a Z2 parity rather than a derived SU(2) action.

## Caution

The parity does not construct a continuous isospin action or supply the missing QCD flip energy.

## Primary source

Paper 9, §9, Registered up–down operation, PDF p.138: "The only registered u ↔ d object is the Os sign map e7 → −e7 (Hu ↔ Hd ; A689 dictionary; read literally, the flip of e7 alone — s1170 shows the phrase also fits full conjugation, and neither map is a Jordan automorphism) — a Z2 parity, not an SU (2)"

## Machine

- url: /library-v2/LIB2-161/
- content_sha256: 1da0dbf7e4438d88577deeb9f05db0ff19c0a064c9a29c7379060101bf1123ef
- candidate_ids: C2-129

## Freshness

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