# LIB2-008 — The Jordan-visible scalar plane fails the Lie-triple criterion

- 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.181)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

The Jordan-visible 54-plane is not a Lie-triple system: its triple brackets have nonzero projection onto the missing-16 sector.

## Caution

This is a scalar sigma-model obstruction for the named plane; vector-sector and other truncation claims do not follow.

## Primary source

Appendix F, §5.3, Jordan-54 Lie-triple test, PDF p.187: "The Jordan-54 is NOT a Lie-triple system: the projection of [[54, 54], 54] onto the missing-16 has order-one components"

## Machine

- url: /library-v2/LIB2-008/
- content_sha256: 5ad50e57739ca64caf3860d4f637aa95fd4a870a77c152917a5948d5c3a504c2
- candidate_ids: C2-033

## Freshness

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