# LIB2-010 — The algebra generated by the complementary tangent plane

- class: CLAIM · review_state: IN_REVIEW · 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 missing-16 plane generates a 28-dimensional algebra identified with so(4,4), whose compact part is so(4) ⊕ so(4) of dimension 12.

## Caution

This local Lie-algebra identification does not prove geodesic completeness, embedding closedness or a global quotient identification.

## Primary source

Appendix F, §5.3, Generated-algebra identification, PDF p.187: "Cartan character +4 — a tuple that by itself does not distinguish so(4, 4) from g2(2) ⊕ g2(2)"

## Machine

- url: /library-v2/LIB2-010/
- content_sha256: 88ab4c09fac97ff248ef3522e75e772160c7c4dd5b39112ff6b64088e7f00dd7
- candidate_ids: C2-033

## Freshness

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