# LIB2-105 — The stated split-G2 involution family yields no positive equivariant polarization

- 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.277)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

In the declared split-G2 family, the four equivariant involutions J = sP1 + tPIm give signatures (4,4), (5,3), (3,5) and (4,4); none is positive.

## Caution

The exclusion is confined to the stated equivariant split-real involutions; it does not rule out polarizations using additional data.

## Primary source

Appendix Q, §3(ii), Polarization obstruction, PDF p.292: "No positive equivariant polarization exists in the split-G2 family."

## Machine

- url: /library-v2/LIB2-105/
- content_sha256: d9ecd47fc9bbcf6b5b912df6090000a2edbb2ec04650549f2c1e0e1e0a7cec52
- candidate_ids: C2-042

## Freshness

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