# LIB2-078 — The frame-free real 56 has no invariant rank-one Higgs projector

- 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.182)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

The bare real 56 admits no E7(7)-invariant rank-one projector; its invariant idempotents have ranks only 0 or 56.

## Caution

The obstruction does not exclude a Higgs orientation supplied by a loaded boundary or selected by additional symmetry-breaking structure.

## Primary source

Appendix F, §7, Theorem 7.1: invariant projectors, PDF p.188: "There is no G0 -invariant rank-one projector on the 56: the only invariant idempotents have rank 0 or 56."

## Machine

- url: /library-v2/LIB2-078/
- content_sha256: 02a37a6ebb0556d14d97e0e4b160dfcdc735e1115e658118c5c49ddcf270823a
- candidate_ids: C2-041

## Freshness

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