# LIB2-191 — The stated bivector simplicity condition cannot be imposed by a linear 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.307)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

Some sums of simple bivectors are nonsimple (e1∧e2 + e3∧e4 has rank 4), so no linear projector retracts onto the full simple-bivector variety; keeping the full condition needs a nonlinear construction.

## Caution

This obstruction does not exclude nonlinear simplicity measures or prove that such a measure has an Einstein limit.

## Primary source

Appendix T, §8, Theorem 8.6: linear-projector obstruction, PDF p.324: "Some sums of simple bivectors are nonsimple (e1 ∧ e2 + e3 ∧ e4 has rank 4, while e1 ∧ e2 + e1 ∧ e3 is simple), so no linear projector retracts onto the full simple-bivector variety: keeping the full condition needs a nonlinear construction"

## Machine

- url: /library-v2/LIB2-191/
- content_sha256: 56a1f9dda5420b910e6e700cac9f79b61cb5065d684a4e857969c5903169dae8
- candidate_ids: C2-094

## Freshness

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