# LIB2-192 — A soft positive simplicity weight exists at finite regulator

- 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.307)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

At finite regulator, a positive nonlinear simplicity weight exists on the compact fixed-norm bivector domain (a sum-of-squares penalty in the five Pfaffian minors), with reflection positivity by the standard paired-multiplication argument at argument tier.

## Caution

The weight is soft: its support is the whole fixed-norm domain, and the Pfaffian variety is reached only in the hard-constraint limit, which is not taken. Finite-regulator existence does not establish Einstein universality or the continuum renormalization-group limit.

## Primary source

Appendix T, §8, Theorem 8.6: nonlinear simplicity measure, PDF p.324: "A positive nonlinear simplicity weight exists at finite regulator: the sum-of-squares penalty exp(−λ i pi (B)2 ) in the five Pfaffian minors pi , on the fixed-norm P bivector domain (compact, so 0 < Z < ∞ for every λ ≥ 0), with reflection positivity by the standard paired-multiplication argument (argument-tier; s922 T6 notes)."

## Machine

- url: /library-v2/LIB2-192/
- content_sha256: a3505dc317432d3c3bede5485a56ca391da7c6119a3ade7b8ecf516601fc883e
- candidate_ids: C2-094

## Freshness

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