# LIB2-113 — Reynolds preservation of the registered raw coefficient ray

- 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.230)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

The loaded U(1)Y Reynolds average PY=0 is the identity on the span of the four displayed Yukawa channel tensors, each of total hypercharge 0, so it retains every coefficient vector on that span without reweighting — in particular the common ray (1,1,1,1) of the registered raw tensor. This is preservation, not selection: nothing in the projection excludes an unequal quartet on the same span.

## Caution

This UV coefficient ray does not predict equal low-energy masses or select a symmetry-breaking compensator. Retention is not protection: excluding an unequal quartet is a separate claim, and it holds only under the trivial multiplicity-one premise, which Appendix K p.234 states as a premise exhibited on the model group S4 and does not derive for the registered four-channel action.

## Primary source

Appendix K, §3.3, Reynolds-forced equal weights, PDF p.241: "(Rev32.9, A1652 F01b/S330.7: through Rev32.8 this paragraph derived the ray from “a group average over a symmetry that acts transitively on the channels”, which is unavailable for both projectors.)"

## Machine

- url: /library-v2/LIB2-113/
- content_sha256: 36236cbc0673f708d32f73e1b72963cd3acbd1dcb1c25c686772f144c071335e
- candidate_ids: C2-046

## Freshness

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