# LIB2-015 — The golden braid-word square root on the frozen carrier

- 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.198)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

In the frozen 56-frame, the braid hyperbolic word Wh has an exact symplectic unimodular square root Hϕ with Hϕ² = Wh and eigenvalues φ⁻¹, 1 and φ of multiplicities 12, 32 and 12.

## Caution

This finite spectral construction does not attach the braid word to a physical mass, an absolute energy scale or an occupied winding level.

## Primary source

Appendix H, §11, Theorem 11.1: frozen-word setup, PDF p.205: "Within the frozen 56-frame let Wh = Q + 32 P + 32 γ1 − γ2 be the braid hyperbolic word and set A = Wh − Q, so that A2 − 3A + P = 0."

## Machine

- url: /library-v2/LIB2-015/
- content_sha256: db97b610554c7278b97a6640cd097c96b114a1b5b40b2924592c8a33d85ce8aa
- candidate_ids: C2-104

## Freshness

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