# LIB2-138 — The compact two-scale Gram class excludes its previously priced half-ratio

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- labels as printed: math_status NOT_PRINTED · attachment NOT_PRINTED · scorecard tier word none (PDF p.351)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

Intersecting the compact two-scale ansatz with the plane-preserving, coset-compatible, SM-invariant Gram family gives l = c and r = l/c = 1, excluding r = 1/2 in that declared class.

## Caution

The exclusion is not universal and does not refute the distinct finite 7/3 index or unification-ratio statement.

## Primary source

Appendix X, §4.3, Collapse to the scalar line, PDF p.373: "with the plane-preserving, coset-compatible, SM-invariant Gram family leaves only the scalar line l = c. Hence r = l/c = 1 exactly, and the previously priced point r = 1/2 is excluded in this declared natural class."

## Machine

- url: /library-v2/LIB2-138/
- content_sha256: b4d6d61e9b9832646b46134422ceebc85efef50b0d0e77bf33fa2d7a70c00821
- candidate_ids: C2-110

## Freshness

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