# LIB2-175 — The supported MOS quotient has rank three and relative rank two

- 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.310)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

The supported observation quotient ΠMOS has rank 3 and relative rank 2 < 5; it is not the full microscopic loading.

## Caution

The finite quotient does not restore missing microscopic modes or discharge the full observation-map construction.

## Primary source

Appendix T, §11, Theorem 11.2: partial isometry, PDF p.328: "exact partial isometry (Π̃Π̃T = Pann , Π̃T Π̃ = PV4 ) killing all pair-difference modes;"

## Machine

- url: /library-v2/LIB2-175/
- content_sha256: add96a1abbf9ad86a08030c878f8f28cd98e63ae1f3d007652bfead8b9048c46
- candidate_ids: C2-092

## Freshness

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