# LIB2-185 — The rank-two support certificate excludes a rank-five extension at the MOS tier

- 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.316)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

An ambient rank-5 extension exists, but the record-support condition excludes it at the printed MOS tier by an exact rank-two support certificate.

## Caution

The support certificate does not exclude a microscopic map outside the printed quotient tier or deny the ambient rank-five construction.

## Primary source

Appendix T, §15.3, Ambient extension and tier-local obstruction, PDF p.334: "A rank-5 extension exists as ambient linear algebra, but the record-support condition forbids it at the printed MOS tier by an exact rank-two support certificate [A1560]."

## Machine

- url: /library-v2/LIB2-185/
- content_sha256: a753bba79e682b499380b8ab998465a50b357e5d1efcc911197d6d7723d0379c
- candidate_ids: C2-135

## Freshness

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