# LIB2-039 — A fixed-grade cubic/current law cannot detect both dark directions

- 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.167)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

In the declared fixed-grade cubic/current class, restriction to grade +2 gives rank 1 for Z ↦ P27 Z P27, so it cannot provide rank-two detection of the registered dark fibre.

## Caution

This fixed-grade exclusion is not an embedding-tensor no-go; that separate class was scoped out for lack of a convention-certified branching artifact.

## Primary source

Appendix E, §6(iv), Fixed-grade detection obstruction, PDF p.173: "The fixed-grade cubic/current class is closed negative for rank-two detection (s1005–s1006)."

## Machine

- url: /library-v2/LIB2-039/
- content_sha256: 2a70a1aa8b3bc411025169b35c38b30059e7baaacd0d85ab6a12e8b845fba4fa
- candidate_ids: C2-105

## Freshness

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