# LIB2-356 — The internal mismatch identity is distinct from atmospheric registration

- 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.59)
- basis: {"pdf_sha256_prefix": "b64ddcd9e16a6dcd", "release": "Rev33.1_S369"}

## Statement

Under DET-7 and N(J) = 1, the internal Jordan-geometry mismatch identity is sin²θmismatch = 7/16; it does not itself select the physical atmospheric-octant registration.

## Caution

This identity does not predict the physical atmospheric octant without a separately justified readout attachment.

## Primary source

Paper 3, §5.4, Internal mismatch corollary, PDF p.63: "The separate internal identity sin2 θmismatch = 7/16 remains a Jordan-geometry theorem: DET-7 + N (J) = 1 fix ⟨J, J # ⟩ = 3 and the norm product ∥J∥2 ∥J # ∥2 = 16, which eliminated AX2 (D575) and gives 7/16 as a corollary"

## Machine

- url: /library-v2/LIB2-356/
- content_sha256: 4863b1159c0276dfab45278b33f38dc0f0ffea80f04951801a3a7f318a7a82f1
- candidate_ids: C2-005 C2-059

## Freshness

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