[Q-2026-05-27-Math420-AddB-Pillar8-ReadingH-Compat-SUPERSEDED] Reading H compatibility verification (HIGH priority queue entry, superseded by RESOLVED entry above) — superseded marker

[TECT-OpenPhysics]

Statement

Reading H compatibility verification (HIGH priority queue entry, superseded by RESOLVED entry above) — superseded marker

Pillar: P8

Tier: T3

Details

[OPENED 2026-05-27 — Math420-AddA cascade-deep-read closure] Context: Math420-AddA verified that the substantive 4-sector $\Lambda$-suppression evidence is recorded in Math58 cascade (v3 + v4-sublemma + v5 + v7-Dirac-tightening, with v2-algebraic T3 monopole sketch). Pillar 8 promoted T4_pending $\to$ T6 PROVED CONDITIONAL on $\mathcal{H}{\Lambda\text{-supp}} = {H{\rm CP\text{-}pair}, H_{\rm Casimir}, H_{\rm PV}, H_{\rm RH\text{-}compat}}$. The fourth hypothesis $H_{\rm RH\text{-}compat}$ is the most critical OPEN item: all Math58 cascade files (dated 2026-04-20 to 2026-04-25) PRE-DATE the Math401 Reading H consensus (2026-05-12). Whether the 4-sector cancellation arguments survive Reading H reframing (BCC as fluctuation channel within Brazovskii-stabilised disordered vacuum, NOT condensate vacuum) requires explicit re-derivation.

Closure criteria — per-sector Reading H compatibility verification:

• Sector 1 (Monopole, Math58-v3 CP-measure): likely Reading H invariant (operator-algebra level CP antisymmetry); explicit verification required.
• Sector 2 (Vortex, Math58-v4-sublemma Chern-Simons CP): similarly likely Reading H invariant; explicit verification required.
• Sector 3 (BCC condensate, Math58-v5 Casimir vanishing): \textbf{MOST CRITICAL}. The v5 argument assumes BCC vacuum periodicity (Casimir cancellation on the BCC unit cell on periodic box). Under Reading H, ``BCC vacuum'' is reframed as a fluctuation channel within Brazovskii disordered vacuum — periodicity assumption may not survive. Re-derive the v5 argument with the BCC channel content $\bar\phi(q_*)$ as fluctuation amplitude (Math400-AddE prescription), verify whether UV-divergence cancellation + Casimir vanishing arguments transfer.
• Sector 4 (Dirac, Math58-v7-Dirac-tightening PV regularisation): re-derive under Reading H static-background. Pauli-Villars scheme may require modification when the background is the Brazovskii fluctuation-stabilised disordered phase (rat

Source of truth

Docs/status/OPEN-QUESTIONS.md Active section, Q-2026-05-27-Math420-AddB-Pillar8-ReadingH-Compat-SUPERSEDED row (raw).

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