Statement
Pillar 8 T7 unconditional promotion path: recursive closure of CP-pair + Casimir + PV + Brazovskii methodologies to terminal textbook axioms — OPENED 2026-05-27 (Math420-AddC + AddD §7 follow-up) — **MEDIUM priority (paper-grade closure
Pillar: P8
Tier: T6
Details
[OPENED 2026-05-27 — Math420-AddC + AddD leading-order discharge closure] Context: Math420-AddC + Math420-AddD parallel same-day dispatch DISCHARGED both $H_{\rm AddC\text{-}done}$ and $H_{\rm AddD\text{-}done}$ at leading-order analytical level. ALL 5 hypotheses of $\mathcal{H}_{\Lambda\text{-supp}}^{\rm post\text{-}AddB}$ are now DISCHARGED. Pillar 8 tier T6 PROVED CONDITIONAL retained (leading-order analytical qualifier is the "conditional" content). T7 unconditional promotion requires recursive closure to terminal textbook axioms.
Closure criteria — 4 methodology recursive closures:
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(a) CP-pairing methodology: functional-integral CP-pairing argument (Math58-v3, Math58-v4-sublemma) to standard Yang-Mills textbook axioms (Peskin-Schroeder Ch.\ 22, Weinberg QFT vol II Ch.\ 23).
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(b) Casimir contact-term methodology: UV-divergence absorption into vacuum-state renormalisation (Math58-v5 + Math420-AddC) to standard QFT renormalisation theory axioms (Collins, Renormalization, Cambridge 1984).
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(c) PV scheme methodology: Pauli-Villars regularisation cancellation (Math58-v7-Dirac-tightening + Math420-AddD) to standard textbook references (Peskin-Schroeder §7.5, Weinberg QFT vol I §12.2; both cited in Math58-v7 itself).
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(d) Brazovskii self-consistency methodology: 1-loop self-consistency for $r_R$ (Math400-AddE Path $\alpha$ + Math420-AddC) to Brazovskii 1975 original derivation + modern extensions (Hohenberg-Halperin 1977 mode-coupling formalism).
Verdict logic:
- All 4 close: Pillar 8 T6 → T7 PROVED unconditional.
- Any methodology cannot close to terminal axioms (e.g., reveals additional implicit assumption): T6 conditional retained with explicit recursive-residual-gap enumeration; Pillar 8 paper-grade closure restricted to T6 framing.
Falsification gate: if any recursive closure reveals a structural circular dependency or implicit assumption beyond textbook axioms, Pillar 8 tier may require revision (downgrade from T6 to T
Source of truth
Docs/status/OPEN-QUESTIONS.md Active section, Q-2026-05-27-Math420-AddE-Pillar8-T7-Recursive-Closure row (raw).
Issue body is auto-synced from canonical source. Manual edits to the body will be overwritten on next sync. Discussion in comments is welcome and preserved.
Statement
Pillar 8 T7 unconditional promotion path: recursive closure of CP-pair + Casimir + PV + Brazovskii methodologies to terminal textbook axioms — OPENED 2026-05-27 (Math420-AddC + AddD §7 follow-up) — **MEDIUM priority (paper-grade closure
Pillar: P8
Tier: T6
Details
[OPENED 2026-05-27 — Math420-AddC + AddD leading-order discharge closure] Context: Math420-AddC + Math420-AddD parallel same-day dispatch DISCHARGED both$H_{\rm AddC\text{-}done}$ and $H_{\rm AddD\text{-}done}$ at leading-order analytical level. ALL 5 hypotheses of $\mathcal{H}_{\Lambda\text{-supp}}^{\rm post\text{-}AddB}$ are now DISCHARGED. Pillar 8 tier T6 PROVED CONDITIONAL retained (leading-order analytical qualifier is the "conditional" content). T7 unconditional promotion requires recursive closure to terminal textbook axioms.
Closure criteria — 4 methodology recursive closures:
Verdict logic:
Falsification gate: if any recursive closure reveals a structural circular dependency or implicit assumption beyond textbook axioms, Pillar 8 tier may require revision (downgrade from T6 to T
Source of truth
Docs/status/OPEN-QUESTIONS.mdActive section, Q-2026-05-27-Math420-AddE-Pillar8-T7-Recursive-Closure row (raw).Issue body is auto-synced from canonical source. Manual edits to the body will be overwritten on next sync. Discussion in comments is welcome and preserved.