Statement
Sector 3 BCC Casimir: Reading-H-native reformulation — OPENED 2026-05-27 (Math420-AddB §7 follow-up) — RESOLVED 2026-05-27 (Math420-AddC same-day parallel dispatch)
Details
[RESOLVED 2026-05-27 — Math420-AddC chemical-potential-shift derivation] Math420-AddC executed explicit Reading-H-native re-derivation: 1-loop free-energy at $\Psi_0 = 0$ with $r_R = +0.4193$ (Brazovskii self-consistency Math400-AddE Path $\alpha$); Casimir UV-cancellation transferred unconditionally (Math420-AddB §5); finite residue identified via differential identity $\partial f_1/\partial r_R = \frac{1}{2}\langle|\Psi|^2\rangle$ as Hartree closed-form $\Delta F^{\rm finite}/V = (u/8)\langle|\Psi|^2\rangle^2$; chemical-potential shift $\delta\mu = (u/4)\langle|\Psi|^2\rangle$ identified via U(1) Noether-charge thermodynamic relation. Result: $\Delta\Lambda^{\rm finite,RH}{\rm BCC} = 0$ at leading order. $H{\rm AddC\text{-}done}$ DISCHARGED at leading-order analytical level.
Theory tag: Math420-AddC-Sector3-RH-Native-v5-Step4-Reformulation-2026-05-27. Cross-references: Math420-AddC note (227 lines) + Codes/supplementary/Math420_AddC_sector3_rh_native.py (5/5 asserts PASS) + Runs/math/Math420-AddC/sector3_rh_native_reformulation.json + CHANGELOG.md top entry.
Source of truth
Docs/status/OPEN-QUESTIONS.md Active section, Q-2026-05-27-Math420-AddC-Pillar8-Sector3-RH-Reformulation 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
Sector 3 BCC Casimir: Reading-H-native reformulation — OPENED 2026-05-27 (Math420-AddB §7 follow-up) — RESOLVED 2026-05-27 (Math420-AddC same-day parallel dispatch)
Details
[RESOLVED 2026-05-27 — Math420-AddC chemical-potential-shift derivation] Math420-AddC executed explicit Reading-H-native re-derivation: 1-loop free-energy at$\Psi_0 = 0$ with $r_R = +0.4193$ (Brazovskii self-consistency Math400-AddE Path $\alpha$ ); Casimir UV-cancellation transferred unconditionally (Math420-AddB §5); finite residue identified via differential identity $\partial f_1/\partial r_R = \frac{1}{2}\langle|\Psi|^2\rangle$ as Hartree closed-form $\Delta F^{\rm finite}/V = (u/8)\langle|\Psi|^2\rangle^2$ ; chemical-potential shift $\delta\mu = (u/4)\langle|\Psi|^2\rangle$ identified via U(1) Noether-charge thermodynamic relation. Result: $\Delta\Lambda^{\rm finite,RH}{\rm BCC} = 0$ at leading order. $H{\rm AddC\text{-}done}$ DISCHARGED at leading-order analytical level.
Theory tag:
Math420-AddC-Sector3-RH-Native-v5-Step4-Reformulation-2026-05-27. Cross-references: Math420-AddC note (227 lines) + Codes/supplementary/Math420_AddC_sector3_rh_native.py (5/5 asserts PASS) + Runs/math/Math420-AddC/sector3_rh_native_reformulation.json + CHANGELOG.md top entry.Source of truth
Docs/status/OPEN-QUESTIONS.mdActive section, Q-2026-05-27-Math420-AddC-Pillar8-Sector3-RH-Reformulation 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.