Statement
Sector 4 Dirac PV: Reading-H Dirac operator IR bound-state verification — OPENED 2026-05-27 (Math420-AddB §7 follow-up) — RESOLVED 2026-05-27 (Math420-AddD same-day parallel dispatch)
Details
[RESOLVED 2026-05-27 — Math420-AddD topological + amplitude + dynamical analysis] Math420-AddD executed explicit verification: (i) defect zero-mode cardinality preserved EXACTLY by Atiyah-Singer index theorem (gauge bundle invariant under Reading H since RH reframes only scalar sector); (ii) low-lying fermion-mode count + energy scale preserved at amplitude-comparison level ($A_{\rm RH}^2 = 0.829 \sim A_0^2 \sim O(1)$ at canonical); (iii) dynamical-background correction $\delta E_{\rm dynamic}/E_F \sim O(10^{-2})$ at canonical TECT params (per Math404 scale identification), finite and absorbable into chemical-potential renormalisation. Result: finite IR shift preserved + absorbable, NOT $\Lambda$ contribution. $H_{\rm AddD\text{-}done}$ DISCHARGED at leading-order analytical level. Math58-v7-AddA Q5 numerical verification queued as Math420-AddD-AddA contingent paper-grade follow-up.
Theory tag: Math420-AddD-Sector4-RH-Dirac-IR-Bound-State-Verification-2026-05-27. Cross-references: Math420-AddD note (244 lines) + Codes/supplementary/Math420_AddD_sector4_rh_ir_bound_state.py (5/5 asserts PASS) + Runs/math/Math420-AddD/sector4_rh_ir_bound_state_verification.json + CHANGELOG.md top entry.
Source of truth
Docs/status/OPEN-QUESTIONS.md Active section, Q-2026-05-27-Math420-AddD-Pillar8-Sector4-RH-IR-Verification 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 4 Dirac PV: Reading-H Dirac operator IR bound-state verification — OPENED 2026-05-27 (Math420-AddB §7 follow-up) — RESOLVED 2026-05-27 (Math420-AddD same-day parallel dispatch)
Details
[RESOLVED 2026-05-27 — Math420-AddD topological + amplitude + dynamical analysis] Math420-AddD executed explicit verification: (i) defect zero-mode cardinality preserved EXACTLY by Atiyah-Singer index theorem (gauge bundle invariant under Reading H since RH reframes only scalar sector); (ii) low-lying fermion-mode count + energy scale preserved at amplitude-comparison level ($A_{\rm RH}^2 = 0.829 \sim A_0^2 \sim O(1)$ at canonical); (iii) dynamical-background correction $\delta E_{\rm dynamic}/E_F \sim O(10^{-2})$ at canonical TECT params (per Math404 scale identification), finite and absorbable into chemical-potential renormalisation. Result: finite IR shift preserved + absorbable, NOT $\Lambda$ contribution. $H_{\rm AddD\text{-}done}$ DISCHARGED at leading-order analytical level. Math58-v7-AddA Q5 numerical verification queued as Math420-AddD-AddA contingent paper-grade follow-up.
Theory tag:
Math420-AddD-Sector4-RH-Dirac-IR-Bound-State-Verification-2026-05-27. Cross-references: Math420-AddD note (244 lines) + Codes/supplementary/Math420_AddD_sector4_rh_ir_bound_state.py (5/5 asserts PASS) + Runs/math/Math420-AddD/sector4_rh_ir_bound_state_verification.json + CHANGELOG.md top entry.Source of truth
Docs/status/OPEN-QUESTIONS.mdActive section, Q-2026-05-27-Math420-AddD-Pillar8-Sector4-RH-IR-Verification 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.