[Q-2026-05-27-Math420-AddB-Pillar8-ReadingH-Compat] Reading H compatibility verification for 4-sector $\Lambda$-cancellation arguments (Math58 cascade) — **OPENED 2026-05-27 (Math420-AddA §5 follow-up)** — **RESOLVED 2026-05-27 (Math420-AddB same-day closure)**

[TECT-OpenPhysics]

Statement

Reading H compatibility verification for 4-sector $\Lambda$-cancellation arguments (Math58 cascade) — OPENED 2026-05-27 (Math420-AddA §5 follow-up) — RESOLVED 2026-05-27 (Math420-AddB same-day closure)

Pillar: P8

Tier: T6

Details

[RESOLVED 2026-05-27 — Math420-AddB per-sector analysis closure] Math420-AddB executed explicit per-sector Reading H compatibility analysis (operator request: discharge $H_{\rm RH\text{-}compat}$ by direct re-derivation). Per-sector verdicts: Sectors 1 (Monopole CP), 2 (Vortex Chern-Simons CP) PASS unconditional (load-bearing arguments at gauge-sector / topological level; independent of scalar background); Sectors 3 (BCC Casimir), 4 (Dirac PV) PASS-CONDITIONAL (UV-cancellation mechanisms RH-invariant; IR / dynamical-background components require explicit follow-up).

Substantive output: the opaque single OPEN gate $H_{\rm RH\text{-}compat}$ is decomposed into TWO explicit, separately-trackable, separately-closable residual gates:

$$\mathcal{H}_{\Lambda\text{-supp}}^{\rm post\text{-}AddB} = {H_{\rm CP\text{-}pair}, H_{\rm Casimir\text{-}contact}, H_{\rm PV\text{-}sum\text{-}rules}, \boxed{H_{\rm AddC\text{-}done}}, \boxed{H_{\rm AddD\text{-}done}}}.$$

Resolution actions executed in Codes/config/pillar_status.json (same commit as resolution):

• Pillar 8 conditional_on restructured from 4 hypotheses (one opaque RH-compat) to 5 hypotheses (3 DISCHARGED + 2 explicit residual gates AddC + AddD).
• Tier T6 PROVED CONDITIONAL retained (T7 promotion contingent on AddC + AddD + AddE closure).

Follow-up: Q-2026-05-27-Math420-AddC-Pillar8-Sector3-RH-Reformulation (Sector 3 RH-native v5 Step 4 reformulation; HIGH); Q-2026-05-27-Math420-AddD-Pillar8-Sector4-RH-IR-Verification (Sector 4 RH Dirac operator IR bound-state verification; MEDIUM-HIGH; converges with Math58-v7-AddA Q5).

Theory tag: Math420-AddB-Reading-H-Compatibility-4-Sector-2026-05-27. Cross-references: Math420-AddB note (396 lines) + Codes/supplementary/Math420_AddB_reading_h_compatibility.py (5/5 asserts PASS) + Runs/math/Math420-AddB/reading_h_compatibility_per_sector.json + CHANGELOG.md top entry.

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Source of truth

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

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