This record contains Version v5. 0e of the author’s modular closure package for the RH/GRH rigidity program in the verified degree ≤ 2 scope. The bundle is organized around a rigidity framework for eliminating density–0 exceptional windows in the Riemann Hypothesis / Generalized Riemann Hypothesis setting. The central proof carrier is `Density0Proofᵥ5. 0e`, which develops a renormalized rigidity functional \ (Gₑ\), combines well-posedness, Wasserstein displacement convexity, and explicit-formula/large-sieve cancellation, and records the Gate (A) /Gate (B) closure architecture for the low-degree setting. The package covers the author’s declared degree ≤ 2 scope: the Riemann zeta function, primitive Dirichlet \ (L\) -functions, and holomorphic \ (GL (2) \) newforms within the stated admissible parameter box. Higher-degree Selberg-class extensions are separated as an optional research layer and do not enter the low-degree closure spine. ### Files in this bundle 1. `ClosureOverviewᵥ1. 3. pdf` A reviewer-facing overview and dependency map for the current closure set. It explains the reading order, import conventions, and the final target-facing interface. 2. `Density0Proofᵥ5. 0e. pdf` Main proof carrier for the density–0 elimination and low-degree closure package. It organizes the proof around H1/H2/H3, Gate (A), Gate (B), and the fixed-target target-detection/front-seal interface. 3. `RHCircleAᵥ5. 1. pdf` Circle A / Track A core note. It supplies the smoothed and density–1 unsmoothing bridge, together with the R-packet target-detection mechanism. The exception-free all-window closure is not claimed inside Circle A itself, but imported from the companion Gate (A) /Gate (B) closure package. 4. `H3AArithmeticUpgradeᵥ1. 5. pdf` Arithmetic pointwise-upgrade note. It isolates the passage from imported window-integrated averaged EF+LS cancellation to density–0 pointwise control using local averaging, grid-point mean-square recovery, Chebyshev, and admissible-grid counting. 5. `H3BRigidityEliminationᵥ1. 7. pdf` Rigidity-elimination note for H3. It isolates the no-exception seal from imported density–0 pointwise control, including the Burden B interface certificate between the arithmetic remainder layer and the abstract rigidity-defect layer. 6. `GateAᵥ1. 4. pdf` Reviewer-facing dyadic-registry note for Gate (A). It records the upgrade from density–1 windowwise control to all sufficiently large windows via spike persistence, common-point mesh transfer, and registry-level \ (L²\) -tail budget counting. 7. `GateBᵥ1. 8. pdf` Fixed-target variational closure note for Gate (B). It records the chain \ DF (T) 0 | Gₑ| (₅, ₓ) 0 Gₑ (₅, ₓ) 0, \ and then formulates the target-facing closure transfer using off-critical detection and the finite-front seal. 8. `RHGuideᵥ5. 0c. pdf` Reader-accessibility guide and proof-navigation document. It gives the quick-start audit path, dependency ledger, glossary, and background explanations for number theorists, analysts, and graduate readers. ### Main structural changes in v5. 0e - H3-A now includes a local-averaging recovery step before applying grid-point Chebyshev estimates. - H3-B now explicitly separates the Burden B compatibility certificate: arithmetic vanishing, positive abstract defect from residual failure, and no detached density–0 cluster component. - Gate (A) is isolated as a standalone dyadic-registry audit note. - Gate (B) is strengthened into a fixed-target variational closure note with an explicit target-detection/front-seal interface. - RH Circle A is reformulated from a fragile R-circle triple criterion into an R-packet target-detection framework. - The overview and guide have been synchronized to the current v5. 0e/v5. 1/v1. 8/v1. 7/v1. 5/v1. 4 structure. ### Scope note The uploaded materials present the author’s theorem-facing closure package and proof architecture. The low-degree RH/GRH claim is stated within the author’s declared verified degree ≤ 2 framework. The higher-degree Selberg-class extension is explicitly treated as optional and conditional on additional family-uniform inputs. ==================================== Author: Byoungwoo Lee (leeclinic@protonmail. com / Daejeon, South Korea)
Byoungwoo Lee (Wed,) studied this question.