Additive-Multiplicative Structure of Prime and Composite Dirichlet Systems: Structural Reductions, Natural Boundaries, 100-Digit Vasyunin Gram Computations, and Axiom-Free Lean 4 Formalization of Classical RH Equivalences (Edition 2.2.0)

Edition 2.2.0 (Journal-Tightened & Audited) contains the updated Master Monograph (59 pages; 0 LaTeX errors, 0 warnings, 0 overfull/underfull warnings), the freshly compiled LeanBlueprint edition with interactive HTML web pages, the axiom-free Lean 4 / Mathlib4 formalization (v4.35.0, commit 56a005855ea1; 3,733 build jobs; 0 sorries; 66 unconditional 0-axiom theorems plus 6 conditional equivalences over ClassicalAnalyticInterface; 22 #print axioms kernel checks), and the 100-dps & 107 numerical verification suite. Journal-Grade Remediation Summary in v2.2.0 Smooth-Cofactor Factorization & Unique 50/50 Parity Exponent s*: Proved ζC(s) = ∑p p−s(Ep(s) − 1) and established global uniqueness of s* ≈ 1.446537622476006 across (1, ∞) via strict derivative monotonicity on (1, 1.50], monotone bracketing on [1.50, 1.73], and ζ(1.73) < 2 on [1.73, ∞). Riemann–von Mangoldt Natural-Boundary & Critical-Strip Tightening: Rewrote Theorem 4.9(b) using square-free k harmonic zero scaling citing Landau–Walfisz (1920) and Fröberg (1968); repaired the Littlewood–Titchmarsh Mertens contour proof (σ0 = 1/2 + ε/2, T = x2); tightened Obstructions 1–3 around non-zero Euler product convergence and Lévy–Steinitz subseries partitioning of η(s). Rank-4 Vasyunin Matrix Factorization & Conditional Labeling: Explicitly formulated UN and symmetric core M4 (det M4 = 1/16 > 0, GN(smooth) = UNM4UNT), proved n+(GN(cot)) ≥ N − 2 via Courant–Fischer min–max, and explicitly labeled Corollary 8.3 as conditional on boundary convergence of copt. Notation Ledger, Typographical Fixes, & Appendix A: Fixed cross-reference labels (Definition 4 → def:composite_set), matched Table 10 to γ1…γ6, added a Master Notation & Epistemic Classification Table, and embedded Appendix A with the two-part Lean 4 ledger and standalone 50-digit Python verifier (d142, d202, GN(smooth) = UNM4UNT). Standing Epistemic Invariant NO_RH_PROOF = TRUE — Establishes structural decompositions, uniqueness results, conditional equivalences, and 100-digit finite certifications without claiming an unconditional proof of RH.