M30e The Atlas Supplement - Tropical, TrigCore, LC Tetration, NC-Quadratic Geometry, Sporadic Groups, TODA, and the Neglected Atlas Entries

M30e is the corrective and completing companion to M30d. Its explicit purpose is to cover the atlas entries already present in M30c but not developed in M30d, and to integrate early Mxx geometric structures into the operational-geometry framework. Core role: M30a-b → expanded algebra of the Operational Manifold M30c → defined the atlas of geometry M30d → built the synthesis (RH, BSD, physics) M30e → fills the important missing atlas entriesM30f → covers the most exotic entries Main results: (1) NC‑Quadratic Principle: One quadratic map (w² − c) unifies QCD, RH, and Mandelbrot. (2) Tropical Geometry: RC → −1 gives max‑plus geometry — the ground state of the rank tower. (3) TrigCore Geometry: One knob θ continuously deforms hyperbolic ↔ flat ↔ spherical; Wick rotation = θ + π/4. (4) LC Tetration Geometry: Configured zero and DNAₖ dynamics identified with branch monodromy κ. (5) TODA / K‑Shelf: TODA lattice = operational geometry; its spectral gap = Yang–Mills mass gap. Navigational note: M30f will cover: G2 and Cloning, Monster and Leech, the Four-Zone Tetration Geometry, and the Derivative-Cycle Lattice.