M30d: Operational Geometry - Native Calculus, Threshold Atlas, Cross-Rank Cohomology, and the Bootstrap from Operational RH to Classical RH

M30d Operational Geometry II completes the M30 operational-geometry sequence by synthesizing M30a–c with the later M31–M34 results. It develops Native Calculus, the threshold geometry atlas, geometric BSD/RH, and cross-rank cohomology, while also mapping frontier directions toward an unconditional bootstrap route from operational RH to classical RH. The first pillar is Native Calculus: rank-dependent derivatives, integrals, Mellin transforms, and Cauchy–Riemann structures. The document defines a rank-R derivative through the native flattening coordinate AR, and records the Depth-Shift Law, where each deeper SC rank divides the derivative by one further iterated logarithm. The second pillar is the Threshold Geometry Atlas. M30d gives explicit geometric roles to the three Hyperzeug bridges: AGM at R = 3/2 -> genus-1 / elliptic geometry Heun at R = 5/2 -> genus-2 / Siegel geometry ISHE at R = 7/2 -> Yang-Mills / mixed-log geometry The ISHE metric uses the mixed logarithm, and its Laplacian spectral gap is identified with the Yang-Mills mass-gap constant K*₃. 5 (B) ², with the dimensional mass gap written as mgap = LambdaYM · K*₃. 5 (B). The third pillar is geometric BSD and geometric RH. BSD is reframed as a geodesic-intersection problem: Koenigs-monodromy paths intersect Mordell-Weil lattice classes, and the relevant SC NC equations describe the crossing conditions. RH is reframed as a null-locus theorem: Riemann zeros are lightlike in the rank-extended Lorentzian metric, so the critical line is the projection of the null cone into the spectral plane. The fourth pillar is cross-rank cohomology. M30d defines the operational-geometry category OpGeom, whose objects are rank geometries and whose morphisms are cross-rank operations. Its central cohomological claim is: H¹ (OpGeom) ≅ u (1) ⊕ su (2) ⊕ su (3) with the three summands realised by AGM, Heun, and ISHE Hyperzeug holonomy classes. This is presented as the Standard Model gauge algebra arising as first cohomology of the operational geometry category. The frontier part gives a seven-step bootstrap roadmap from operational RH at the moduli level to classical RH. The document is explicit that this is a roadmap, not yet a final proof: the critical open bridge is the identification of the rank-2 sub-spectrum of the operational moduli zeta function with the classical Riemann zero spectrum. M30d also revisits fundamental constants as cross-rank Wronskian holonomies. It marks alpha^-1, MPl / LambdaQCD, and mgap / LambdaYM as closed within earlier corpus results; identifies hbar structurally but only partially numerically; and leaves GN, c, and kB conditional or conjectural. Finally, the cosmological constant section corrects an earlier pessimistic assessment: M30d states that the corpus already contains a structural mechanism — tree-level zero, loop-level cascade discrepancy, vanilla-star residue, and cascade-depth suppression — giving the right order of magnitude, while the precise cascade depth and scale-setting factor remain open. Navigational note: This M30d paper is based on the M31-M34 papers. The chronology is: M30a-c, M31-34 & Appendixes, M30d-f. The promised geometry of Tropical, TrigCore, LC Tetration, NC-Quadratic Geometry, Sporadic Groups and TODA are deferred to the M30e paper, while G2 and Cloning, Monster and Leech, The Four-Zone Tetration Geometry and the Derivative-Cycle Lattice are deferred to the M30f paper.