Arithmetic Geodynamics on the 6N Skeleton: A Measured Atlas and Its Honest Boundaries — A Unified Review of Volumes I–III (Parts I–XXXVI)

This review consolidates thirty-six parts of an experimental study of prime constellations, prime-rich nonlinear sequences, and pseudoprimes on the 6N skeleton — the coordinatisation in which every prime exceeding 3 sits on a wing 6N±1 of an integer centre N. The programme rests on a single empirical scale (the twin-centre line density ρ) and a single microscopic root, P(q | N, twin) = 1/(q−2), the conditional probability that a prime q>3 divides a twin centre. Read through the modular dead(q) mechanism, this one object is shown to be the common source of the macroscopic Hardy–Littlewood constants, the parameter-free collapse of the Goldbach and Polignac comets, the closed-form two-centre correlation tensor and its quasi-periodic diffraction spectrum, the arithmetic-geodynamic tuple-size law d ln ρ_m/dℓ → −m, and the rigid factor-wing barrier governing Carmichael pseudoprimes. Volume I (Parts I–XIX) mines the skeleton empirically to the depth direct enumeration reaches; Volume II (Parts XX–XXIV) develops, in closed form on the congruence phase-space torus, the two frontiers Volume I left open; Volume III (Parts XXV–XXXVI) turns the same instrument on new objects — the skeleton zeta function, the Erdős–Kac variance, quadratic and Fermat-type sequences, the wing-transition memory, and the Carmichael numbers — and audits the programme against itself. A strict honest ledger runs throughout: the inputs are the classical Hardy–Littlewood heuristic and the Hardy–Ramanujan–Mertens law; only first moments are treated until Volume III; no statement is made anywhere about the infinitude of any constellation; and every geological or thermodynamic image is declared a mnemonic, not a law. The review closes with an explicit map of the programme's limits: the directions in which the 6N lens re-derives known analytic results (the Rubinstein–Sarnak character spectrum, the Lemke Oliver–Soundararajan consecutive-prime bias) rather than discovering new ones; the quantities whose asymptotic laws are unidentifiable in any reachable computational window; and the combinatorial-explosion wall that bounds the enumeration itself. The result is offered as an atlas: a measured chart of a single arithmetic mechanism, drawn to the edge of what measurement can establish, and honest about that edge.