Arithmetic Geodynamics on the 6N Skeleton: A Review of Parts I-XIX

A cumulative synthesis of Parts I–XIX of the experimental "arithmetic geodynamics"programme on the 6N skeleton, where every prime > 3 lies at 6N±1 and the integer Nis the constellation "centre." The review assembles the programme's single empiricalscale — the twin-centre line density ρ — and traces it through: the ω-stratificationof centres and the resulting gap lockdown; the two-centre CRT shield and itsmicro-to-macro bridge from the local factor 1/(q−2) to the Hardy–Littlewood singularseries 𝔖₂ = 2∏(1−1/(q−1)²); the closed-form survival law with its second-orderresidual; the universal collapses of the Goldbach and Polignac coefficients ontonarrow bands (coefficient of variation below 0.3%); the two-centre distortions thatexplain the ×4.8 twin enrichment and the shared-member cousin/sexy degeneracies; andthe extensions to triplets and semiprimes. Its centrepiece is the arithmetic-geodynamics law d ln ρ_m/dℓ → −m (tuple size equals stratum decay rate in the properdepth ℓ = ln ln X), verified on a four-rung ladder — twin, triplet, quadruplet,quintuplet — down to shell S11. The review closes with the dual outlook developed inVolume II: the vertical extreme-ω "wind tunnel" and the horizontal congruence-phase-space correlation. An honest ledger is maintained throughout: Hardy–Littlewoodheuristics are taken as input, only first moments are claimed, the Erdős–Kac-typeω-variance is left open, closed-form extrapolations are labelled as model behaviourrather than prime observations, and no infinitude of any constellation is asserted.