Artemis II and the Emergent Cosmos: Gravity as a Geometric Projection from a Non-Linear Compactified 5D Manifold — A Synthesis and Lunar Test Proposal with ROCKY

NASA’s Artemis II mission (1–10 April 2026) has delivered the cleanest macroscopic free-fall acceleration dataset since Apollo. This paper presents a synthesis and modest extension of Kaluza–Klein geometry, Verlinde entropic gravity, and recent holographic approaches. Gravity emerges as the 4D projection of neutral-particle geodesics in a non-linear compactified 5D manifold, while charged-particle extra-dimensional momentum yields electromagnetism. The central advance is a frequency-dependent non-linear + entropic screening mechanism α(ω) = α₀ / (1 − iωτ_ent) with β = 2 power-law suppression arising from quadratic non-linearities in the 5D Einstein equations. This mechanism satisfies all terrestrial bounds yet predicts a measurable lunar deviation δg/g ≈ 2 × 10⁻¹⁵ (R_5 = 10⁻⁴ m, τ_ent ≈ 10⁻² s) with SNR > 5 in the Artemis-accessible low-frequency window (ω ≪ 2π/T_orbit). The 150 kg modular dual-species ⁸⁷Rb/³⁹K atom-interferometer payload Rocky is fully compatible with Starship HLS and CLPS and is targeted for the lunar South Pole near Shackleton Crater. Phase 0 re-analysis of public Artemis II data already tightens the (R_5 – τ_ent) exclusion contour by 40 %. Full repository: https://github.com/andrewdeece/rocky-kk-yield