Paper ORT-GRAVITY v3.0: Emergence of 1/r^2 Geodesic Attraction from Discrete Null-Token Statistics, Shadow Screening, and Dynamical Confinement on the Face-Centered Cubic Substrate

Paper ORT-GRAVITY v3.0 presents the rigorous microscopic derivation and numerical verification of Newtonian and Einsteinian gravitation from the discrete, entity-free carrier substrate (Floor 0) of Ontological Resolution Theory (ORT v3.0). Standard continuous gravitation relies on phenomenological smooth metrics gμν, curvature singularities, and continuous actions. In ORT, Floor 0 possesses neither continuous coordinates, metric tensors, nor smooth potentials: it is strictly a conservative, reversible register automaton executing permutations on the 12-slot cuboctahedral coordination shell C12 over the Galois field F2. Definitive Architectural Theorems: Autonomous Load Equalization (LASER-SYNC v2.1): Complete elimination of non-local Maxwell-demon arbitration (Ntransfer = |ΔP|/2) from coupled transceiver dynamics. Coupled discrete cavities achieve autonomous statistical load balancing via purely local reversible Fredkin swaps (det M ≡ 1 mod 2), strictly preserving bit-exact reversibility (Erev ≡ 0 bits) and machine-tick energy conservation (E(n) ≡ Etot) across 100,000 cycles. Emergence of the 1/r2 Flux Law on ΛFCC: Discrete token dispersion along the 12-regular cuboctahedral network proves that the local node flux density scales as Φ(r) ∝ r−2 with an empirical lattice discretization noise of only 3.99%, achieved without invoking continuous spherical geometry (4πr2) or metric coordinates. Full Huygens wave simulations confirm 100.0% spatial node illumination across all coordinate shells. Resolution of the Gravitational Sign Problem (Shadow Screening): Gravitational attraction is proven to arise not from repulsive radiative push, but from Le Sage–Casimir shadow screening of the isotropic, parity-symmetric vacuum background (A1g). A massive defect captures transit capacity (Dwell Latency), creating a localized flux deficit that forces external bodies toward the defect under background momentum imbalance. Analytic Derivation of Geff: The effective gravitational coupling constant is derived directly from register parameters: Geff = 7 / (12 · Kcell2 √2 π) ≈ 7.422473 × 10−6 [hop3 / τ02] yielding an exact hierarchy ratio Geff−1 ≈ 134,725.98. Resolution of OP-CONF (Dynamical Confinement): Register headroom exhaustion (κv → 0 for W ≥ Wcrit = 96 bits) induces an exponential phase-mismatch barrier on outer ports, dynamically reducing branching from q = 11 to qeff ≤ 3.028 < √11, locking >99.9% of the soliton energy inside the C12 coordination shell over 500 execution cycles. Hardware Primitive: Includes a synthesizable SystemVerilog auditor (ort_gravity_shadow_auditor) for wire-speed verification of discrete flux conservation and Level I-B continuity invariants.