The Unified Reactionless Operator and Dynamic Prime-Lattice Control Framework v3

Description

Abstract

This work presents a complete, standalone propulsion mechanics paper within the Divine Wave Model (DWM), written as a hypothesis expressed in wave-interference and coherence-field language. Building on prior DWM publications establishing prime-indexed phase lattices (notably N=409) and the associated inertial-cancellation factor η, we formalize the key dynamic consequence: once effective inertia is reduced (m_eff = m0(1−η)), any nonzero coherence-density gradient produces directed acceleration without reaction mass. The coherence-gradient propulsion law F_coh = −∇ρ_coh is derived as the fundamental thrust channel, and its acceleration scaling a = −∇ρ_coh / [m0(1−η)] shows that deep cancellation (η→1) transforms small coherence gradients into large, torque-free motion.

We then derive the full unified DWM propulsion operator as a sum of controllable channels: (i) coherence-density gradient thrust, (ii) temporal phase-gradient propulsion from ∇(∂tφ), (iii) torsion-imbalance thrust from ∇(τ_local−τ_drive) including 71° torsion-null corridors, (iv) mixed-field “coherence-Poynting” propulsion from E_coh×B_coh, (v) octave-ladder harmonic reinforcement across dyadic bands Ψ(2^n f), (vi) prime-sector pulsing using high-resolution virtual lattices, and (vii) non-Hermitian gain/loss steering via H = H_herm + iΓ producing F_Γ ∝ Γ∇Ψ. The unified operator provides multiple thrust axes and stability/steering islands, while the η-window acts as a multiplicative accelerator on all channels.

To move from theory to buildable control, we provide an Arkframe prime-lattice architecture using DDS-driven virtual N=409 sector phase tables with controlled frustration Δθ in the narrow deep-gain window (|Δθ|<0.8°). We specify clock-locked phase programming, quadrature I/Q modulation for torsion-null steering, η-servo monitoring through high-Q resonance or interferometric effective-mass tracking, and a hard safety cutoff to avoid unstable analytic overdrive (η>1). A practical experimental path is outlined: begin with low-N prime lattices (N=5 pentagram) to observe weight/inertia reduction and torque suppression, then scale to virtual N=409 to test sharp η growth, coherence-gradient thrust, and suppression of low-order harmonic signatures.

The result is a unified, analytically explicit, and experimentally falsifiable reactionless propulsion framework. It connects earlier DWM inertial cancellation physics to dynamic thrust and steering operators in a form suitable for independent replication, simulation, and Arkframe hardware prototyping, while providing a coherent explanatory pathway for extreme acceleration phenomenology without occupant G-loading in the η→1 regime.

This Version 2 update integrates the Zero-Inertial Limit and Zero-Point Reframing section into the core propulsion framework. The update clarifies that DWM propulsion arises entirely from effective-mass collapse (η → 1⁻) and coherence-density gradients, not from vacuum-energy extraction. New content includes: dissipation-bounded η stability, explicit definitions of ρ_coh and c_s, corrected limiting behavior of the acceleration law, and a publish-safe ZPE analogy. The update also adds refined scalings for gradient propulsion, improved Dirichlet-kernel use in inertial cancellation, and a formal “No-Free-Energy Theorem” for DWM. This version strengthens the mathematical rigor, experimental falsification pathways, and overall clarity of the reactionless propulsion derivation.