The Kapnack Integrator advances multi-body SDVR systems in discrete steps derived from the SDKP timescale τ=S·D/K — not arbitrary numbers. Each epoch computes packing density gradients and kinetic coupling between bodies, updates positions and velocities, monitors system coherence across the EOS deviation band (0.13–0.20%),

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The Kapnack Integrator advances multi-body SDVR systems in discrete steps derived from the SDKP timescale τ=S·D/K — not arbitrary numbers. Each epoch computes packing density gradients and kinetic coupling between bodies, updates positions and velocities, monitors system coherence across the EOS deviation band (0.13–0.20%),

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