nx_research_dynamics_gate.nx

nx_research_dynamics_gate.nx -- TIME-STEPPING dynamics simulation, sovereign + fixed-point (no float), with a conservation-law verifier (operator NEXT: "time-stepping dynamics sims"). Simulates a harmonic oscillator (a = -x, unit mass/stiffness) two ways and lets the verifier tell them apart by ENERGY conservation: LEAPFROG (symplectic): v_half=v - x/(2D); x'=x + v_half/D; v'=v_half - x'/(2D) -- energy stays BOUNDED. FORWARD-EULER (naive): x'=x + v/D; v'=v - x/D -- energy DRIFTS upward. The well-known physics: a symplectic integrator conserves energy to bounded error over arbitrarily many steps; Euler injects energy and the orbit spirals out. The verifier measures max energy deviation; LIAR-KILL: Euler produces a perfectly plausible trajectory but FAILS the conservation bar leapfrog passes -- a drifting integrator cannot be rubber-stamped as energy-conserving. Fixed-point integers, deterministic. GREEN iff 6/6. license_tier: ORIGINAL