nx_dpendulum_gate.nx

nx_dpendulum_gate.nx -- the DOUBLE PENDULUM, the continuous chaotic system named as the sim workstream's flagship "no-float determinism under chaos" vehicle (companion to the discrete nx_chaos_logistic_gate). Pure integer/no-float fixed point (all quantities x1e6 = "q"); reuses the Taylor sin/cos from nx_pendulum. Equal masses + lengths (m1=m2=1, l1=l2=1, g=9.8); full nonlinear COUPLED equations of motion (myphysicslab form), denom = 3 - cos(2(th1-th2)) in [2,4] => no singularity. Semi-implicit (symplectic-style) Euler: update omega from current theta, then theta from the new omega -- energy-bounded enough to integrate the chaotic regime over a short horizon. THREE measured properties + liar-kill (GREEN means it discriminates): (1) SENSITIVE DEPENDENCE: at LARGE amplitude (th1=th2=2.5 rad) two runs whose th2 differ by 1 micro-rad DIVERGE to O(1 rad) -- deterministic chaos. (2) DETERMINISM: the SAME integer run recomputed gives a BIT-IDENTICAL max-separation (no-float => exactly reproducible even under chaos = the Reproducibility-EXCEEDS property). (3) NEGATIVE CONTROL: the SAME integrator at SMALL amplitude (th1=th2=0.05 rad) is quasi-linear (two normal modes, NOT chaotic) -> the 1-micro-rad perturbation stays bounded/tiny. So the gate cannot be fooled into calling regular motion "chaos". GREEN needs all three. Sovereign: imports only nx_syscalls. Additive. license_tier: ORIGINAL