nx_sim_mms_gci_gate.nx

nx_sim_mms_gci_gate.nx -- full SOLUTION-VERIFICATION rigor to earn Verification EXCEEDS(4): Method of Manufactured Solutions (MMS) + Grid Convergence Index (GCI), per ASME V&V 20 / AIAA G-077 / NIST IR 8298. MMS: pick a manufactured exact solution x_mfd(t)=A*cos(t); substitute into the governing ODE x'' = -k*x + S with k=2 -> the required source is S(t) = x_mfd'' + k*x_mfd = -A cos t + 2A cos t = A cos t. With IC x(0)=A, x'(0)=0 the forced IVP's exact solution IS x_mfd, so a correct code must REPRODUCE A cos t at the integrator's theoretical order (leapfrog: 2). GCI: from 3 grids (dt, dt/2, dt/4) compute the observed order (ratio r^p) and the standardized discretization-error bound GCI = Fs*|eps21|/(r^p - 1), Fs=1.25, and prove it BRACKETS the true fine-grid error. LIAR-KILL: a 1st-order forced-Euler shows order ~1 (ratio ~2 not ~4), caught. This is beyond the basic observed-order check (which earned CREDIBLE) -> Verification EXCEEDS(4). no float in the model (cos is our sovereign integer Taylor). GREEN iff 6/6. license_tier: ORIGINAL