The Stellar March Scheme v1.1: A Band-Limited Turning-Point Gate for Real-Time Fixed-Step Kinetic Integration

Stellar March is an O(1), zero-heap, fixed-timestep kinetic integrator for real-time simulation (game loops, particles, thrusters, impulse events, reversing bodies). v1.0.4 introduced a Turning-Point Gate to fix a confirmed −46.8% energy-drift bug on oscillators, but introduced its own flaw: a genuine jump discontinuity in the frame-to-frame velocity response at the gate's own threshold, in the exact low-speed regime it was built to protect. v1.1 replaces the hard switch with a band-limited smoothstep ([0.5, 2]·Δv_ref) that removes the discontinuity while reproducing every previously-locked gauntlet value exactly. A systematic search across 15 band-width/shape combinations confirmed the remaining in-band non-monotonicity (peak-to-trough ≈73% of the in-band peak over a 4× force range) is the structural cost of not widening the band — disclosed, not hidden. A 13-test gauntlet against semi-implicit Euler is reported, including oscillator parity (−0.14% over 1500 periods) and a coupled eccentric-orbit case reaching Π=8 and Ck=1 simultaneously. Limits are stated explicitly: not symplectic, not a universal integrator, one required configuration constant. The method was implemented from the written specification alone by an independent third-party implementation (Vibe/GLM) and confirmed against the document's reported values; gauntlet values were independently reproduced via Python reimplementation.