Common-Mode Shielding During Finite Population Changes

Abstract

We study a nominal admission controller with a nonempty protected cohort and finitely many shielded newcomers. Complete coherent residual tables centered on the protected cohort cancel all shielded physical residuals from its mean acceleration. Protected departures and gated promotions have explicit position and velocity coordinate maps. Each population or role event invalidates the preceding residual epoch and uses a bounded zero-correction waiting law. With finitely many born incarnations, at most one promotion per incarnation, the stated delayed-priority contracts, and the parent factored-gain small-age condition, a final continued shield phase captures every remaining newcomer. A finite group release is then admissible, and final relative geometry recovers with position and velocity retained at the switch. Uniform protected-relative and event-seam bounds require an explicit family of uniformly bounded histories, service, forcing, event counts and stability margins; capture time and newcomer effort may grow with initial distance. We derive the final group-release mean response and distinguish summable limiting shifts from summable whole-response envelopes. Proofs concern exact nominal dynamics. New finite rational checks corroborate selected algebra only; no online release detector, collision, actuator, radio, rigid-body or perpetual-churn result is established.