Boundary Information Theory X17.3: A Sparse Event-Triggered Architecture for Adaptive Runtime Systems

BIT-X17.3 presents a unified mathematical framework for adaptive runtime systems based on theprinciple that critical system information resides at geometric topological boundaries ratherthan in dense interior volumes. The framework introduces the Sparse Event-Triggered BoundaryArchitecture (SETBA) governed by the Master Integration Equation:State(t+1) = Boundary(Geometry(Synchronization(Dynamics(State(t))))). Key results:- 10 core mathematical operators (X17.M1–M10) with formal proofs- Boundary Runtime Module (X17.M11): Trigger(E,K) = 1 if E > E_crit OR K < K_min- Lyapunov stability proof: dV/dt <= 0 across all operating regimes- Kuramoto phase-locking threshold: K_c(D) = 2/(pi*g(0)) + c*D^(2/3)- Neyman-Pearson optimal threshold derivation- 99.2% compute reduction vs MPC baseline (8x8 simulation, N=64) Applications: satellite swarm coordination (BIT-XR.1.1), tokamak plasma boundary control(BIT-XR.1.2), ultra-high-density network routing (BIT-XR.1.3). Related work: GART (Geometry-Aware Resolution Transition) — DOI: 10.5281/zenodo.20456647