What does this research mean for the field?

A sparse event-triggered boundary architecture (SETBA) based on boundary information theory reduces computational overhead by 99.2% compared to model predictive control baselines while guaranteeing Lyapunov stability in adaptive runtime systems. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to present a mathematical framework that enhances adaptive runtime systems by focusing on boundary information.

June 1, 2026Open Access

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

Key Points

The aim is to present a mathematical framework that enhances adaptive runtime systems by focusing on boundary information.
Introduced Sparse Event-Triggered Boundary Architecture governed by Master Integration Equation.
Provided formal proofs for 10 core mathematical operators and developed Boundary Runtime Module.
Analyzed through simulations demonstrating compute reduction capabilities.
Achieved 99.2% compute reduction compared to baseline with an 8x8 simulation (N=64).
Established Lyapunov stability across all operating regimes with dV/dt <= 0.
Derived Kuramoto phase-locking threshold as K_c(D) = 2/(pi*g(0)) + c*D^(2/3).

Abstract

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 > Ecrit OR K < Kₘin- Lyapunov stability proof: dV/dt <= 0 across all operating regimes- Kuramoto phase-locking threshold: Kc (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

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

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