The REAL E3 Stability Triad A Compositional Stability Certificate

This paper certifies the compositional stability of the REAL E3 Stability Triad: Field Guard, the Presence Layer, and the Relational Field Stabilizer composed as a state-decoupled parallel system. The parallel boundedness, joint Lyapunov bound, state decoupling, cascade BIBO, and combined field load bound are machine-checked in Lean 4 with zero sorries and no added axioms in the REALE3.COMP module. The joint ISS gain is dominated by Field Guard at 39.5. This restricted edition contains the full composition argument, coupling parameters, and the complete Lean proof structure. Subject to patent application PRH2, filed with the Finnish Patent and Registration Office, April 1 2026. RE3 are proprietary systems of REAL E3 Systems Oy, Finland. This document discloses the mathematical stability certificate for independent verification purposes only. The harness implementation code, state extraction methodology, and REAL-E3 internal architecture are proprietary and not disclosed. Publication does not constitute a licence to implement, reproduce, or deploy any component of the REAL-E3 architecture. This notice also applies to all prior publications by REAL E3 Systems Oy. Licensing enquiries: [email protected]