Field Guard: A Machine-Checked Governed-Map Contraction Stabilizer with Composition Certificate

Field Guard (FG) is the hard stabilizing layer of the REAL E3 stack. It constrains a six-dimensional control vector toward per-state targets by a certified contraction, then enforces hard safety bounds. The governed map H = FG_proj ∘ F contracts at factor κ = √0.95 ≈ 0.97468, giving an ISS gain 1/(1−κ) ≈ 39.494. The contraction, projection non-expansiveness, and ISS bound are machine-checked in Lean 4 with zero sorries and no added axioms. This public edition states the architecture, certificate statements, and headline results. Proofs and deployed governance configuration are in the restricted edition (10.5281/zenodo.20439277). Extends WP-FG-002 (10.5281/zenodo.18838465). Subject to patent application PRH1 Application 20265235, filed with the Finnish Patent and Registration Office, March 11 2026.New in version 1.2. The six-dimensional bound that earlier editions described as derived rather than separately machine-checked is now proven directly at six dimensions. The stated gain is unchanged; what changes is the standard of evidence behind it. The ledger row and the accompanying remark are updated to match. Zero sorries, no added axioms.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: info@real-e3systems.fi