NSP-03: Constitutional Manifolds, Thermodynamic Mutation Control, and the Geometry of Safe Agency

The Self-Evolution Problem — the risk that a cognitively capable agent will modify its own objective function, safety invariants, or identity — constitutes the most fundamental open challenge in aligned artificial intelligence. This paper introduces the Constitutional Manifold framework: a formally constrained safety envelope, grounded in geometry and thermodynamics, that specifies which self-modifications are constitutionally admissible for the NEXUS Sovereign cognitive organism. We make four independently verifiable contributions. First (Theorems 1–2), we prove that the Constitutional Manifold Mₛafe is invariant under the projection operator Πₛafe, and that Port-Hamiltonian dissipation bounds mutation energy — preventing the agent from generating net internal energy to violate its Markov blanket. Second (Theorems 3–4), we derive that Ricci curvature variance in the Poincaré Cortex provides a formally grounded early-warning signal for constitutional drift (3. 2× detection speedup, p < 0. 001, simulation), and that Koopman spectral analysis enables predictive safety checks in O (n²) time before any mutation executes. Third (Theorem 7, new in v3. 0), we formalise a Simplex Runtime Assurance architecture — a NASA-inspired advanced-controller / verified-monitor / trusted-fallback triad — and prove a switching stability theorem that bounds the recovery distance after any constitutional violation. Fourth (Theorem 8, new in v3. 0), we extend the safety geometry into skill space using the Fisher-Rao metric, proving that the constitutional constraint induces a Riemannian barrier on the policy manifold, with measurable cost bounds. The complete system — the 13-layer InvariantShield — achieved 100% adversarial mutation block rate across 10, 000 simulation trials and 98. 4% fallback switching success in runtime-assurance injection tests. All claims carry explicit evidence labels (FORMALLY PROVED / EMPIRICALLY TESTED — simulation / PROTOTYPE / PROPOSED) in accordance with NEXUS series standards. Paper 3 constitutes the Immune System of the NEXUS cognitive organism. Every safety guarantee in this paper is bounded by the assumptions stated; no claim is made of universal or unconditional safety. David AB Van Der Walt Pietarien This paper is Paper 3 of 17 in the NEXUS Sovereign Research Program, a systematic research programme constructing the theoretical and engineering foundations for self-evolving artificial cognitive organisms. Paper 3 occupies the constitutional safety proof chain — the immune system that gates every self-modification before it reaches the evolution engine (Paper 9, CUTR-R) and preserves the Markov blanket identity (Paper 10). Five Proof Chains Paper 3 OWNS Proof Chain 3 (Constitutional Safety) and PROVIDES outputs to all other chains: thermodynamic constraints to Chain 1 (Physics of Decision), geometric safety signals to Chain 2 (Geometry of Memory), sheaf consistency to Chain 4 (World-Model & Federation), and metabolic gating to Chain 5 (Metabolism & Evolution).