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 M_safe is invariant under the projection operator Π_safe, 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).