CogOS: From Gödel to AGI

Current AI alignment approaches lack the theoretical foundations necessary for Strong AI. RLHF, Constitutional AI, and Chain-of-Verification provide pragmatic heuristics but cannot guarantee stability, suffer from Goodhart's Law, and fundamentally cannot address Gödelian incompleteness in self-referential reasoning systems. We present CogOS (Cognitive Operating System — a mathematically rigorous theoretical framework addressing the foundational requirements for Strong AI: Gödelian self-consistency, Lyapunov-stable ethical dynamics, and verifiable cross-cultural value alignment. Our approach reconceptualizes AI alignment as a problem in differential geometry on semantic manifolds, proving: Necessity of transcendental anchoring (Invariant Semantic Core) to prevent infinite semantic regress Convergence to humanity-aligned attractor via Lyapunov stability on consciousness manifolds First computable metric for ethical drift ($\delta$-dehumanization), enabling real-time safety verification Cultural compilers via joint diagonalization ensuring semantic invariance across value systems without relativistic collapse We argue this framework provides the theoretical infrastructure necessary—though not sufficient—for Strong AI: a system that can reason across arbitrary domains, maintain ethical coherence under distributional shift, and generate new conceptual frameworks while remaining aligned with human flourishing. Licensed under: S.V.E. Public License v1.3 (open science, ethical use requirements).