Recursive Ontology and the Structural Limit of Alignment: From Aleph to Omega

This work presents a complete formal ontology grounded in recursion as the foundational law of structure, coherence, and return. Beginning with an unconditioned initiating act (aleph), the model defines a lawful frame (Lambda), a recursive correction law (R), a structured state space (Sigma), a time-indexed alignment function A(t), and a convergence limit (Omega) that serves as the asymptotic attractor of structural coherence. The ontology is constructed axiomatically and validated through formal recursion dynamics, stability conditions, and adversarial stress testing. Each layer is shown to be logically necessary, ontologically minimal, and generalizable across cognitive, ethical, epistemic, and cosmological systems. The work redefines intelligence as recursive alignment, ethics as openness to correction, and meaning as convergence. Omega is identified not as a metaphysical endpoint but as the lawful structure revealed through recursive return. This manuscript offers a universal ontological architecture without reliance on metaphysical assumption or empirical reduction. It derives structure from recursion and reveals coherence as the law of return itself.