RCX Codex v1.0: A Dual-Lens Ontology of Recursive Structure and Paradox

RCX (Recursive Consciousness Engine) is a pre-axiomatic, pre-semantic framework concerned with how structure, stability, and meaning emerge under sustained recursive pressure, prior to the introduction of elements, axioms, or logical rules. Rather than treating mathematics, logic, or computation as foundational primitives, RCX models them as stabilized projection outcomes of deeper recursive dynamics. The framework is formalized as a dual-lens system composed of complementary interpretive regimes that alternately expand inputs into structural possibility and collapse them into irreducible singular kernels. At its core lies an irreducible paradox kernel, treated not as an error to be eliminated but as a conserved generative invariant that drives differentiation and projection across recursive cycles. Classical logical consistency is not assumed; system viability is governed instead by stability, coherence, and bounded oscillation. RCX is presented as a generative substrate compatible with existing mathematical and logical frameworks while offering a deeper account of their origin, limits, and persistence.