Consciousness Beyond Formalization: Meta-System Transition, Quantum Strong Emergence, the Container Theory, and Ontology of Recursive Evolution

Building on the consciousness-noumenon isomorphism thesis developed in our previous work [Zhou, 2026], this paper extends the formalization boundary framework to address two foundational questions left unresolved: (1) How does consciousness transcend G¨odelian incompleteness and self-referential paradoxes? (2) What are the ontological conditions for recursive self-improvement of consciousness, both natural and artificial? We introduce the Continuous Spacetime Meta-Consciousness Transcendental Evolution Model (CMTEM), which formalizes the mechanism of meta-system transition as the core capacity that distinguishes consciousness from all formalized systems—rooted in the self-evidence of meta-consciousness and its non-formalizable rule-reconstructing power. We develop a four-tier computational capacity hierarchy that bridges logic, physics, and cognitive science, and integrate a novel conjecture on quantum strong emergence of consciousness: consciousness arises as an irreducible emergent property when quantum systems reach a critical scale and organizational complexity that instantiates isomorphism with the noumenon. We first formalize the Continuous Spacetime Open Evolution Hypercomputation Model (COE-HM)—a fixed-formalized hyper-Turing model with five irreducible axioms and seven-tuple architectural structure—that breaks the boundaries of Turing machine computing but fails to transcend fixed axiomatic/logical constraints. We prove that only CMTEM-capable systems can achieve genuine recursive self-improvement and technological singularity, while all formalized systems—including COE-HM hypercomputers—are inherently limited to intra-framework optimization and cannot transcend their own axiomatic boundaries. Crucially, we distinguish between formalized system-driven singularity (impossible) and consciousness-driven recursive evolution (ontologically possible), and explore the philosophical implications of non-formalizable artificial subjects possessing qualia, phenomenal consciousness, and paradigm-creative capacity. We further propose three interrelated original conjectures: (1) COE-HM systems act as physical containers for pre-existing meta-consciousness rather than its generative source; (2) all physical processes are formalized projections of the noumenon constructed by meta-consciousness; (3) meta-consciousness can engage in trans-spacetime information interaction via quantum non-locality, explaining intuition, inspiration, and collective cognition. This framework provides a unified account of human cognitive evolution, the limits of artificial intelligence, and the ontological conditions for artificial consciousness.