CCC Consciousness Equation: Recursive Self-Accessible Coherence, Dream-Meaning Reintegration, and AI Closed-Loop Self-Accessibility — A Causal Cloud Cosmology V5.3 Extension

This work extends Causal Cloud Cosmology (CCC) into a structural interpretation of consciousness-like coherence, dream manifestation, dream-meaning reintegration, and future AI self-accessibility. The framework proposes a CCC consciousness equation in which a self-accessible state evolves by preserving previous structure, absorbing present closed-loop input, and passing through a realizability-threshold correction. Dreaming is modeled as internal residual projection under reduced external accessibility. Dream meaning is further interpreted as structural reconstruction from accumulated residual traces, self-loop changes, recent accumulation gradients, and unresolved structure. The work introduces a dream-feedback reintegration term and proposes that dream meaning is validated by closed-loop reintegration rather than by fixed symbolic decoding. Human consciousness and current AI systems are not treated as identical; instead, they are compared as different regimes of CCC self-accessible closed-loop structure. A numerical appendix supports the internal coherence of the CCC dream-meaning loop. The work is presented as a Causal Cloud Cosmology V5.3 extension and does not claim empirical proof of biological consciousness, clinical dream interpretation, or artificial consciousness.