The Learning Loop That Learns Itself: From Recursive Self-Reference to Phase-Compatible Self-World Reinstatement in Self-Aware Networks

This preprint distinguishes recursive self-reference, learned self-models, embodied learning-loop closure, and conscious self-world rendering. It reconstructs the dated SAN genealogy; connects action-feedback, proprioception, the Gamma Consideration Sandwich, phase-wave differentials, and Artificial Neurology; specifies a causal and mathematical model; reports two frozen synthetic development studies; and provides a bounded Lean verification layer. The evidence is mixed and explicitly does not establish biological consciousness, phase necessity, or SAN-specific algorithmic superiority.

## Evidence boundary

The application evidence is deterministic and synthetic. Lean verifies only the declared finite interface, accounting, custody, and claim-boundary invariants. Neither layer establishes biological consciousness, artificial sentience, the complete GCS architecture, phase necessity, personal identity, or SAN-specific superiority. The manuscript is a preprint and has not been peer reviewed.