Cognition as Non-Closing Δ-Indexing: A Syntactic Model of In'ei Dynamics

This paper formulates cognition as an iterative ∆-indexing process over a non-closing trace surface under non-commutative projections. Cognition is not convergence toward sta- ble representations but sustained deviation (∆ ̸= 0), where local coherence emerges without global closure. Time is reconstructed as the indexing of deviation (t := ∆i), and “under- standing” is treated as a projectional artifact of partial alignment. The framework unifies the Bounded Non-Closure cosmology, BNCT, and CASIS/TPre stack into a single syntactic model of observer dynamics, demonstrating that consciousness is structurally identical to the Deviation-as-Cycler mechanism.