Bounded Non-Closure and the Syntactic Cosmology: Motion, Deviation as Cycler, and Trace-Indexing

Existence is not presupposed; it emerges only as trace-consistent coherence under bounded non-closure. This work presents a syntactic cosmology in which motion is defined as non-closed update, trace as finite cross-section, and indexing as the sole temporal operator. Deviation arises from non-commutativity under finite projection and functions as a cycler, not by driving updates, but by rendering termination structurally undefined. Physical invariants are relocated from ontology to trace-consistent syntax. Space is reinterpreted as a cost structure of alignment, light as the minimal unit step of consistency, and gravity as a gradient in cost density. Singularity is treated as a non-convergent boundary where internal reference becomes undefined. The framework operates strictly under bounded non-closure, where termination is not defined.