Dimensional Compression and Infratier Gauge Closure A Generative Algebra from Phase-Spatial Coherence to Closure Exhaustion

This paper develops a formal architecture for an infratier closure framework in which effective dimensional compression is interpreted as a reduction of independently discloseable degrees of freedom accompanied by growth of internal relational structure. The central primitive is a hypothesized phase-spatial disclosure state of effective dimension sectorized. The residue is then used as a single elementary compression increment, generating the exact sequence . The first three post-primitive states are interpreted respectively as phase, chiral, and constraint closure regimes; the fourth is treated not as an additional gauge tier but as a closure-exhaustion coordinate. On the mathematical side, nested resolution maps imply non-increasing observable differential rank, while Lipschitz quotient maps permit corresponding non-increase of suitable fractional disclosure dimensions. Internal gauge structure is treated as the automorphism structure of closure fibers or stabilizers of preserved relational data. Standard results then give for a one-component complex phase carrier, for an oriented Hermitian two-frame, and for an oriented Hermitian three-frame. A three-dimensional exterior/Clifford closure argument provides a candidate stopping rule: for , while the top-grade pseudoscalar satisfies , allowing phase-like structure to reappear at maximal spatial closure. The manuscript carefully separates established mathematics, conditional constructions, physical hypotheses, and open derivation problems. The main unresolved tasks are to justify the physical admissibility of the -dimensional phase-spatial primitive, derive the compression law dynamically rather than stipulate it, connect the closure stabilizers to the observed gauge interactions, and test whether closure exhaustion has measurable consequences.