Invariant Density in Mathematical Representations: A Syntactic Framework for Presentation Reduction

This work introduces a purely syntactic framework for reducing equational presentations by identifying and eliminating redundant relations while preserving all derivable invariants. It formalizes invariant density as a ratio between derivable relations and syntactic description length, and demonstrates how invariant-preserving transforms induce monotonic density gains under explicit derivability bounds. The framework is constructive, deterministic, and grammar-relative: all reductions are mechanically witnessed, no semantic interpretation is assumed, and no claims of optimality or completeness are made.