A Regulated Spectral–Geometric Formalism
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The author presents a purely mathematical formulation of the Additive–Multiplicative (AM) Regulator as a constrained operator system acting on accumulated quantities. [1][2] The framework is developed axiomatically independent of physical interpretation yet admits well-defined degeneracy limits that recover established structures in geometry, analysis, statistics, and mathematical physics. [3][9][10] Numerical comparative tables, schematic graphs, and constraint hierarchies are included to demonstrate how the same formal object projects consistently across domains without violating internal purity. [4][5] The formalism does not claim unification; rather, it constrains admissible structures such that known theories arise as low-degeneracy projections. [6][7]