Sci - Dimensionless Mathematics: A Pre-Geometric Framework for Closure, Persistence, and Invariant Objecthood

Sci - Dimensionless Mathematics: A Pre-Geometric Framework for Closure, Persistence, and Invariant Objecthood Armstrong Knight — intent-tensor-theory.com This paper formally introduces Dimensionless Mathematics as a proper noun and a named domain of mathematical inquiry, distinct in kind from all classical uses of 'dimensionless' as an adjective in physics and engineering. Classical nondimensionalization operates inside a given geometry, stripping units from equations that already exist in a coordinate frame. Dimensionless Mathematics operates before geometry, asking what conditions must be satisfied for stable structure to exist before spatial or temporal coordinates are treated as fundamental. The framework rests on three formal axioms: Axiom I (Null Phase Residue), proved via the de Rham–Stokes apparatus as a theorem of differential topology; Axiom II (Topological Proximity Collapse), replacing Euclidean distance with resonance proximity; and Axiom III (Persistence Criterion), governing objecthood through a dimensionless retention-to-dissipation ratio S ≥ 1. The unified Dimensionless Closure condition is established, and the ICHTB (Inverse Heisenberg Cartesian Tensor Box) is described as the primary operational tool implementing the three axioms. Running implementation: intent-tensor-theory.com/applied-itt