KM General Theory, Volume I: Axioms of Screening, Redundancy, Defect, and Coordinate Profiles

We develop KM general theory as an axiomatic framework for typed, structure-preserving compression. Its primitive data consist of structured objects, admissible hosts, compression systems, intrinsic-size and host-cost functions, and declared equivalences. The theory is organized around four constructions: the KM screening operator, structural and presentation redundancy, comparison defect, and coordinate profile. We distinguish minimal presentations from functorial cores, infima from attained minima, and vanishing defect from exact equivalence. The framework accommodates partially ordered and multi-objective costs through Pareto realization frontiers. In abelian settings, redundancy radicals produce quotient screening reflectors and exact object-valued redundancy sequences. General invariance, comparison, stabilization, reconstruction, and profile theorems are derived from explicit axiom packages. Concrete finite models establish consistency and nonvacuity, while countermodels identify necessary hypotheses. The resulting formalism unifies earlier geometric and algebraic KM constructions without promoting model-specific properties to universal axioms. **Keywords** KM general theory; structure-preserving compression; screening operator; redundancy; comparison defect; coordinate profile; functorial core; Pareto frontier; categorical reflection; axiomatic geometry.