Philip Lilien

Closure Fields and Closure Classes: Mathematical Foundations for Gauge Structure, Particle Identity, Quantum Closure, and Emergent Geometry

We develop a mathematical framework in which physical description is organized through predictively sufficient closure of richer realization spaces. A closure map identifies realizations that are equivalent relative to specified observables, while dynamic sufficiency requires the...

Closure Fields and Closure Classes: Mathematical Foundations for Gauge Structure, Particle Identity, Quantum Closure, and Emergent Geometry

We develop a mathematical framework in which physical description is organized through predictively sufficient closure of richer realization spaces. A closure map identifies realizations that are equivalent relative to specified observables, while dynamic sufficiency requires the...