Philip Lilien

From PSOC4 to Electroweak Resolution Generator Levels, Null Coherence, and the 4 → 7 → 15 Closure Architecture A Closure-Theoretic Bridge Between Phase-Spatial Worldhood, Internal Gauge Structure, and the Shared Null Phase

This paper develops a closure-theoretic interpretation of the relation between a four-generator phase-spatial structure, a seven-generator electroweak-capable resolution level, and a fifteen-generator SU(4)-scale algebraic envelope. The central distinction is between generator re...

Reduction Without Resolution: Physical Boundaries as Closure Operators Quotients, Partial Closure, Effective Law, and the Architecture of Observation

Unified Coherence Closure Framework / Closure Mathematics A physical interaction can reduce an admissible state space without uniquely resolving an outcome. This distinction—reduction without resolution—provides the starting point for a general framework of physical observation,...

Reduction Without Resolution: Physical Boundaries as Closure Operators Quotients, Partial Closure, Effective Law, and the Architecture of Observation

Unified Coherence Closure Framework / Closure Mathematics A physical interaction can reduce an admissible state space without uniquely resolving an outcome. This distinction—reduction without resolution—provides the starting point for a general framework of physical observation,...

Kernel–Quotient Unification Four-Dimensional Spinor Reconstruction, Partial Closure, and the Origin of Internal Symmetry

Enlargement versus kernel–quotient unification. Conventional unification embeds known sectors in a larger effective symmetry. Kernel–quotient unification instead asks whether internal and external sectors are differentiated roles of a richer pre-disclosure structure. The diagram...