Philip Lilien

FROM TRIALITY TO GENERATOR RESOLUTION S₃ Augmentation, Determinant Closure, and the Emergence of a 3 + 2 Mode Architecture

Why should a group containing only six permutations have anything to do with the richer continuous symmetries used in physics? The reconstruction developed here answers by refusing to treat S₃ as a small version of a gauge group. S₃ instead describes something more primitive: thr...

FROM TRIALITY TO GENERATOR RESOLUTION S₃ Augmentation, Determinant Closure, and the Emergence of a 3 + 2 Mode Architecture

Why should a group containing only six permutations have anything to do with the richer continuous symmetries used in physics? The reconstruction developed here answers by refusing to treat S₃ as a small version of a gauge group. S₃ instead describes something more primitive: thr...

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...

CLOSURE MATHEMATICS AND THE CONSTRUCTION OF WORLDS — V From Agency to Cognitive Worldhood

Cognition is often characterized through memory, prediction, control, internal models, abstraction, or flexible behavior, but these capacities need not coincide. A system can retain information without constructing a world model, predict without preserving causal or counterfactua...

CPT as Composite Symmetry Closure From Constituent Symmetry Violation to Relational Invariance

This paper asks when that survival is mathematically exact, physically faithful, and experimentally testable. For a reader coming to CPT for the first time, the letters can make the subject look more mysterious than it is. C denotes charge conjugation, P parity, and T time revers...

Creating Value Through History and The Future - The Evolution of Wealth, Work, Intelligence, and Value Creation

Wholonomics White Paper Series Core Disclosure Human history is the progressive amplification of value-creating agency. The future of economics depends on whether this amplified agency is directed toward extraction, coherence, or ultimately ontological wealth. This paper is not o...