Solid Relations and Patterns: Geometric Relation Theory and the Grammar of Relations

This preprint presents Johannes Wall’s PKT framework for exploring relations and patterns among integers and prime numbers. Using the T-values 4, 6, 8, 12 and 20, it examines five-position structures called pentavs, their connections, and the clusters formed through shared prime numbers. The work includes formulas, worked examples, geometric illustrations and exploratory computational methods. This is the English translation of the Swedish original, Solida förhållanden och mönster. Mathematical results, hypotheses and potential applications are presented for further examination and independent verification. An interactive simulator allows readers to explore the model and vary its parameters: PKT-kristallsimulator