Square Logic and Coherent Lattices: A 4D Quarter-Turn Framework for Discrete Geometry

Square logic establishes a discrete orientation system based on quarter-turn symmetry embedded within cubic replication. A square supplies a minimal orientation set. A cube supplies a minimal volumetric container that preserves this orientation structure. Replication of cubes generates a lattice whose internal constraints determine viable spatial and temporal pathways. Stable resonance emerges as a consequence of geometric compatibility. Frequency functions as an expression of repeating geometric modes. This framework formalizes the structure, examines internal logic, and explores implications for coherence, stability, and resonance. coherent lattices, discrete geometry, quarter-turn symmetry, 4D orientation framework, base-12 geometry, orientation lattices, geometric resonance, state-space coherence, cubic lattice architecture, discrete rotational states, lattice dynamics, structural resonance modes, coherence theory, orientation quantization, crystal-like spacetime models, discrete spacetime analogues, topological symmetry systems, geometric constraint theory, resonant path structures, pattern-driven physics, nonlinear lattice behavior, coherent mode propagation, rotational symmetry groups, emergent order frameworks, sacred geometry analogues, temporal lattices, field coherence models, geometry-driven physics, structure-first cosmology, resonant information fields, coherent pattern universes, geometry as primary ontology