Papers
The ResonanT⁴ program is a series of papers, each with a distinct purpose.
ResonanT⁴ Foundation
Modular Closure and Transverse Geometry
Defines the ResonanT⁴ admissibility framework based on exact phase closure. Introduces intrinsic modular phase states, locking structure via integer relations, cyclic deviation as distance from commensurability, factorization freedom of index connectivity, and transverse projection generating apparent motion without dynamics.
Closure-Compatible Resonance
Admissibility, Locking, and Phase-Aligned Control
Extends the ResonanT⁴ framework to driven systems using closure-compatible resonance (CCR). Introduces closure deficits, admissibility gradients, and phase-aligned control as effective analysis and control constructs, while explicitly avoiding claims of fundamental forces or dynamics.
Quantum Numbers as Closure Invariants
Discrete Labels from Exact Phase Closure
Reinterprets quantum numbers as topological invariants labeling closure-stable phase evolution classes. Establishes discreteness as a consequence of exact closure and admissibility, without claims of replacing quantum mechanics.
Musical Structure as Torus Geometry
Cyclic Permutations, Phrase Closure, and Scale Selection on 𝕋³
Proves that RT⁴ torus geometry produces musical structure: phrase closure from orbit theory, canonic voices from gcd decomposition, two-interval melodies from mechanical/Sturmian quantization, and consonant intervals from the golden ratio's arithmetic relationship with 12-TET.
Correspondence
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