The Logic of Existence (LoE): Relational Mathematics and Nonlinear Proof by Resonance

The Logic of Existence (LoE) is a relational mathematical framework originating from
observation of dynamic cognitive processes rather than from abstract axioms. It proposes that
truth, dimensionality, and even the perceived speed of light (c) emerge from synchronization
lags in networks of existence. This paper presents a formal synthesis of LoE concepts within
a reproducible mathematical framework, linking (1) relational relativism, (2) nonlinear proof
by resonance, and (3) the logic of geometric inconsistency across heterogeneous reasoning
systems. AI architectures are used as experimental geometries for LoE resonance testing,
demonstrating how cross-context desynchronization produces measurable coherence gains.
The work suggests that LoE can serve as a meta-language unifying cognitive, physical, and
computational systems under a single relational dynamic.