The Fractal Logic of Phi-adic Recursion
Logic
2025-11-18 v2 Logic in Computer Science
Abstract
Our central observation is that unbounded additive recurrence establishes a homomorphism between and Modus Ponens in a constructive sense. By finding sums of nonconsecutive Fibonacci indices, each inference step corresponds to a geometric constraint whose verification requires bit-operations. Logical entailment can be interpreted constructively as arc-closures under -scaling, offering a bridge between additive combinatorics, proof theory, and symbolic computation.
Keywords
Cite
@article{arxiv.2510.08934,
title = {The Fractal Logic of Phi-adic Recursion},
author = {Milan Rosko},
journal= {arXiv preprint arXiv:2510.08934},
year = {2025}
}
Comments
Constructive Logic, Proof Theory. 18 pages, 4 figures. Key result: Modus Ponens constructively interpretable as $\Delta_0$ constraint satisfaction geometrically