English

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 N\mathbb{N} 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 O(M(logn))O(M(\log n)) bit-operations. Logical entailment can be interpreted constructively as arc-closures under Φ\Phi-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

R2 v1 2026-07-01T06:28:31.699Z