The Fractal Logic of Phi-adic Recursion
By: Milan Rosko
Potential Business Impact:
Makes computers prove math ideas faster.
Our central observation is that unbounded additive recurrence establishes a homomorphism between $\mathbb{N}$ 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 $O(M(\log n))$ bit-operations. Logical entailment can be interpreted constructively as arc-closures under $Φ$-scaling, offering a bridge between additive combinatorics, proof theory, and symbolic computation.
Similar Papers
The Fractal Logic of $Φ$-adic Recursion
Logic
Makes proving math ideas faster using number patterns.
On the Realizability of Prime Conjectures in Heyting Arithmetic
Logic
Proves computers can't always prove numbers are prime.
On the integrality of some P-recursive sequences
Number Theory
Finds patterns in number sequences.