This repository contains a series of works exploring a simple arithmetic function based on digital roots and modular reduction.
The function is defined as:
F(n) = n mod dr(n)
where dr(n) is the digital root of n.
- The output space is restricted to a small finite set
- The function converges in at most two iterations: F(F(n)) = 0
- The computational cost is extremely low
- Certain values are structurally excluded (e.g., 8 in base 10)
- V1 – Intuitive introduction of the idea
- V2 – Formal mathematical framework and structural analysis
- V3 – Exploration of possible practical and computational applications
The core idea and underlying mechanism were independently developed by the author.
The mathematical formalization was refined with the support of assistive tools.
Andrea Esposito
This project is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).