FTNILO: Explicit Multivariate Function Inversion, Optimization and Counting, Cryptography Weakness and Riemann Hypothesis Solution Equation with Tensor Networks

TL;DR

This paper introduces FTNILO, a novel formalism using tensor networks to explicitly invert, optimize, and analyze multivariable functions, with applications including solving the Riemann hypothesis.

Contribution

The paper presents FTNILO, a new tensor network-based formalism that extends existing algorithms for function inversion and optimization, enabling explicit solutions and applications like the Riemann hypothesis.

Findings

Explicit integral equation for Riemann hypothesis solution

Method can determine zeros of functions using tensor networks

Algorithm requires no deep mathematical knowledge

Abstract

In this paper, we present a new formalism, the Field Tensor Network Integral Logical Operator (FTNILO), to obtain the explicit equation that returns the minimum, maximum, and zeros of a multivariable injective function, and an algorithm for non-injective ones. This method extends the MeLoCoToN algorithm for inversion and optimization problems with continuous variables, by using Field Tensor Networks. The fundamentals of the method are the conversion of the problem of minimization of $N$ continuous variables into a problem of maximization of a dependent functional of a single variable. It can also be adapted to determine other properties, such as the zeros of any function. For this purpose, we use an extension of the imaginary time evolution, the new method of continuous signals, and partial or total integration, depending on the case. In addition, we show a direct way to recover both the tensor networks and the MeLoCoToN from this formalism. We show some examples of application, such as the Riemann hypothesis resolution. We provide an explicit integral equation that gives the solution of the Riemann hypothesis, being that if it results in a zero value, it is correct; otherwise, it is wrong. This algorithm requires no deep mathematical knowledge and is based on simple mathematical properties.