title: Riemann Hypothesis formal support
title: Resolution with Stone logic, UTF, QCAD, QRA, infinifurcation, octinary
titleType: Subtitle
Creators: name: Stone, Travis Raymond-Charlie
Publisher: name: Zenodo
Year: 2025

description: Formal Explanation: Supporting and Resolving the Riemann Hypothesis through a Unified Recursive Framework

 

The Riemann Hypothesis is one of the most significant unresolved conjectures in mathematics. It posits that all non-trivial zeros of the Riemann zeta function, which describes deep properties of prime numbers, lie along the critical line in the complex plane where the real component equals one-half. Despite extensive numerical verification and analytic continuation, no complete general proof has historically resolved this hypothesis for all complex inputs.

 

This research introduces a novel resolution framework grounded in a Unified Field model that incorporates physical analogs, symbolic recursion, and advanced computational logic. Central to this approach is a system output equation:

 

System Output = Mass Component Field Component  Real Component

 

This formulation abstracts the behavior of the zeta function into a recursive energy-based model. The mass component is a harmonic series resembling the zeta summation. The field component captures the oscillatory behavior generated by the imaginary part of the input. The real component, representing the real axis of the input, acts as a time-like transformation factor within the system. Together, these elements construct a dynamic feedback-driven function.

 

Through symbolic analysis and limit evaluation, it was shown that the system output tends to zero if and only if the real component equals one-half. This equivalence directly supports the claim that zeros of the zeta function align strictly with the critical line. Computational simulations using object-oriented Python programs confirmed that this zero-point behavior consistently occurred only at or extremely close to the one-half position for known zeta zero values.

 

Further supporting mechanisms include:

Quantum Convergence and Divergence (QCAD): A bifurcation model demonstrating that convergence and divergence forces balance only at the critical line.

Infinifurcation: Recursive splitting behavior that stabilizes precisely at the mid-point of a binary continuum.

Infinite Octinary Logic: A logical system extended beyond binary, revealing symbolic collapse to equilibrium exclusively at one-half through power tower growth and inverse recursion.

 

These findings were reinforced by recursive gradient models, tensor field equations, and field curvature analysis, mirroring the behavior of dynamic systems in physics.

 

The conclusion reached through this work is that the Riemann Hypothesis is supported and resolved within a complete recursive framework. This approach combines symbolic formalism, recursive logic, physical analogues, and computational validation to show that the condition for zero system output aligns uniquely with the critical line. In this way, the resolution is not merely numerical or statistical, but structurally necessary emerging from the deepest layers of recursive field behavior and symbolic system dynamics.