Quark Structure Calculator A Loop-Based Structural Model for Quark Mass Hierarchies

This paper introduces a boundary-based structural framework for particle mass generation, focusing on quark-level internal loop and branch configurations. The work provides a reproducible analytical model and is accompanied by an independent computational tool for verification. This work presents a theoretical framework, referred to as the Quark Structure Calculator, which models particle masses as emergent properties of internal structural configurations rather than as fundamental input parameters. The central idea is that quark and hadron masses can be expressed through branch structure (δ) and internal loop counts, interpreted as discrete structural degrees of freedom within an underlying interaction field. Within this framework, mass values arise deterministically from normalized structural parameters, enabling direct comparison with Particle Data Group (PDG) reference masses. Key features of this paper include: A structure-first formulation of particle mass, avoiding phenomenological mass fitting Explicit treatment of branch polarity and internal loop multiplicity Normalized mass representation with percentage-based comparison to PDG values Clear separation between theoretical formulation (this paper) and computational implementation (supplementary tool) The accompanying computational tool (released separately with its own DOI) implements the equations described here and allows independent verification, visualization, and parameter exploration. Importantly, the conclusions of this paper do not depend on the tool itself; the tool serves only as a reproducibility aid. This work is intended as a foundational reference, suitable for citation in studies of particle mass hierarchy, non-standard mass generation mechanisms, and structural or emergent approaches to quantum field theory.