A Set of Objective‑Free Mathematical Equations Solve the 60‑Year‑Old Quark Confinement Puzzle Strong interaction originates from constraints of proportional balance instead of gluon exchange. All deductions are consistent with experimental results from LHC, RHIC and lattice QCD

This paper addresses the sixty‑year‑old puzzle of quark confinement in particle physics. Based on ontological principles and microscopic proportional constraints, a set of objective‑free mathematical equations is established for complete theoretical derivation. It is demonstrated that the absence of free quarks stems from the imbalance and restoration of matter’s intrinsic proportionality, rather than the color charge and gluon exchange described by Quantum Chromodynamics (QCD). This work conducts a systematic comparison with mainstream theories including the MIT Bag Model, QCD and lattice QCD, and analyzes their theoretical frameworks, equation systems and inherent flaws. The proposed equations require no extra fitting parameters or artificial postulations, and all derivations are fully consistent with experimental data from the LHC, RHIC and lattice QCD. This study clarifies the essential nature of the strong interaction, remedies core defects within the Standard Model, and provides empirical support for subsequent research on the general unified theory.