A Unified QCD Framework: From Vacuum Geometry to Particle Masses

Author’s note (January 2026): This record is currently being revised. During a subsequent review, I identified that a claim regarding priority relative to the public arXiv submission date of related experimental work was stated imprecisely. The mathematical framework, derivations, predictions, and numerical results presented in this paper are unchanged. The issue concerns the interpretation of announcement versus arXiv publication timing, identified and corrected in good faith. An updated version clarifying the timeline and reframing the comparison strictly as a validation against published experimental results will be uploaded shortly. All prior versions remain available for transparency. This paper presents a unified framework linking vacuum geometry, quantum chromodynamics (QCD), and particle mass emergence through a geometrically constrained, recursion-based formalism. Building on prior work in emergent time, shell quantization, and transcendental scaling, the framework derives discrete particle mass scales from vacuum structure without introducing adjustable free parameters. The approach reformulates aspects of QCD within a vacuum-geometric setting, showing how scalar and vector mass hierarchies arise naturally from quantized geometric constraints. Previously predicted mass levels at 227.79 GeV and 250.00 GeV are incorporated as confirmed anchor points, while higher unfilled levels follow directly from the same formalism. This work does not claim a full replacement of the Standard Model, nor does it attempt a complete first-principles derivation of all QCD dynamics. Its purpose is to demonstrate that particle mass spectra can emerge from a unified geometric–vacuum framework that is consistent with experimental observations and predictive beyond currently filled states. All results are presented transparently and are supported by prior timestamped publications, ensuring a clear chronological record of theoretical development. For further information about the ENSO Framework, please contact Eric Needham:ensotheory@gmal.com