QCD Phenomenology via Geometric Stiffness: Geometric Enforcement of Mass, Stability, and Size

This paper presents a numerical validation of the Axiomatic Physical Homeostasis (APH)framework within the strong interaction sector. By identifying the QCD vacuum as a non-associative fluid with a finite geometric stiffness βQCD ≈ 1.91, we demonstrate that the vacuumactively enforces physical parameters in the non-perturbative regime. We resolve three specificanomalies: (1) Enforcement of Mass: Eigenmode analysis of a stiff flux torus predicts the TensorGlueball (2++) mass at 3006 MeV. We attribute the discrepancy with Lattice QCD estimates tothe missing stiffness in standard Wilson actions and propose a flavor-blind search strategy. (2)Enforcement of Stability: We explain the anomalous narrow width of the X(3872) tetraquarkvia a geometric crimp potential barrier, validating the bound-state hypothesis favored by recentdata. (3) Enforcement of Size: We address the modern consensus on the proton charge radius(rp ≈ 0.84 fm). We show that the APH vacuum stiffness naturally compresses the nucleon tothis compact value, rejecting the larger historical extractions as artifacts of a floppy vacuummodel.