QLCD The Kernell Hallo Law

This work proposes the kernel–halo principle: hadrons are stabilized by a finite stress density that fixes the proton’s kernel as a universal anchor, with higher-energy states forming transient halos that scale in radius as R∝E−1/3. The principle provides a simple dimensional rule linking confinement energy to spatial extent, offering a structural complement to QCD. Applied to the proton, the kernel saturates the finite-stress limit, consistent with its exceptional stability, while lighter mesons and resonances exceed the bound and decay rapidly. The scaling also clarifies anomalies in measured charge radii and form factors by distinguishing kernel size from halo contributions. In addition, the modified stress distribution yields a natural correction to hadronic vacuum polarization, producing a shift in the muon g−2 of order 10−10, consistent with the observed deviation. The framework is directly testable: if hadronic radii measured across families fail to follow the E−1/3 law, or if proton stability is found inconsistent with a saturated kernel, the principle would be falsified. Thus, the kernel–halo rule supplies a minimal, testable refinement to our understanding of hadron structure.