Stepwise Vacuum Structure and Energy Decit in the Ontopole Field Model

AbstractWe develop the stepwise vacuum structure implicit in the Ontopole winding numberformula α−1(n) = 2πn−π/16−1. The vacuum is not a featureless ground state buta discrete hierarchy of energy levels indexed by the eective vortex winding numbern. Each transition n → n−1 releases exactly Δα−1 = 2π and increases the couplingstrength by a calculable fraction. Four structural results are established. First, theeld existence boundary nmin = (1+π/16)/2π ≈ 0.190 denes an absolute forbiddenzone: below this threshold the coupling inverse becomes negative and no vortex canbe sustained. Second, the empty rst quantum between nmin and nstrong has widthexactly 1/(2π) and contains no physical interaction it is the primordial uncoupledvacuum. Third, the phase decit π/16 constitutes a fraction (π/16)/(2πn) of thetotal accumulated phase at each level n; at n = 22 (electromagnetic vacuum) thisfraction is 0.142%, growing to 8.93% at the strong interaction threshold. Fourth,dark energy is identied with the global sum of unclosed phase decits: the universeoperates as a system permanently displaced from perfect vortex closure, with theunclosed fraction δφ/2πn playing the role of cosmological vacuum tension. Theenergy decit per level, the forbidden zones, and the approach to the existenceboundary are computed explicitly.Zenodo Preprint, 2026 O. GlushkovStepwise Vacuum and Energy DecitKeywords: stepwise vacuum, vacuum structure, energy decit, phase decit, windingnumber, Ontopole eld model, forbidden zones, dark energy, eld existence boundary,vacuum tension, discrete coupling.Related: DOI 10.5281/zenodo.19975312 (winding number formula and uniedinteractions).2