Integrated Scretching–Planck Research on Quantum and Gauge Theory

The Scretching–Planck (SP) density–phase action is locally equivalent to the Schrödinger equation wherever the density is positive. Reconstructing a global wavefunction also requires single-valuedness and compatible nodal and boundary conditions. Relativistic and gauge extensions require independently specified fields and dynamics. Varying the combined action for gauged matter and an independently specified parity-even Yang–Mills kinetic term yields the classical Yang–Mills equations with a matter current. On a finite spatial lattice, the physical spectral gap equals the vacuum-weighted Poincaré constant multiplied by the Hamiltonian’s kinetic prefactor. Constructing the four-dimensional continuum theory and establishing a uniform positive gap in physical units remain open. In the separate two-dimensional \(O(N)\) model, the strict large-\(N\) Gaussian saddle has a gap bounded below by \(0.9624236501\) times the fixed saddle mass throughout the stated cutoff range. The reduced-mass Coulomb calculation for hydrogen gives a ground-state energy of \(-13.5982873\) eV and a \(1S\)–\(2P\) interval of \(10.1987154\) eV before additional recoil and level corrections. The muon lifetime serves as a closure calculation, and the true-muonium values are potential-model estimates. The charmonium and helium-ion calculations illustrate how the choice of potential, radiative corrections, and reference levels affect the results [V1–V15].