Scale Generation: A Bridge from Planck Geometry to the Standard-Model Vacuum

This working paper investigates whether a Planck-normalized geometric-spectral framework can provide a physically meaningful bridge to the electroweak vacuum scale of the Standard Model. The analysis distinguishes scale matching from genuine scale generation and formulates the problem in terms of dimensionless geometric variables, renormalization-group consistency, and an independently defined scale-selection condition. A benchmark construction is evaluated without using the Fermi constant, Higgs mass, or weak-boson masses as forward inputs. It yields a characteristic scale of approximately 246.09 GeV, compared with the established electroweak vacuum scale of approximately 246.22 GeV. The residual is about 0.054%. The agreement is therefore reported as a numerical correspondence, not as a completed derivation. The main result is a falsifiable framework for testing whether a low-energy scale is dynamically generated from high-energy geometric data or merely reparametrized. The work provides a foundation for further studies of RG flow, spectral scale selection, and possible laboratory analogues.