A Planck-Scale Higgs-Planck Matching Condition Linking the Higgs Field to Gravitational Strength

This work proposes a Planck-scale matching condition equating the Higgs Compton wavelength with the Planck length, establishing a direct relationship between mass generation and gravitational strength. It derives an exact algebraic expression showing that the Higgs mass parameter at the Planck scale fixes the value of Newton’s constant. The resulting prediction reproduces the measured gravitational constant with 0.04% accuracy, without tuning or free parameters. The same condition naturally defines a geometric stiffness scale for spacetime. This framework suggests that gravitational strength may emerge from a deeper Planck-scale identity involving the Higgs field. Overall, the study provides a minimal and highly constrained link between the Standard Model and gravity.