Fading Mass: A Conformal Extension of the Standard Model

If the geometry that supplies physical rulers and clocks evolves, how do particle masses evolve with it? The difficulty reaches beyond the Higgs mechanism: most proton mass comes from strong-interaction dynamics, so moving the electroweak scale does not automatically move composite matter. We formulate the Standard Model within the Conformal Emergent Reality Model (CERM), whose scale factor Ω=φχ contains the accumulated curvature history χ, called Chronos. A moving Higgs minimum and a declared physical matching postulate carry the electroweak and QCD scales together, giving ordinary masses a common inverse-Chronos law with fixeddimensionless mass ratios on the matched tracking branch. The matching postulate is a declared physical input; its quantum protection and derivation from the geometric action remain future work. The exact conformal Dirac identity carries this mass law through the full relativistic wave equation, and the geometric clock yields ordinaryquantum evolution in physical proper time at semiclassical test-matter order. A nonlinear finite-interval bound determines when the Higgs actually follows its moving minimum. The selected Majorana-neutrino interaction gives a conditional test: a Higgs tracking departure changes every nonzero neutrino mass-squared splitting relative to the electron mass squared by the same factor (1+e)², while charged-fermion mass ratios remain fixed. These results give CERM explicit elementary andcomposite matter, consistent quantum propagation, and geometric feedback, connecting evolving laboratory standards to the ordinary-matter fading of its aeonic completion. Status of this version. Fading Mass Preprint v1.0. The mathematical derivations and technical appendices are complete; the prose is undergoing final editorial revision. Revised versions will be posted to this record as new versions.