A Geometric Photon Mass-Gap Conjecture: Spectral Gaps for Photonic Operators

 We formulate a precise Geometric Photon Mass-Gap Conjecture asserting that Laplace-type operators modelling photonic dynamics on compact manifolds with photonic coupling admit a strictly positive spectral gap above zero under explicit geometric and bundle-theoretic hypotheses. We define a class of Laplace-type photonic operators acting on sections of vector bundles with photonic connection and potential terms, state the conjecture with an explicit lower bound depending on curvature, flux, injectivity radius and volume, and prove a special-case lemma establishing positivity of the first eigenvalue under a coercive potential hypothesis. Heuristics based on heat-kernel asymptotics, Weitzenböck identities and Cheeger-type inequalities are given to motivate the form of the bound. Finally we outline a numerical verification plan using finite-element eigenvalue solvers for our geometries and discuss possible experimental signatures of a photonic mass gap.