Curvature-Locked U(1) Gauge Fields

A photon mass usually violates gauge symmetry or requires a Higgs-like scalar, neither of which is observed. We propose an alternative: restrict, rather than break, configuration space by a curvature-locking constraint on a golden-ratio logarithmic spiral. The integrated helicity on this spiral is forced to equal 2πN, which, in the stiff-constraint limit λ→∞(with λϵ≡mγ2 fixed), yields an emergent Proca term without explicit symmetry breaking. This predicts a monochromatic 5.933 keV photon (γm) from γγ→γm γ, which Belle II can already search for in its existing data. The resulting photon mass is mγ≡αtop=5.933±0.00017keV, where α_top (formerly written as α) denotes the topological mass parameter, distinct from the electromagnetic coupling. Belle II’s ∼30fb-1 data should yield O(15) signal events withS/B>5. Beam-dump searches (e.g. NA64++, DarkQuest) offer complementary reach. Traditional Coulomb-law tests (m_γ≲10-13 eV) and astrophysical X-ray bounds do not apply, because keV photons are re-absorbed in stellar plasmas and no free streaming occurs. We discuss next steps: searching Belle II, extending curvature locking to fermion masses, and exploring spin-2 locking for a small positive Λ.