Topological Projection, Curvature Orientation, and Charge Sign in a Unified QCD Mass Framework

Electric charge and rest mass, though distinct in the Standard Model, display systematic correlations in hadron multiplets. We show that both emerge from a unified projection principle acting on a curvature-mediated Hilbert manifold representing QCD color flux. Integrating out a mediator field coupled to mass and absolute charge densities yields a natural mass–charge binding operator. Charge corresponds to curvature orientation: outward flow produces positive charge, inward flow negative, and symmetric flow neutrality. A unified variational model including electromagnetic self-energy and a β self-consistency loop reproduces strange-baryon mass splitting (Σ, Ξ) to ≲1 MeV with constituent quark inputs. The effective coupling agrees in scale with lattice QCD measurements of topological susceptibility. Internal absolute charge amplitude, rather than net charge, governs the mass–charge binding, explaining the observed ordering of Σ⁺, Σ⁰, and Σ⁻ masses.