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A Direct Algebraic Pathway to Hadronic Observables in the Contact Model

We present a novel algebraic framework for computing hadron properties directly within the contact interaction model. Utilizing Fierz transformations, the method recasts the Bethe-Salpeter dynamics into equations for a minimal set of \emph{projected amplitudes} for bound-state static properties and form factors, bypassing the conventional need for the meson wave function. This approach is fully demonstrated for the vector meson, enabling the direct extraction of its decay constants and form factors. The formalism provides a more efficient and unified pathway to hadron observables, with clear potential for extension to baryons and more sophisticated interactions.