Emergent Dirac Equation from the Universal Ψ Lagrangian - Spin, Gamma Structure, and Relativistic Fermions as Functional Eigenmodes.

We show that the Dirac equation, its gamma structure, antiparticle symmetry, and spinor degreesof freedom emerge naturally from the Universal Ψ Lagrangian. The first-order relativistic operatordoes not need to be postulated: it follows from the linear decomposition of the universal quadraticvariational operator around a stationary coherent solution Ψ0. The universal eigenvalue problemyields paired positive and negative mass modes, which form the canonical Dirac doublet. Thegamma matrices arise as the representation of the functional linear operator connecting temporaland spatial derivative terms, determined uniquely by the ratio of the kinetic coefficients. Theentire spinor structure is therefore emergent, parameter-free, and directly derivable from the closeduniversal variational principle.