Deficit-Fractal Governance as a Finite-Scale Spectral Field Theory

This working paper presents the finite-scale spectral core of the Deficit-Fractal Governance framework. It defines governance instability through a computable operator AV=TV−DL(m)A_V = T_V - D L^{(m)}AV=TV−DL(m) on finite graph skeletons, where interaction pressure is represented by TVT_VTV and containment or diffusion capacity by DL(m)D L^{(m)}DL(m). The paper establishes the finite self-adjoint instability criterion and a conservative proxy hierarchy linking the dominant eigenvalue λV\lambda_VλV, operator norm, and Hilbert-Schmidt instability functional S[V]S[V]S[V]. The scope is explicitly restricted to finite skeletons with self-adjoint or symmetrized interaction operators. Directed, non-normal, stochastic, memory-driven, and fractal-limit extensions are deferred to companion papers in the series. The paper also includes notation conventions, assumption boundaries, calibration logic, and counterexamples showing why the self-adjoint restriction is necessary. This is Paper 1 of the six-part DFG Unified Interaction Field Theory Series. The series is framed as a structured theoretical research programme, not as a global empirical validation claim.