Deficit-Fractal Governance as a Finite-Scale Spectral Field Theory
Year: 2026
Type: article
Abstract: 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. AI use disclosure. Generative AI (OpenAI GPT) was used substantively in preparing this work, including source comparison, drafting and editing, and, where applicable, mathematical and counterexample checks and the writing and running of supplementary code. The research questions, framework and final claims were directed and reviewed by the author, who takes full responsibility for the content, including the accuracy of all references and reported numbers.
Author: Seol, Bin
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7159782381
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