A Constitutive Derivation of Stationary Bulk Fields from a Topological Boundary-Flux Invariant

This work develops the stationary Bulk sector of the Signature Framework from a conserved topological boundary-flux invariant. The modeled spatial region is the source-free exterior of a finite reaction surface. Within this domain, flux conservation across homologous enclosing surfaces gives rise to an Omnidirectional Spherical Process-Load Domain (OSPLD), in which the local radial flux density undergoes Gauss-surface-like (1/r^2) geometric dilution. The paper shows that the spherical OSPLD field is the unique minimum-energy representative of the prescribed flux class. Its associated local Bulk process-load density scales as (1/r^4), while its total exterior state-energy remains finite. The construction requires neither a point source nor a volumetric source within the modeled exterior domain. This work constitutes Paper I of the constitutive Bulk–Shift–Spin development of the Signature Framework and provides the stationary baseline for the subsequent kinematic sectors. The constitutional terminology and foundational definition of the OSPLD are established in: Firtl, M. A. (2026). Foundation Lemma: Constitutional Principles and Nomenclature of the Signature Framework. Zenodo. doi: 10.5281/zenodo.20575293