The Structural Unified Field Equation: A Minimal Geometric Bridge between Classical, Electromagnetic, and Quantum Regimes

Since the development of modern physics, a central unresolved problem has been the absence of a minimal structural principle capable of bridging classical mechanics, electromagnetic field theory, and quantum phenomena within a single coherent geometric framework. While existing unification efforts often introduce increasing mathematical complexity or domain-specific assumptions, they frequently leave unanswered whether a shared boundary-based structure governs stability, transition, and breakdown across physical regimes.

This work introduces the Structural Unified Field (SUF) equation as a minimal geometric formulation based on boundary-constrained tension. Rather than postulating a new force or interaction, the SUF framework characterizes systems through a dimensionless structural ratio, β, representing proximity to an intrinsic boundary condition. The resulting SUF function defines a universal geometric constraint on stability, transition, and collapse that is independent of scale and physical substrate.

Crucially, the SUF equation is not proposed as a complete domain-specific theory, but as a generative structural kernel capable of projection into multiple applied domains. Under domain-specific interpretations of β, the same boundary-based geometry gives rise to distinct but structurally homologous models. This projection principle distinguishes SUF from conventional unification approaches by emphasizing structural transferability rather than reductive unification.

Recent work has demonstrated how this minimal geometric structure can be instantiated within concrete domains. In the economic domain, the SUF geometry underlies the Economic Relativity Model (ERM), where β corresponds to incentive-boundary proximity and governs macroeconomic instability and crisis formation. The ERM framework provides a falsifiable, data-driven application of SUF to real economic systems:

Economic Relativity Model (ERM):
https://zenodo.org/records/17538941

In the cognitive domain, the same SUF geometry gives rise to the Structural Cognitive Field (SCF), where β represents the ratio between encoded information and encodable informational capacity within a system. SCF models attention, awareness, and cognitive focusing as structured tension states within an informational field, offering a domain-agnostic geometric account of consciousness and cognition:

Structural Cognitive Field (SCF):
https://zenodo.org/records/17927709

At the behavioral and political level, the SUF geometry is instantiated through Behavioral Boundary Relativity (BBR), which applies the same boundary-based structural constraints to collective behavior, political stability, and regime transition. In BBR, β characterizes proximity to behavioral and legitimacy boundaries, providing a falsifiable framework for analyzing stability, collapse, and regime change across political systems:

Behavioral Boundary Relativity (BBR):
https://zenodo.org/records/18139321

Taken together, these instantiations demonstrate that the SUF equation functions as a transferable structural kernel rather than a standalone physical theory. Classical, electromagnetic, quantum, economic, cognitive, and behavioral systems can be viewed as distinct projections of the same boundary-based geometry, each inheriting identical stability constraints while differing in domain-specific interpretation.

For a comprehensive exposition of the SUF framework—including its conceptual motivation, geometric formulation, and cross-domain implications beyond the scope of a single article—the full structural development is presented in monographic form:

Structural Unified Field: Boundary, Tension, and the Geometry of Existence
https://www.amazon.com/dp/B0FTTGVCNJ

The present work establishes the minimal mathematical form of the Structural Unified Field equation and clarifies its role as a unifying geometric bridge, leaving detailed empirical validation and domain-specific elaboration to specialized frameworks such as ERM, SCF, and BBR.