Section 4: Formal Mathematical Structure
By Brian Miller
The Structure of Everything Interaction (SEI) theory is grounded in a precise mathematical framework that captures the essence of emergence. This section introduces six foundational equations, each modeling a distinct dimension of SEI's triadic dynamics. Where conventional physics relies on forces, particles, or curvature alone, SEI formalizes interaction as the fundamental origin of all phenomena.
$$\mathbb{SEI} = \nabla \cdot (\vec{A} \otimes \vec{B}) + \frac{dX}{dt}$$
Models the emergence of structure from polar tension and dynamic mediation. The tensor product \( \otimes \) captures directional relationships between the poles, and the divergence \( \nabla \) plus time derivative reveals the dynamic unfolding of structure.
$$\frac{dC}{dt} = f(A, B, X)$$
Expresses how consequence \( C \) evolves over time from interaction. The function \( f() \) represents the generative transformation driven by the asymmetry between \( A \) and \( B \) through \( X \).
$$T_{SEI} = \frac{\delta X}{\delta(A - B)}$$
Time, in SEI, is not a fixed dimension but a gradient of interaction. It emerges from the rate at which \( X \) transforms across the structural difference between \( A \) and \( B \).
$$R^{\mu\nu}_{SEI} = \Gamma^{\mu}_{\alpha\beta}(X) - \Gamma^{\nu}_{\beta\alpha}(X)$$
Models how structured tension in the interaction layer creates curvature. This parallels general relativity but derives geometry from the triadic field, not mass-energy alone.
$$\psi_{AB} = \psi_A \otimes \psi_B + \phi(X)$$
Entanglement in SEI results from shared interaction fields. When \( A \) and \( B \) co-participate in the same \( X \), coherence arises not from distance, but from structural linkage.
$$\frac{dS}{dt} = \mathbb{X} \cdot d\vec{l} + \Phi_{AB}$$
This equation models the systemic flow of emergence. The circulation of \( X \) through a boundary and the polarity flux between \( A \) and \( B \) determine the overall rate of structured change.
Together, these equations express a unified system of generative logic: emergence is calculable, time is relational, curvature is interactional, and entanglement is structural. This mathematical language provides SEI the ability to unify quantum mechanics and general relativity under one generative principle.