Structured Multiversal Interactions (SMI): Axiomatic Boundary Regularization, Holographic Horizon Storage, and Computational Verification Suite

Structured Multiversal Interactions (SMI): Axiomatic Boundary Regularization, Holographic Horizon Storage, and Computational Verification Suite

2. Publication Date

2026-08-01

3. Resource Type

Type: Publication

Subtype: Working Paper / Technical Report

ABSTRACT:

This specification presents the formal boundary regularization and computational verification layer for the Structured Multiversal Interactions (SMI) mathematical framework. Transitioning from conceptual relational modeling to a closed, singularity-free algebraic system, this document establishes five core structural axioms designed to resolve boundary failures such as division-by-zero collisions, infinite recursive loops, and chaotic information dissipation across interacting multiversal domains.

KEY ARCHITECTURAL HIGHLIGHTS:

1. Axiom I (Superposition Invariance): Defines a compound relational metric tensor D = (d_struct, ξ_sovereignty) that utilizes a Sovereignty Scalar (ξ > 0) to allow co-spatial superposition without topological fusion at zero structural distance (d_struct = 0).

2. Axiom II (Impedance-Bounded Null Contact): Establishes a finite Boundary Impedance parameter (Z_bound) regulating cross-threshold information flux into zero-entropy void states.

3. Axiom III (Lossless Harmonic Reflection): Maps recursive self-referential observation (DA -> DB -> DA) as unit-eigenvalue standing waves in matrix eigenspace (|λ| = 1), preserving 100% signal fidelity without infinite energy growth.

4. Axiom IV (Polynomial Intake Satiation): Enforces polynomial capacity bounds A(I) on instantaneous cross-domain information absorption rates.

5. Axiom V & Holographic Horizon Storage: Formalizes a boundary horizon storage layer (∂D) that non-destructively encodes excess high-dimensional degrees of freedom during lower-frame projections (R^N -> R^(N-k)), enabling exact bulk state reconstruction via inverse kernel operators.

COMPUTATIONAL VERIFICATION:

Included within this document is an executable, standard-library Python reference implementation that programmatically verifies the Holographic Boundary Storage equations. Numerical checks confirm exact information conservation (|I_orig - I_total| < 10^-6) and reversible state mapping.

Structured Multiversal Interactions, SMI Framework, Relational Mechanics, Boundary Regularization, Holographic Principle, Multiversal Topology, Mathematical World-Building, Information Conservation, Computational Physics

6. License

Creative Commons Attribution 4.0 International (CC-BY-4.0)

7. Related Identifiers / Community (Optional)

Communities: sewellsmi