Information-Topological Interaction as a Fundamental Force in an L--T--I Coordinate Continuum

This paper presents a unified theoretical and computational model of information-topological interaction in an L--T--I coordinate continuum. The model is formulated as a formal description of a fundamental interaction whose operative variable is informational organizing potential and whose effective action is expressed through active-mass redistribution, structural impedance, directed graph topology, stochastic defect dynamics, topological plasticity, gauge-covariant structural order, and useful organizing work. The model defines the dimensional, gauge, thermodynamic, stochastic, topological, spectral, and algebraic core of the interaction. It introduces boundary conditions for structural conductance, formulates variational, dissipative, stochastic, gauge-field, and birth--death layers, and specifies a numerical simulation protocol for directed weighted networks. The gauge sector resolves the real-scalar versus complex-phase conflict by assigning local \ (U (1) I\) covariance to a complex structural order parameter \ (\), while the physical informational potential remains the real observable \ (I=₀^*\). The model also introduces explicit dimensions for \ (\) and \ (₀\), Wilson links on graph edges, an informational field-strength tensor, gauge-field equations of motion, overdamped gauge-field relaxation integrated by RK4, Legendre thermodynamic closure, Feller-parameter mapping from physical drift variables, generalized fluctuation--dissipation closure, Jacobi-type bounded diffusions, Milstein stochastic integration, and network birth--death operators. The computational layer includes Monte Carlo robustness analysis, scalable graph experiments, Sobol sensitivity indices, sparse data structures, benchmark tables, complex-spectrum visualization, topological-plasticity visualization, dynamic cycle-basis recomputation for Wilson-loop curvature, phase unwrapping for graph curvature continuity, and persistent open-science archival requirements. The result is a falsifiable theoretical-computational framework that claims dimensional, gauge, thermodynamic, variational, spectral, stochastic, topological, and numerical admissibility for the proposed fundamental interaction, while empirical confirmation requires independent experimental validation.