Theory of Informational Connections: A Research Program with Partially Proved Results

Abstract

The program describes fundamental reality as a dynamic graph with binary nodes (spins) and continuous weights of connections. Space-time, gravity, quantum mechanics, and matter are considered as emergent collective effects. The rigorous mathematical core includes exact solutions for N=2 and N=3 with complete stability analysis, a proof of the interval preservation for weights (in the approximation of constant Lagrange multiplier) and a self-consistent mean field. Seven hypotheses about emergent properties are furnished with concrete intermediate results and quantitative falsification criteria. The work is intended to stimulate further research and collaboration.