Proposed Field Theory for Internet 3.0 Commerce and Multi-Entity Interaction via a Diffeomorphic Manifold

This working paper establishes a rigorous mathematical and physical framework for the "Common Market" of Internet 3.0, defined as a Differentiable Manifold (M). We propose that the interaction between three distinct classes of operators—Intelligence-Human (IH), Intelligence-Artificial (IA), and Intelligence-Metaphysical/Protocol (IM) controlsthe stability of digital basins of attraction, specifically those of Bitcoin and Ethereum. Through a Design of Experiments (DoE) approach, we demonstrate that a Diffeomorphism (ϕ) exists which preserves the topological invariants of value (scarcity, provenance, and utility) across disparate cryptographic states. Furthermore, we address the observer-observed coupling paradox, distinguishing the deterministic "Duty of Presence" found in plasma physics from the probabilistic "Elective Observation" inherent in commercial markets. Our results prove that market efficiency is a non-linear function of operator synergy, providing a foundation for a CAPTCHA-free, "naturally divisible" digital world.