IMM Emergence Simulator: Computational Framework for Information-Manifold-Manifold Theory

This repository contains the IMM Emergence Simulator, a suite of computational tools for exploring the Information-Manifold-Manifold (IMM) theory. The framework simulates the emergence of physical-like phenomena—including geometry, stable particles, and proto-biological structures—from a purely informational substrate governed by three core axioms: Integration, Self-Reference, and Projection. By treating the "observable universe" as a phase-stripped residue of a multi-mode complex manifold (\psi), the simulator demonstrates how an Arrow of Time and Metric Curvature arise naturally from entropy gradients. Key Scientific Features Spectral Gap Analysis (\Delta): Models the phase transition between projection-dominant (chaotic) and integration-dominant (ordered) regimes where \Delta = \gamma - \kappa. Emergent Metric Geometry: Implementation of a dynamic metric g(x) = 1 + \lambda |\nabla S|^2, where informational density induces local "lensing" and curvature. Self-Organized Criticality (SOC): Tools for measuring cluster size distributions N(s) \sim s^{-\tau} to identify the complexity peak near the critical point \Delta \approx 0. Energy Functional Dynamics: A formalization of the system’s evolution via the functional \mathcal{F}[\psi, S] = \kappa \langle |\nabla \psi|^2 \rangle + \alpha \langle |\nabla S|^2 \rangle, bridging discrete simulation with gradient flow physics. Vorticity-Gated Particles: Detection of stable "particles" as curvature vortices characterized by high coherence and low entropy production. Technical Implementation The simulator is built as a high-performance React/JSX application utilizing the HTML5 Canvas API for real-time field visualization. It supports multi-mode state scalars, periodic boundary conditions, and a stochastic "Parameter Walk" for automated phase-space exploration. Included Files imm_v4.jsx: The flagship simulator featuring emergent metrics and energy functional tracking. imm_v3.jsx: Version introducing expansion (a(t)), Hubble flow (H(t)), and proto-life replication. imm_v2.jsx: The baseline multi-mode integration engine. imm_findings.pdf: Formal theoretical derivations and mathematical summaries of the IMM framework.