Replication Data for: Appendix A – Mathematical Foundations of M3E

This repository contains a set of computational simulations designed to validate the theoretical framework and mathematical derivations presented in Max (2025) and its Appendix A, "Mathematical Foundations of M3E". The simulations provide numerical and computational evidence supporting the core concepts of the "Mind, Motion, and Multiscale Emergence" (M3E) framework, including attractor dynamics, the emergence of Markov blankets, and the relationship between the framework and Bayesian inference.<br>
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Specifically, the simulations address:<br>
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<li><b>Lemmas (I.A - I.F)</b>: These simulations demonstrate the numerical tractability and stability of recursive representations, the consistency of Markov blanket modes (weak vs. strong), the grounding of symbolic representations, the emergence of computational primitives from sensorimotor dynamics, and the stability of linguistic representations built upon these primitives.</li>
<li><b>Theorems (II.A - II.C)</b>: These simulations illustrate the emergence of Markov blankets from attractor geometry, the optimal exploration-exploitation tradeoff within the framework, and the conditions under which the framework subsumes Bayesian inference.</li>
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Simulation files are named according to the corresponding sections in Appendix A (e.g., L.I.A, T.II.B). The repository also includes raw output data and Python script files, allowing for full reproducibility of the figures presented in Appendix A and further exploration of the model's parameter space.