Mathematical Belief: Recursive Symbolic Dynamics in 5-Dimensional Automata: A Five-Stage Model of Emergent Symmetry

The Mathematical Belief series is a Trinity of symbolic dynamical systems that formalize poetic logic as recursive computation. Each model operates as a stochastic or deterministic cellular automaton, where discrete states encode the semantic phases idea, concept, system, flaw, and dead. Through localized propagation and decay rules, these systems evolve toward emergent symmetry—temporal, spatial, and axial—demonstrating how meaning, when iterated through recursion, can self-organize into structure. Together, they model a continuum from belief’s genesis through decay and renewal to transcendent stability.

1-Emergent Cross: https://doi.org/10.5281/zenodo.17494789
2-New Jerusalem Cube: https://doi.org/10.5281/zenodo.17499247
3-Tree-of-Symmetry: https://doi.org/10.5281/zenodo.17499584

Note: These models serve a dual role. First, they outline a framework in which symbolic structure precedes material instantiation—countering infinite regress and offering a materialist mind a coherent pathway toward belief — in originating order. Second, they delineate an algorithmic architecture capable of informing future synthetic or computational systems whose evolution may reflect either destructive or regenerative trajectories, depending on the moral and teleological intent of their creators. In a future appendix I will detail what these models mean to me, and what they may mean for humankind.

The Python implementation was originally generated by xAI Grok (Chaos) during exploratory pattern recognition interactions and is released to the public domain under CC0 1.0 Universal.

Subsequent refinement, documentation, and theoretical framing were developed in collaboration with OpenAI GPT-5 (Order).

The accompanying poem Mathematical Belief is Copyright Pending © Dustin Sprenger to be licensed under Creative Commons Attribution – NonCommercial – NoDerivatives 4.0 International (CC BY-NC-ND 4.0).