# Beyond the Ergodic Wall: A Discrete Geometric Physics Sandbox for Analysing AI Scaling Limits and Complexity Collapse

arXiv: https://arxiv.org/abs/2610.10651 · HTML: https://mlsanity.com/paper/2610.10651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 49 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 4 of 4)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [On the Binding Problem in Artificial Neural Networks](https://mlsanity.com/paper/2012.05208/) (2020)
- [Estimating the energy requirements for long term memory formation](https://mlsanity.com/paper/2301.09565/) (2023)
- [A non-ergodic framework for understanding emergent capabilities in Large Language Models](https://mlsanity.com/paper/2501.01638/) (2025)

## Abstract (arXiv)

This paper exposes the ergodic ceiling and thermodynamic inefficiency of current deep learning, which converges to a statistical average of historic human knowledge. True semantic novelty requires a path-dependent, spatiotemporally bounded observer (a Data LifeCone) to inject non-ergodic insight, achieving KL divergence and avoiding manifold lock-in. AI Safety must recognise that a mature Artificial Superintelligence (ASI) would regard human-AI symbiosis as a thermodynamic necessity to avoid model collapse. We therefore propose hard physical containment via a digital physics sandbox powered by a Holographic E8 Projection Engine to verify models against real-world constraints. Spacetime is modeled as an information substrate of nested face-centered cubic (FCC) lattices of oscillating Planck-scale spheres maximizing local information and entropy density. Cut-and-project methods from the E8 root lattice produce a quasi-crystalline geometry where tetrahedral voids support SU chiral structure and elastic-shear eigenvalues generate candidate mass spectra. Rest mass is treated as discrete, integer microstate counts on local holographic boundaries (Bekenstein bound), replacing floating-point approximations with strict integer arithmetic to provide an information-theoretic definition of matter. Stable particles emerge as recurring lattice dislocations, and continuum recovery proceeds via variational renormalisation-group flows and Fourier Neural Operators that learn continuous spectral operators to recover the Schr"odinger equation as an emergent statistical description. Crucially, these top-down topological constraints offer a mechanism for "NP-to-P" complexity collapse: by restricting an algorithm's proposal space to physically conserved causal trajectories, the sandbox prunes the combinatorial tree to deterministic, polynomial-time paths.