Beyond the Ergodic Wall: A Discrete Geometric Physics Sandbox for Analysing AI Scaling Limits and Complexity Collapse
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Computer Science > Machine Learning
arXiv:2610.10651 (cs)
[Submitted on 7 Oct 2026]
Title:Beyond the Ergodic Wall: A Discrete Geometric Physics Sandbox for Analysing AI Scaling Limits and Complexity Collapse
Authors:Simon Richard Daniel
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Abstract: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 Schrödinger 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.
| Comments: | 17 pages, 8 core pages including tables, 9 pages references tables (updated references to bbl) |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| MSC classes: | 68T07 (Primary), 65N80, 82C28, 52C17, 94A17 (Secondary) |
| Cite as: | arXiv:2610.10651 [cs.LG] |
| (or arXiv:2610.10651v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10651
arXiv-issued DOI via DataCite (pending registration)
|
Submission history
From: Simon Richard Daniel [view email][v1] Wed, 7 Oct 2026 15:58:54 UTC (268 KB)
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