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

arXiv机器学习 2026-10-09 12:00 4 阅读 查看原文

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.