Harmonic Quantization of Semantic Discontinuities in Large Language Models

Harmonic Quantization of Semantic Discontinuities in Large Language Model Embeddings Version 3.0 -- Pre-Submission Final Validation and Cross-Architectural Scaling Release (August 2026) This release finalizes the pre-submission framework for Nature Machine Intelligence, incorporating comprehensive methodological refinements, expanded cross-architectural validations, and rigorous statistical auditing: Title and Conceptual Evolution: Formally transitioned from preliminary archetype nomenclature (The Stone Guest) to an operational framework (Harmonic Quantization of Semantic Discontinuities in Large Language Models), focusing strictly on manifold topology, geometric density inversion, and harmonic scaling ratios. Statistical Corpus and Robustness (n = 30 and Bootstrap n = 10,000): Implementation of an expanded evaluation set comprising 30 coherent and 30 scrambled sentence instances per language across all checkpoints, reinforced by non-parametric bootstrap resampling confirming high-confidence stability. Normalized Semantic Density Metric (S): Mathematical refinement of the density operator S, strictly bounded to the [0, 1] interval while preserving directional phase invariants (Delta S) across diverse model scales. Corpus-Density Boundary Control (GPT-2 Suite): Integration of the OpenAI GPT-2 model family (124M-1.5B parameters, WebText trained) as an architectural probe, mapping out the structural absence of geometric inversion to substantiate the Corpus Density Conjecture (CDC). Cross-Architecture and Multi-Scale Validation: Empirical confirmation of threshold T6 via High-Flyer DeepSeek-MoE-16B (evaluated on the Patagón Supercomputer with an error < 0.3 percent) and validation of T6-bis using Alibaba Qwen2.5-32B-Instruct. Refined Harmonic Projections (T7): Updated power-law fit of harmonic proportions (r_n = 1 + 1.98 * n^(-0.44)), projecting the subsequent critical threshold T7 within the 40-50B parameter range. Key Findings (v3.0): Formalization of semantic emergence as a quantized harmonic sequence rather than a smooth continuum Rigorous cross-validation across Pythia, DeepSeek-MoE, and Qwen architectures Extreme statistical significance for DeepSeek-MoE-16B (p < 10^(-12), g = -2.56) and Qwen2.5-32B (p < 10^(-13), g = -2.94) GPT-2 anomaly formalized as a corpus-density boundary condition (WebText vs. The Pile) Multi-linguistic validation across Spanish and English (n = 30 each) Implications: Establishes harmonic quantization as a fundamental principle of semantic scaling Enables predictive capability thresholds for future frontier architectures Provides a falsifiable geometric framework for emergent-semantics research Demonstrates corpus density as a primary determinant of representational geometry Computational experiments were executed on the Patagón Supercomputer (Universidad Austral de Chile, FONDEQUIP EQM180042). Code and Data: Complete implementation: https://github.com/geosemantica-social/TheStoneGuest Licensed under CC BY-NC-ND 4.0 Continuity Note: This work extends and empirically verifies the geometric predictions introduced in The Purloined Letter of AI (Cerda Seguel, 2025). DOI: 10.5281/zenodo.17329747 Previous versions: v2.0 (June 2026): 10.5281/zenodo.17329747 v1.2 (Nov 2025): 10.5281/zenodo.17633069 (c) 2025-2026 Diego Cerda Seguel -- Corporación Sintesys / Teoría del Sentido Tensorial (TdST)