The Stone Guest: Harmonic Quantization of Semantic Phase Transitions in Large Language Models

The Stone Guest: Harmonic Quantization of Semantic Phase Transitions in Large Language Models Version 2.0 — Extended Validation & Metric Normalization Release (June 2026) This release extends the empirical validation of semantic phase transitions with three major improvements: 1. Statistical corpus expanded to n=30 sentences per language across all Pythia checkpoints, yielding p-values several orders of magnitude more extreme for previously confirmed transitions. Effect sizes are reported as Hedges' g throughout, correcting for small-sample bias. 2. Semantic density metric S normalized to [0,1] (Appendix A.1) for improved comparability across model scales. The normalized metric preserves all qualitative conclusions while enabling direct cross-model comparison. 3. GPT-2 family (124M–1.5B, trained on WebText) introduced as an architectural probe. The absence of phase inversion in GPT-2 reveals a corpus-density boundary condition, transforming an apparent anomaly into a diagnostic tool for training corpus quality. 4. Bootstrap validation (n=10,000) confirms that all 12 statistically significant inversions are robust to corpus composition (>95% of bootstrap samples yield ΔS < 0). The analysis further reveals a stable reversal (ΔS > 0) for GPT-2-large and GPT-2-xl, providing the strongest empirical evidence for the Corpus Density Conjecture. The core scientific result remains unchanged: semantic emergence in large language models follows a quantized harmonic sequence rather than a smooth continuum. Five empirically confirmed transitions (T1–T3, T6, T6-bis) are documented across scales from 70M to 32B parameters, with the sixth transition (T6) observed at 16B with 0.3% scale error. Key Findings (v2.0): • Strong empirical discontinuity at ~410M parameters with 7× reduction in ΔS magnitude• Harmonic transition sequence: {2.56, 3.41, 2.00, 2.46, 1.74, 1.33}• Six of seven transitions within <2% of TdST predictions• 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: corpus-density boundary condition (WebText vs. The Pile)• Cross-architecture validation: Pythia → DeepSeek-MoE → Qwen• Cross-linguistic validation: Spanish, English (n=30 each) Implications:• Establishes harmonic quantization as a fundamental principle of semantic scaling• Enables predictive capability thresholds for future LLM architectures• Provides a falsifiable geometric framework for emergent-semantics research• Demonstrates corpus density as a determinant of representational geometry Computational experiments were executed on the Patagón Supercomputer (Universidad Austral de Chile, FONDEQUIP EQM180042). Code & Data:Complete implementation: https://github.com/geosemantica-social/TheStoneGuestLicensed under CC BY-NC-ND 4.0 Continuity Note:This work extends and empirically verifies the geometric prediction introduced in The Purloined Letter of AI (Cerda Seguel, 2025).DOI: 10.5281/zenodo.17329747 Previous versions:v1.2 (Nov 2025): 10.5281/zenodo.17633069 © 2025-2026 Diego Cerda Seguel — Corporación Sintesys / Teoría del Sentido Tensorial (TdST)