Data Update — November 6, 2025

Overview

This update to Evans’ Law incorporates new cross-family testing data gathered between October 20 – November 6, 2025, expanding the original Evans M¹·⁵ Scaling dataset to include models from four major architectures: GPT, Claude, Gemini, and Grok.

All tests used identical prompt suites (knowledge recall + factual consistency under long-context stress) with temperature = 0.2, deterministic sampling, and uniform stop criteria based on first incoherence detection.

Updated Regression Findings

Regression analysis on log-scaled parameters (M, billions) and hallucination thresholds (L, tokens) yields:

L = c \times M^{\alpha}

where the best-fit parameters are:

This diverges from the theoretical α = 1.5 proposed in the original Evans Law model, indicating that observed coherence length increases far more slowly with model size than predicted.

Interpretation

The updated exponent α = 0.36 represents a significant flattening of the coherence scaling curve. Across all model families, hallucination onset appears 4–5× earlier than the M¹·⁵ prediction.

This supports the existence of “coherence cliffs” — nonlinear inflection points where attention entropy overwhelms scaling gains.

These cliffs correlate with rising entropy in self-attention weights and measurable drift in factual recall above ~70 % of each model’s context budget.

Implications

• Theoretical: Evans’ Law remains valid as a scaling framework but requires an empirical correction term for context-length efficiency.
• Applied: Developers should assume effective coherence ≈ 0.7 × model limit and implement dynamic truncation or retrieval at that threshold.
• Operational: Enterprise AI systems should monitor token utilization and entropy variance in real time (“Coherence Health”) to prevent silent failure beyond coherence cliffs.

Data Availability

All raw logs, analysis notebooks, and visualization scripts are versioned under

PatternPulse.AI / EvansLaw v3 (Nov 2025)

• Dataset: evanslaw_v3_2025_11.csv
• Visualization: evanslaw_plot_v3_2025_11.png
• Regression Notebook: evanslaw_analysis_v3_2025_11.ipynb

Persistent DOI: (to be assigned via Zenodo or arXiv v2)

Citation

Evans, J. (2025). Evans M¹·⁵ Scaling Law: Empirical Update and Cross-Family Validation. PatternPulse.AI / B2B News Network, Version 3 (November 2025).