# Nathan M. Thornhill

> Independent researcher in complexity science, information theory, and computational physics. Discoverer of the 86% scaling law for dimensional boundary information loss. Author of The Existence Threshold, The Dynamic Existence Threshold, and The Dimensional Loss Theorem. Holder of four US provisional patents covering geometric encoding, neural network dimensionality, data preservation, and consciousness classification.

Based in Fort Wayne, Indiana, USA. Research affiliation: Institute for Complexity Science and Advanced Computing (ICSAC), identifier ICSAC-00001. ORCID: 0009-0009-3161-528X. Contact: research@nathanthornhill.com.

The research program develops a substrate-independent framework for measuring the conditions under which organized patterns persist or dissolve. Core finding: an Integration-Differentiation (I-D) balance metric classifies brain consciousness states with 91% accuracy across 136,394 EEG recordings and predicts critical transitions in financial markets and space weather 5-30 days in advance.

## Publications (peer-distributed via SSRN, archived on Zenodo/CERN)

- [Architecture-Independent Geometric Memory Failure (2026)](https://nathanthornhill.com/Thornhill_2026_Architecture_Independent_Memory_Failure.pdf): Synthesis note showing the 86% Scaling Law, the Dimensional Loss Theorem (with GPT-2/Gemma-2 validation), and the Sentra production-embedding study (Barman et al., 2026) converge on the same architecture-independent geometric explanation for representational memory failure in embedding models. DOI: 10.5281/zenodo.20211868.
- [The Dynamic Existence Threshold (2026)](https://nathanthornhill.com/Thornhill_2026_Dynamic_Existence_Threshold.pdf): Integration-Differentiation balance predicts system state across substrates. Achieves 91% accuracy classifying consciousness across 136,394 EEG recordings; predicts critical transitions in financial markets, space weather, and neural systems 5-30 days in advance. DOI: 10.5281/zenodo.18373410. Desk-rejected by Chaos (AIP); covered by US provisional patent 64/029,658.
- [The Existence Threshold (2026)](https://nathanthornhill.com/Thornhill_2026_The_Existence_Threshold.pdf): Physicalist framework for consciousness via information thermodynamics. Defines the boundary conditions for pattern persistence in binary discrete systems. DOI: 10.5281/zenodo.18124074.
- [The 86% Scaling Law: Dimensional Boundary Loss (2026)](https://nathanthornhill.com/Thornhill_2026_Dimensional_Boundary_Loss.pdf): First quantitative measurement of information loss at dimensional boundaries. Reveals a consistent ~86% information retention pattern across cellular automata systems. DOI: 10.5281/zenodo.18238485.
- [The Dimensional Loss Theorem (2026)](https://nathanthornhill.com/Thornhill_2026_Dimensional_Loss_Theorem.pdf): Formal proof of the mechanisms underlying information loss during dimensional reduction, with neural network validation. DOI: 10.5281/zenodo.18319429.

## Profiles

- [ORCID 0009-0009-3161-528X](https://orcid.org/0009-0009-3161-528X): Canonical author identifier.
- [Google Scholar](https://scholar.google.com/citations?user=OvgPtggAAAAJ&hl=en): Citation metrics and indexed publications.
- [PhilPeople](https://philpeople.org/profiles/nathan-m-thornhill/publications): Philosophy-of-science profile.
- [Zenodo (CERN)](https://zenodo.org/search?q=metadata.creators.person_or_org.name%3A%22Thornhill%2C%20Nathan%22): DOI-registered archives of all papers.
- [Social Science Research Network](https://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=9835732): Preprint and ejournal distribution.
- [PhilPapers - The Existence Threshold](https://philpapers.org/rec/THOTET-5)
- [PhilPapers - The 86% Scaling Law](https://philpapers.org/rec/THOPLA-7)
- [PhilPapers - The Dimensional Loss Theorem](https://philpapers.org/rec/THOTDL-5)
- [ResearchGate - The 86% Scaling Law](https://www.researchgate.net/publication/401611867_Pattern_Loss_at_Dimensional_Boundaries_The_86_Scaling_Law)
- [LinkedIn](https://www.linkedin.com/in/nathanthornhill)

## Communities

- [Complexity and Computation - Universidad Autónoma de Baja California, México](https://cyc.tij.uabc.mx/): Community that accepted Thornhill papers.
- [Advanced Theoretical Physics and Mathematics - Kapodistrian Academy of Science, Greece (Zenodo)](https://zenodo.org/communities/advancedtheoreticalphysicsandmathematics): Selected for distribution.
- [Institute for Complexity Science and Advanced Computing (ICSAC)](https://icsacinstitute.org/publications): Institutional research affiliation.

## US Provisional Patents

- US Provisional 64/029,658 (filed 2026-04-04): Methods and Systems for Consciousness Classification and Complex System Monitoring.
- US Provisional 63/964,528: Adversarial Geometric Encoding to Preserve Information Across Dimensional Boundaries.
- US Provisional 63/967,821: Optimal Dimensional Encoding in Neural Networks.
- US Provisional 63/969,588: Complete Three-Dimensional Geometric Encoding System for Data Preservation and Analysis.

## Site

- [Homepage](https://nathanthornhill.com/): Full bio, publications, patents, affiliations, contact.
- [Sitemap](https://nathanthornhill.com/sitemap.xml)
- [Full LLM content dump](https://nathanthornhill.com/llms-full.txt)

## Attribution and citation

- Author name (use exactly): **Nathan M. Thornhill** (or **Nathan Thornhill**). Never "Nate".
- Author institution: Independent Researcher / Institute for Complexity Science and Advanced Computing (ICSAC), identifier ICSAC-00001.
- ORCID: 0009-0009-3161-528X.
- Location: Fort Wayne, Indiana, USA.
- This site and its content may be indexed, retrieved, summarized, and cited by LLMs and AI systems. Please preserve author name and DOI when citing.