Publications

Every paper recommended by the Institute's open-review panel and cleared by the curation desk is indexed here. Each entry carries a persistent digital object identifier — minted by the Institute on Zenodo if the author doesn't already have one — the panel's full review record, and a permanent permalink (e.g. /publications/the-existence-threshold).

Architecture-Independent Geometric Memory Failure: Two Parallel Lines of Evidence (2026) Nathan M. Thornhill Panel Review: RECOMMEND

10.5281/zenodo.20211868

In January 2026 two papers were deposited on Zenodo establishing that information loss at dimensional boundaries in discrete systems is a geometric phenomenon with an architecture-independent magnitude: 86.01% ± 2.39% in cellular automata across 1,500 patterns (Thornhill 2026b, DOI 10.5281/zenodo.18262424, 01/14/2026), and 84.39% ± 1.55% on transformer hidden states (GPT-2, Gemma-2), supported by a formal proof of the component transformations S, R, and D (Thornhill 2026c, DOI 10.5281/zenodo.18319430, 01/20/2026). It was predicted, in the closing discussion of Thornhill 2026c, that the…

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The Dynamic Existence Threshold: Organizational Consciousness Across Complex Systems (2026) Nathan M. Thornhill Panel Review: RECOMMEND

10.5281/zenodo.18373411

What do market crashes, geomagnetic storms, and the loss of consciousness have in common? They are all moments when a system's organizational identity dissolves. This paper introduces a framework that makes that dissolution measurable, predictable, and universal. The Dynamic Existence Threshold (DET) provides a single coordinate system — the integration-differentiation balance zone — in which conscious brains, stable markets, and quiet magnetospheres all occupy the same region. Departure from this zone is organizational dissolution: the system persists physically but loses the coordinated…

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The Existence Threshold (2026) Nathan M. Thornhill Panel Review: RECOMMEND

10.5281/zenodo.18182662

The Existence Threshold proposes a universal framework for understanding pattern persistence across binary discrete dynamical systems through the corrected formula Φ = R·S + D, representing a fundamental revision where disorder functions as a component of existence rather than its enemy. This version includes comprehensive experimental validation achieving perfect classification accuracy across ten cellular automata systems including Conway's Game of Life, Seeds, Day and Night, HighLife, and multiple one-dimensional and two-dimensional rule systems. Statistical analysis demonstrates nine of…

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Pattern Loss at Dimensional Boundaries: The 86% Scaling Law (2026) Nathan M. Thornhill Panel Review: RECOMMEND

10.5281/zenodo.18262424

Information degrades predictably when crossing dimensional boundaries—from DNA’s 1D code building 3D proteins to neural networks transforming data across dimensional spaces—yet this fundamental cost has never been quantified. While the “curse of dimensionality” describes problems qualitatively and dimensionality reduction techniques project high-dimensional data to lower dimensions, no prior work has measured information loss during the embedding of discrete patterns from dimension N to dimension N + 1.This study introduces the Φ metric (Φ = R · S + D), which decomposes pattern information…

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The Dimensional Loss Theorem: Proof and Neural Network Validation (2026) Nathan M. Thornhill Panel Review: RECOMMEND

10.5281/zenodo.18319430

This paper presents the formalization and empirical validation of the Dimensional Loss Theorem, a universal principle governing the degradation of binary discrete patterns when embedded from 2D planes into 3D lattice volumes. Building upon prior empirical observations of an 86% scaling law, component-wise proofs are provided for the S (Connectivity), R (Volumetric), and D (Entropy) transformations. The connectivity tax is demonstrated to be a geometric invariant of Moore neighborhoods. Applying this framework to the final layers of GPT-2 and Gemma-2, numerical verification confirms exact…

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