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March 2, 20260 citationsOpen Access

Defining Boundary Knowledge Without Ontology: Tier-8 Limits and Admissibility in the Paton System

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APAndrew Simon Paton

Key Points

  • The research aims to establish a method for defining boundary knowledge without relying on ontology.
  • Analyzes boundary regions in scientific frameworks
  • Focuses on Tier-8 limits within the Paton System
  • Examines concepts of breakdown behavior and curvature dominance
  • Proposes a formal definition of stopping boundaries
  • Establishes boundary knowledge as negative and limiting
  • Defines admissibility-governed boundaries
  • Provides a framework that preserves continuity in scientific theories

Abstract

Scientific frameworks routinely encounter boundaries that resist internal description, including singularities, horizons, undecidable regimes, and scale limits. These regions are often treated either as incomplete ontology or as prompts for speculative extension. This paper argues for a disciplined alternative: boundary regions may require precise definition without descriptive content. Within the Paton System, Tier-8 represents such a limiting condition. It is not an ontological layer, but a formally defined stopping boundary inferred from breakdown behaviour, curvature dominance, and constraint saturation. The contribution is methodological rather than physical: it establishes boundary knowledge as negative, limiting, and admissibility-governed. The framework preserves continuity, prevents speculative overreach, and formalises a principled stopping rule fully compatible with existing scientific theories.

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Cite This Study

Andrew Simon Paton (2026) studied this question.

synapsesocial.com/papers/69a52e56f1e85e5c73bf1e5fhttps://doi.org/10.5281/zenodo.18795444
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