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May 26, 2026Open Access

Toward a Formal No-Tear Theorem in a Continuous Substrate Framework

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Authors

WPWilliam T Partin

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Overview

Develops a No-Tear Theorem demonstrating geometric continuity in physical states of a continuous substrate.

Key Points

  • The research aims to establish a No-Tear Theorem that confirms geometric continuity under specific conditions within a continuous-substrate framework.
  • Developed a continuity-layer result in a continuous-substrate framework.
  • Represented physical states as admissible pairs on a differentiable manifold.
  • Analyzed the closure of geometric discontinuities under continuity conditions.
  • Confirmed that geometric discontinuities cannot occur if substrate continuity and geometry map continuity are met.

Cite This Study

William T Partin (2026) studied this question.

synapsesocial.com/papers/6a1538ebb5d9c58d83e8c8f9https://doi.org/10.5281/zenodo.20362694
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