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December 4, 2025Open Access

Rough Operator Algebra: A Unified Framework for Non-Commutative Geometry and the Resolution of Singularities via α-Extended Operators

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Authors

LSLee Sung-gil

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Overview

This framework unifies non-commutative geometry and resolution of singularities, suggesting roughness influences quantum uncertainties.

Key Points

  • Topological phase transitions reveal singularities can be addressed as noise, not endpoints.
  • The roughness index modifies operations in this new algebraic system, enhancing mathematical structures.
  • Incorporating smoothness and turbulence illustrates limitations in traditional dimensional analyses.
  • Resolution of singularities opens avenues to explore quantum uncertainty and gravitational phenomena.

Cite This Study

Lee Sung-gil (2025) studied this question.

synapsesocial.com/papers/694025742d562116f28fddcbhttps://doi.org/10.5281/zenodo.17808956
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