Sci - Dimensionless Mathematics: A Pre-Geometric Framework for Closure, Persistence, and Invariant Objecthood

Laboratoire de Chimie Théorique

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Abstract

Sci - Dimensionless Mathematics: A Pre-Geometric Framework for Closure, Persistence, and Invariant Objecthood Armstrong Knight — intent-tensor-theory.com This paper formally introduces Dimensionless Mathematics as a proper noun and a named domain of mathematical inquiry, distinct in kind from all classical uses of 'dimensionless' as an adjective in physics and engineering. Classical nondimensionalization operates inside a given geometry, stripping units from equations that already exist in a coordinate frame. Dimensionless Mathematics operates before geometry, asking what conditions must be satisfied for stable structure to exist before spatial or temporal coordinates are treated as fundamental. The framework…

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Topics & keywords

Keywords
  • Dimensionless quantity
  • Invariant (physics)
  • Covariance and contravariance of vectors
  • Cartesian coordinate system
  • Domain (mathematical analysis)
  • Axiom
  • Covariant transformation
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