Concept of ln 2 as a Curvature Invariant of Classical and Quantum Distinguishability in the Theory of Entropicity (ToE)

The concept of ln 2 

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 as a Curvature Invariant, specifically termed the Obidi Curvature Invariant (OCI) and used as a fundamental measure of distinguishability, has been posited by John Onimisi Obidi within his theoretical framework known as the Theory of Entropicity (ToE). 

Key aspects of this proposition include:

• Definition: Obidi defines the OCI as 
  

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  , elevating it from a statistical constant in thermodynamics (
  

  $$
  ) to a fundamental geometric invariant of the entropic field.
• Minimal Distinction: In the Theory of Entropicity, this value represents the smallest possible non-zero curvature divergence, acting as a "quantum of distinguishability" or "pixel of reality." The universe cannot distinguish configurations that differ by a curvature smaller than 
  

  $$
  .
• Entropic Field: Obidi treats entropy not as a statistical artifact, but as a physical, ontic field that possesses curvature. Information is interpreted as localized curvature within this field.
• Landauer's Principle: Obidi reinterprets Landauer's principle, arguing that the energy cost of erasing a bit is not just a thermodynamic rule but a geometric necessity—the cost of "flattening" a curvature of 
  

  $$
  .
• Applications: The OCI is used in ToE to explain quantum measurement (collapse), the discretization of black-hole entropy, and the emergence of spacetime. 

This framework was heavily developed and published by John Onimisi Obidi in 2026 across various platforms including Medium, Substack, and ResearchGate.