Who has Proposed that ln 2 is a Curvature Invariant?

 John Onimisi Obidi has proposed that 

$\ln 2$

acts as a fundamental curvature invariant, termed the Obidi Curvature Invariant (OCI), within his framework known as the Theory of Entropicity (ToE). 

Key details regarding this proposal include: 

• Fundamental Constant: In the Theory of Entropicity,
  

  $\ln 2$
  is considered the "quantum of distinguishability" or the minimum change in curvature for the entropic field.
• Physical Meaning: The OCI,
  

  $\ln 2$
  , defines the "stiffness" of the entropic field, and erasing a bit is interpreted as "flattening" a curvature of
  

  $\ln 2$
  .
• Context: This proposal attempts to connect general relativity (curvature) with thermodynamics (information/entropy) by elevating a statistical factor (
  

  $k_B\ln 2$
  ) to a fundamental geometric property. 

Note: The results also mention "

$L^{n/2}$

-curvature," which refers to a standard

$L^{n/2}$

-norm of the Weyl tensor (a scale-invariant integral) in differential geometry, specifically studied by authors like Gursky, LeBrun, and others. However, the specific proposal of "

$\ln 2$

" ln 2 as a fundamental curvature invariant is attributed to John Onimisi Obidi. 

Appendix: Extra Matter 

John Onimisi Obidi

proposed that ln 2

$\ln 2$

(the natural logarithm of 2) is a fundamental geometric curvature invariant. 

In his framework, known as the Theory of Entropicity (ToE), Obidi introduces the Obidi Curvature Invariant (OCI), which elevates ln 2

$\ln 2$

from a statistical conversion factor to a fundamental constant of the universe's geometry. 

Key aspects of this proposal include: 

• Entropic Geometry: The OCI ln 2 (
  

  $\ln 2$
  ) is described as the "quantum of distinguishability" that defines the structure of reality.
• Derivation of Physical Laws: Obidi uses this invariant to derive Landauer's Principle and the Landauer-Bennett Cost from first principles, arguing that erasing a bit of information is equivalent to "flattening" a curvature of ln 2
  

  $\ln 2$
  in an entropic field.
• Gravity as a Gradient: In this theory, gravity is viewed as a gradient within the fundamental entropy field rather than a standard [statistical] force.