pith. machine review for the scientific record. sign in
def definition def or abbrev high

omegaCDM

show as:
view Lean formalization →

The declaration fixes the cold dark matter density parameter at 0.26. Cosmologists working inside the Recognition Science framework cite this value when matching the five-candidate count (configDim D = 5) to observed densities. It is introduced by direct numerical assignment with no computation or lemmas.

claimThe cold dark matter density parameter is defined by the assignment $0.26$.

background

The module treats five canonical dark-matter candidates (WIMP, axion, sterile neutrino, primordial black hole, self-interacting DM) as the objects counted by configDim D = 5. It places the cold dark matter density parameter inside the interval (0.25, 0.27) while remaining inside RS-native units where c = 1 and the phi-ladder supplies the mass scale. The module doc states that Lean status is zero sorry and zero axiom.

proof idea

This is a direct definition that assigns the constant 0.26 to the real number omegaCDM. No lemmas or tactics are invoked; the body is a single literal.

why it matters in Recognition Science

The definition supplies the numerical anchor required by the downstream CDMDensityCert structure (five candidates and the band condition) and by the theorem omegaCDM_band that verifies the open interval. It therefore closes the cosmology section to the RS claim that exactly five candidates arise when configDim equals 5.

scope and limits

formal statement (Lean)

  27noncomputable def omegaCDM : ℝ := 0.26

proof body

Definition body.

  28

used by (2)

From the project-wide theorem graph. These declarations reference this one in their body.