Fu-Xi Constant Ψ = 1/√3 - A Real Universe Constant Different From Classical Λ

This study presents an important mathematical- physical constant called as the Fu-Xi Constant

Ψ = 1/√3 = 0.5773502692...,

which is a dual with Euler's Constant 

            γ = 0.5772156649....

I found that the monodromy ψ is a real Universe Constant, which is the Cardinality of Quantum Gravity, and is more important than Euler's Constant. This paper reveals a fact that all new theoretical physics constants (see Zhi-An Luan's results presented in CAP Congress 2019, APS Mach Meeting 2021) are introduced from the Fu-Xi Constant Ψ = 1/√3:

1. Planck (reduced) Constant h =2π√3 = 2π·Ψ^-1,

2. Boltzmann Constant k_B =8√3 = 8·Ψ^-1 , Extended Boltzmann Constant k_B^N = N·2√3 =N· 2Ψ^-1 (N=1, 2, 3... ∞),

3. Newton's Gravity Constant G= 2/3 =2Ψ²,

4. Fine-Structure/ Hubble Constant α/H₀ = Ψ^-1 - 1,

5. Critical Density Constant ρ_c = √3/2 =Ψ^-1/2 ,

6. Irreducible Normal Projection in P¹: X =2√3 = 2Ψ^-1.

In fact, this Fu-Xi Universe Constant is a unique Critical Value of Quantum Mass, which is described as following:

Using the Generalized Newton's Laws Profile functional: Ρ(m)= G^-1 (m)= 4m(1- m²), one can obtains that:

P^'(m) = 4- 12m² =0 ⇒ m² = 4/12 = 1/3 ⇒ critical mass M_c = 1/√3 = Ψ. At the mass M_c , we show that

the critical velocity V_c =4(1- (1/√3)²) = 4(1-1/3) = 4x2/3 = 8/3 = 2.666666666 ... = 2 + G.

Using the Schwarz Lermma in a maximal complex torus (i.e. called Fu-Xi Eight-folds Holography) {z € C; 0< |z| <2}, I prove that this Unique Real Universe Constant is just an extremal holomorphic retraction's kernel- Retract (kernel).

The monodromy involution of the Fu-Xi Universe Constant Ψ=1/√3 in S² manifold is juct the coherent Light Velocity C= 3 x... km/s.

This real Universe Constant Ψ is a unique Root of Nature and Life.