Cohomology of the Generalized Newton's Laws Manifolds

I describe the triplet (G, h, k_B) as a kernel of the Generalized Newton's Laws, where G- Newton's Gravity Constant G=2/3 = 0.666 666...; h- Reduced Planck Constant = 2π√3 = 1.088279619x 10 ...; Boltzmann Constant k_B = 8√3 = 1.385640646 ... . Above three fundamental constants as exact non-dimensional monodromy varieties have deep importances in theoretical physics. I also found that gcd(h, k_B) = gcd (2π√3, 8√3) = 2√3, which is a projection P¹ in classical Fano manifolds. This paper will cast new extended Fano complex 2-d manifolds based on an important fact: the first natural sheaves are constant sheaves. These all three classical constants: G, h, k_B recast as real constant sheaves such as G_i, h_i, k_Bi i = 1,2,3, ..., such that the Boltzmann sheaves k_Bⁿ =2√3 × n, where integer n = 1,2,3,4, ... ∞; the Planck sheaves h^μ =2π × μ, where real numbers

μ = 0, √n^-1, ... √5^-1, √3^-1, 1=Id, √3, √5, ... √n ... ∞.

Theorem 1. Using Courant Algebroid (CA), there exist an important isomorphic map - circle boundary length l = 2√3×n× tan(π/n)|_n→∞ = 2π√3 = h^μ=√3 = h reduced Planck Constant.

I give out all energy deformation retract with coherent sheaves of the Planck Constant. Instead of working with functions of the energy, I define a new coordinate z by

z² = - E, where real z corresponds to the "forbidden" region of negative E. In fact this z is just the r_coh variety in the Generalized Newton's Laws, and r_coh² is just the speed V. Hence the representation of momentum can be showed as extended Planck sheaves h^z = 2π × z = 2π × r_coh, such that, sequences 2π√0, 2π√5^-1, 2π√3^-1, 2π×1, 2π√3, 2π√5, ... ,2π√n=∞. Using these geometry data and the Courant Algebroid with extended Dirac operators TX + T^*X in a maximal complex torus, I give follow second result:

Theorem 2. The Planck Constant sheaves have important deformation retract form:

{2n ± √3 + (2n ± √3)^-1} |_n=1 = 4; {2n ± √5 - (2n ± √5)^-1}|_n=1 =4. Then the maximal limit light speed is 4 rather than c =3...km/s.