Messing with the Lagrangian

As opposed to Lagrange numbers. I know they are connected, Lagrange numbers likely come from applying Lagrangian systems to estimation theory.

OK, Why am I doing this? I want the Euler Lagrange equations converted to finite system, convert the function q(t) into a Lucas sequence, put that into the hyperbolic, show all that match points between Boltzmam, Temperature, chemical potential, the Hamiltonian, the coupling constant, kinetic energy, uniform convergence ot the q(t), relationship between time and quant number. Then relate the boson and fermion to their nature ratio of hot wythoff moves to total moves, adjust the unit one with kT, to account for an adapted system that adds motion to obtain uniform convergence, and then establishes the sample rate needed to remain adiabatic. Boltzman is mostly about the change in elasticity of an ensemble of colliding bubbles. Then show that Shannon sets minimum action and all this resolves into the finite precision Lagrangian. It works because with finite precision any multi-dimensional system can be decomposed into a recursive order of two  dimensional systems, and still be within precision. The TOE is a real thing, the basics of adapted system with no empty space.  Believe it.

For example. When we deal with a Lucas sequence, q(n) = P*q(n-1) + Q*q(n-2), then we get the asymmetric Hyperbolic condition.  When we regroup the parameters, we should get, on the right, a 1/(kT)^2, or equivalent, which is the coupling energy.  The Shannon channel rate changes.  The chemical potential which is fermion native hot move ratio will imply kinetic energy in the variable Shannon calls noise.  The numerators, information rate are the hot moves for bosons, and signal the hot moves for fermion that retain stability. But every thing goes back to normalized two period lookahead, but the derived base forms a convergent series in b and 1/b for the Lucas sequence.  We shouod get boson and ferion statistics. Stuff like that should happen.

The final outcome will be:

[1-(1/b)^(1/N)] + [1+b^(1/N)]  = 1/N for some finite N which makes the power series in b and 1/b match. The difference 1/N is the coupling energy, and should include kT. The error after order N is the uncertainty in the finite self adapted system. This is the finite log solution in the TOE, and I think it will work for the general case of adapted, finite  systems. Does this get us all the powers of powers, or do we have to apply this recursively? Dunno, you tell me.

Why am I tell you all this? Because friggen brilliant mathematicians should know this is the next step in the unification.  There is going to be a bunch of next steps as we redo math and science to match the TOE. So, you brilliant young, soon to be wealthy mathematicians and physicists; this is what I am doing, please beat me to it.