Natural Qubit Matrix of Primary Elements of Matter

The arithmetic limits of natural bit calculations are strictly established. The natural quantum metric system has been developed. Only seven scaling units that generate thirteen invariant values are necessary and sufficient for an accurate estimation and a mutual coordination of the fundamental constants of quantum physics. For the first time, the calibration constants of quantum physics were obtained, calculated and identified analytically with almost an absolute accuracy, which is limited only by a bit capacity of a computer. The basic constants of quantum physics are, in fact, the dynamic parameters of the functional relationships of the transcendental numbers PI and E with natural numbers, which draw a holographic picture of the motion of spherical wave fronts.


Introduction
The first attempt to develop the absolute metric system was made by Gauss in the early nineteenth century.An attempt was unsuccessful due to the inconsistency of parabolic, elliptical and hyperbolic geometry.The inverse logarithmic relationships of the transcendental numbers PI and E resolve this problem and create the absolute metric without any artifacts and without measurements at all.It suffices to postulate the number PI as the universal unit of space and the number E as the universal unit of time.Then the first derivative of PI by E can be considered as a unit of speed, and the second derivative is the unit of acceleration.Geometrically, PI is the perimeter; E is the diameter of the space-time sphere.E/2 is the radius, 4*PI*(E/2)^2 is the surface of the sphere, and 4/3*PI*(E/2)^3 is the volume of the sphere, PI*(E/2)^2 is the surface of a circle, N*(PI*E^2)/4 is a discrete set of the cylinder volumes.A functional relationships between these space-time geometric parameters and an infinite set of integers N constitute the basis of the natural [E...PI] binary calculations of the parameters of wave motion [1][2][3][4][5].
The basic principles of universal arithmetic and geometry were developed by Newton, Leibniz and Euler at the beginning of the eighteenth century.The principles led to the creation of the differential calculus and analysis: Unit 1 generates a natural set: 1+1+1+... = 1... (N+1).There is no absolute infinity.Unit 1 and a natural set generate the inverse natural set: 1/(1+1)...1/(N+1).There is no absolute zero.Unit 1 is a quantum of the progressive natural set.Units 1/(N+1) are the quanta of the inverse natural set.An inverse natural set generates a universal spatial unit PI = (1+1)*Sum{d(1/N)/Sqrt(1-1/N^2)} as a circle perimeter.An inverse natural set generates a universal temporal unit E = (1+1/N)^N as the base of natural logarithms.
The modern science has emerged after the discovery of logarithms.But it was impossible to resolve the fundamental problems of infinitesimal calculus before the discovery of the laws of thermodynamics and electrodynamics, from which an approximate scaling unit of temperature K (kelvin) and a scaling unit of the rotational speed C (the speed of light) were obtained.It will be shown below that K and C are essentially fundamental mathematical units of the inverse natural calculus, such as PI and E of the standard analysis, and they can be obtained analytically from the mutual functional relations of the transcendental numbers PI and E. As the result, all other constants of quantum physics can also be obtained analytically, and their physical meanings can be explained geometrically.

Arithmetical limits of natural computations
Any two numbers can be a basis of the calculation system, for example binary [0...1], decimal [0...9], quantum binary [0.000>...The 6-bit integer 42331 and the 16-bit integer 4233108251307479 are prime numbers.This fact limits an accuracy of computations of the hyperbolic functions Cosh and Sinh in the decimal calculation system with floating point.
The characteristic feature of natural differentials (ND) is an appearance of very long sets of digits 9.It is obvious that 0.9999 ... = 1 and 9.999 ... = 10.An infinite sequence of 9 is generated as the integer B = 602214183 and the integral of Avogadro as BS = Sum {B/10^(3*N+11)} = 0.0060281699999999 = 0.00602817.
The characteristic feature of natural medians (NM) is an appearance of the "golden sequence" 1618 over 12-bit [PI...E].This fact limits an accuracy of the natural median computations of harmonic functions Cos and Sin in decimal system with floating point.