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• l_f, m_f and t_f are the fundamental measures, more precise expressions for Planck’s units – length, mass, and time – that consider the effects of length contraction associated with discrete measure.
• θ_si can be measured as the polarization angle of quantum entangled X-rays at the degenerate frequency of a maximal Bell state. As an angle θ_si=3.26239 rad ± 2 μrad; as a momentum θ_si=3.26239030392(48) kg m s^-1 and with respect to the Target Frame, θ_si has no units. The relation of angle and mass is mathematically demonstrated, as well, by No-Ping Chen, et. al.
• Q_L is the fractional portion of a count of l_f when engaging in a more precise calculation.
• n_Lr describes the count of l_f representative of the position of an observable with respect to the frame of a center of mass.
• n_M is a count of m_f representing the mass corresponding to a gravitational field.
• c is the speed of light which may also be written as c=n_Ll_f/n_Tt_f=299,792,458 m/s such that n_L=n_T=1 is physically significant.
• G is the gravitational constant, 6.6740779428(56) 10^-11m³kg^-1s^-2 such that its value considers the effects of length contraction associated with discrete measure at the upper count limit. Italicized G identifies a measure not at the limit (e.g., G=6.6738448362(53) 10^-11m³kg^-1s^-2 at the blackbody demarcation).
• M is a mass.
• v is velocity measured between an observer and a target.
• r is the distance between an observer and the center of a gravitational mass.
• m_l is a measure of mass with respect to the observer’s frame of reference.
• m_o is the observed mass subject to the effects of motion and/or gravitation.

The quantization crossover describes that point where the count of m_f per increment in elapsed time t_f exceeds the Planck frequency. Importantly, the phenomenon of gravitational curvature associated with this bound is also constrained. Thus, the quantization crossover - a function of the density profile of a system - offers one means to directly assess the physical significance of the upper bound to baryonic mass density.

In consideration of the expressions for special and general relativity, there are values that can be assigned to terms in the denominator of the speed parameter that produce singularities. Such expressions fail to provide physically significant descriptions of observed phenomena.

Informativity is a field of science that applies the principles of Measurement Quantization (MQ) to the description of phenomena. But, differing from the usual classical understanding of a non-discrete spacetime, MQ offers support demonstrating that measure with respect to the Measurement Frame of the observer is discrete while measure with respect to the Target Frame of the universe is non-discrete. This physically substantiated understanding not only allows us to resolve expressions and values for the physical constants and laws of nature, but resolves and obviates those conditions that lead to singularities. That is, with a discrete model composed of counts of fundamental measures, there is a clear physical correlation with measured phenomena as to where bounds to measure begin and end (i.e., 1 to the Planck frequency). And, when we describe the upper count bound to mass density, we also resolve the upper count bound for the speed parameter without singularities.

To briefly review, MQ is a nomenclature whereby measure is written instead as a count product of fundamental measures and counts of those measures. When using a discrete description of gravitational curvature along with MQ expressions for Heisenberg's uncertainty principle, escape velocity and the speed of light, we observe that the measure terms cancel out leaving us with only counts. Further analysis of the physical significance of this reduction demonstrates the three properties of measure: discreteness, countability and in reference to three frames of reference. Most important to this discussion is countability. That is, all measure is physically significant only where a whole-unit count of a reference measure. Any non-integer portion of that whole-unit count Q_L is lost at each moment in elapsed time t_f.

To describe this, resolving the relation between a count of fundamental units of length with respect to a count of fundamental units of mass, we find that n_Lr > 2n_M.

Organizing this relation into the same form taken by the speed parameter with respect to a gravitational field, then

And as such we see that the observed mass m_o can never have a magnitude that reaches infinity,

The role of upper and lower bounds fills a gap in modern theory that has not yet been considered. We leave with an example, the quantization crossover, an expression that describes what is presently called the dark matter phenomenon. The quantization crossover specifically addresses the flatening of star velocities across a galactic disk. A full description of all features of the dark matter phenomenon can be found here.