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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.
• 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).
• ħ is the reduced Planck constant, 1.054571817 10^-34 m² kg s^-1. When accounting for the Informativity differential at the upper count bound, this term is not italicized (i.e., ħ=1.0545349844(45) ^-34 m² kg s^-1).

The fundamental expression can be resolved with respect to the MQ expressions which describe the fundamental measures, more precise versions of Planck's unit expressions. The fundamental expression describes the simplest relation between the three dimensions. With respect to the Measurement Frame of the observer, the expression is also known as the Planck momentum.

In principle, the fundamental expression is a derivative of the three fundamental measure expressions. Importantly, the fundamental measures differ from those of Planck's unit expressions. They are more precise, accounting for a length contraction effect associated with discrete measure. Moreover, both the fundamental measures and the fundamental expression do not contain the reduced Planck constant.

Notably a solution to the fundamental expression cannot be solved with respect to existing classical expression. The reason for this, from a general point of view, is that classical mechanics and all the expressions that constitute this discipline, are defined with respect to the discrete Measurement Frame of the observer. This frame is self-referencing. And in practice, this is why Planck was unable to resolve a derivation of the Planck unit expressions as a function of more fundamental component terms.

We succeed with the introduction of the non-discrete Target Frame of the universe. Using the Pythagorean theorem to describe the relation between the discrete Reference, Measurement and non-discrete Target frames, we offer a new discrete description of gravitational curvature. This is used to resolve an expression for G in terms of the fundamental measures. And along with the expression for the speed of light and that of Heisenberg's uncertainty principle, we have all the component features needed to derive the fundamental expression and each of the fundamental measures without self-referencing source measures.

We call expressions written in terms of the fundamental measures example of the Measurement Quantization (MQ) approach. Notably, it is the associated counts of these fundamental reference measures that is most significant, recognized in expressions such as the uncertainty principle, whereby the measure terms all cancel upon reduction leaving only the counts. For this reason, we identify comparisons of dimensions as a function of their associated counts, that being, their:

• length frequency c=l_f/t_f
• mass frequency m_f/t_f
• frequency 1/t_f
• length-to-mass frequency l_f/m_f.

Yes, we will sometimes describe frequency as a function of the associated measure terms, but the use of the term 'frequency' is specifically a description of the associated counts for each reference dimension.

Most physical constants can be shown to be a composite of the fundamental measures. The fundamental measures include the fundamental constantθ_si. Example physical constants written using only the fundamental measures include:

• G=(l_f/t_f) (l_f/t_f) (l_f/t_f) (t_f/m _f)
• ħ=2θ_sil_f
• H_U=2θ_si.

The fundamental expression cannot be reduced further as it consists entirely of references. That said, there are circumstances whereby all terms reduce to a logical unity (i.e., 1=1). This is often a result of a Target Frame definition, as in such cases one is working only with counts.