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There are no inputs needed to resolve these expressions.

• 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.
• n_Lc describes the count of l_f* representative of a change in position of light measured with respect to the observer’s frame of reference.
• n_Lo is the count of l_f observed with respect to the observer’s frame of reference.
• n_Ll is the count of l_f measured with respect to the observer’s frame of reference.
• n_L, n_M and n_T are physically significant discrete counts of l_f, m_f and t_f respectively.
• Q_L is the fractional portion of a count of l_f when engaging in a more precise calculation.
• l_l is a measure of length with respect to the observer’s measurement frame.
• l_o is the observed length subject to the effects of motion and/or gravitation.
• 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.
• t_l is a measure of time in the local frame of reference.
• t_o is the observed time subject the effects of motion and/or gravitation.
• v is velocity measured between an observer and a target.
• 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.

The argument for a description of the distortion of measure realative to a gravitational mass is an outgrowth of existing arguments presented in the section regarding the contraction and dilation of measure with respect to an inertial frame. Notably, that argument begins with the Pythagorean theorem written in a nomenclature of discrete units and then demonstrates that the effects described by relativity are better resolved as a background independent geometry.

We recognize that the fundamental measures are physically significant references as demonstrated by measurement of a length contraction effect unique to discrete measure. In that there are no subfeatures to references, references cannot contain additional features such as curvature. What we perceive and describe as curvature is a count difference Q_L, which reflects an increasing loss in measurable space as we consider distances nearer a center of mass.

It is with respect to this physical foundation that the presentation for the distortion of measure with respect to a gravitational mass is made. More specifically, this approach begins with a quantized form of the gravitational constant (fundamental measures multiplied by a count thereof) and is then reduced. The approach differs from prior considerations in that we consider not a specific relation, but all possible relations between the lower and upper count bounds of respective fundamental measures.

Secondly, the Measurement Quantization (MQ) approach clarifies why singularities do not occur. Such that both SR and GR implementations consist entirely of count terms and such that all count terms contain values between or equal to one and the Planck frequency, undefined results are not possible.

Thirdly, this shared, external set of physically correlated terms allows us to then compare count terms resolved with respect to an inertial frame with those of a gravitational frame to demonstrate equivalence. This is a feature of MQ not previously afforded.

The physical and numerical equality of these two frames establish the basis for a Principle of Equivalence. Therein, the correlation allows us to then extend the geometry associated with an inertial frame to that of a gravitational frame and vice versa.

It deserves mention that the ratio in each expression describes not just a bound, but a frame of reference. The term n_Lc identifies the count bound corresponding to the speed of light. Conversely, n_Lr identifies the count of l_f between the observer and a phenomenon. The two expressions describe physically equivalent count ratios.

MQ is a nomenclature that side-steps modern field theory to describe the laws and constants of nature in terms of references. The laws and constants of nature exist because of the difference between the discrete Measurement Frame of the observer and the non-discrete Target Frame of the universe.

In addition to a lengthy body of experimental support, we also note that our very understanding of references corresponds and defines these two frameworks. That is, a self-referencing system of measures exists because there exists an external frame (the universe) against which the internal measures are defined. This external frame in turn predicates discreteness and creates the bounds and relations between the measures.

In contrast, the universe has no external frame and as such is non-discrete. These observations complete a description of the laws and constants of our universe, why they exist, why the values are what they are and why the universe appears as it does.