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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 Measurement Quantization (MQ) argument for a description of the distortion of measure relative 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 counts of the fundamental measures and then demonstrates that the effects described by relativity are more precisely resolved using MQ. Moreover, their physical instantiation is then rooted as an emergent geometric property of the expanding sphere of information which constitutes the universe.

We recognize that the fundamental measures are physically significant references as demonstrated by measurement of the contraction of length, a geometric property of the discrete Internal Frame of the universe. In that there are no subfeatures to references, references cannot contain additional features such as curvature. What we perceive and describe as curvature is the loss of the fractional count difference Q_L with each increment in elapsed time.

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 MQ approach clarifies why singularities do not occur. Such that both the 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 to classical mechanics.

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

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 approachs classical mechanics without the use of field theory. MQ is immensely successful, able to derive expressions and values for the physical constants entirely in terms of the fundamental reference measures. This is achieved as many of the physical constants are resolved by taking the difference between the discrete Internal and the non-discrete System Frames of the universe.

Finally, we bring to the reader's attention that relativity is an approach which identifies measure in terms of frames of reference, that of the observer and that of the observed phenomenon. MQ recognizes two additional frames of physical significance, the System and Internal Frames of the universe.

Like SR and GR, the System Frame resolves the properties of measure as an emergent property of the expanding sphere of information which constitutes the universe. One feature of that frame is a physically significant set of fundamental measures, each which have significance relative to the Internal Frame. All observations are then some count of these fundamental reference measures. Conversely, the universe has no external reference and as such measure of those same phenomena relative to the System Frame is non-discrete.