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• 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.
• 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.

• 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 a change in position of an observable measured with respect to the observer’s frame of reference.
• S is the symbol assigned to the unknown constant when resolving a description of gravity. The symbol is replaced with θ_si.
• r is the distance between an observer and a target.
• 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).

Before we can address discrete gravity, it is necessary to understand the properties of measure. There have been several clues. The clues make up a picture, but the puzzle pieces do not match. It is as though we are missing that piece which connects so many others that we cannot resolve the picture.

Here, we present a series of expressions that resolve the missing piece. Importantly, we do not introduce new axioms. We do not entertain new physics. And we do not introduce concepts new to our classical understanding of nature. Rather, we consider only the existing classical laws we are familiar with in an effort to resolve the properties of measure.

Consider then three expressions. First, Heisenberg's uncertainty principle. Secondly, light, specifically its speed. And third, escape velocity. Next, we introduce an expanded nomenclature we call Measurement Quantization (MQ), a terminology consisisting of fundamental measures and counts of those measures. We do not assume the fundamental measures are physically significant. We do not assume they are countable. And we do not assume any specific value for the counts or the measures. As noted prior, we proceed only with the three expressions, to which we will present in an MQ nomenclature.

With the expressions written using only the fundamental measures and counts thereof, we then take the expressions, combine and reduce. It is in this effort that we are able to resolve the properties of measure.

• Measure is discrete
• Measure is countable
• Measure exists with respect to three frames of reference
  • Reference Frame
  • Measurement Frame
  • Target Frame

This analysis allows us to resolve the minimum count value of each measure. It also allows us to resolve the value of each of the fundamental measures. And it allows us to resolve the underlying structures which contribute to their evaluation.

Most relevant to a description of discrete gravity are the three frames, two discrete with the remaining non-discrete. Only when taking the difference between the non-discrete and discrete frame don we resolve an expression for discrete gravity.

Notably, the derivation is more complex than one might at first expect, best explained in this paper. The most significant challenge in this derivation is avoiding circular logic. To derive new improved versions of Planck's units requires that we also resolve the relation between the fundamental measures. Those relations are unknown, and as is the case with Planck, resolved by comparison, not by derivation. Thus, we find we cannot use Planck's expressions to resolve the properties of measure, as they are physically uncorrelated. We solve that problem by deriving the three expressions above using a new discrete approach to gravitational curvature.

Consider then that given a reference (side a of a² +b²=c²) and a known count of that reference (side b – the distance) then the unknown reference count (side c) will always have a fractional component Q_L which is less than the reference count 1. Given that the fractional count Q_L cannot be measured with respect to the discrete Measurement Frame of the observer, as it is less than the reference, it is conjectured that Q_L is lost at each instant of elapsed time t_f.

When compared to Newton's expression for gravity, the construct describes gravitational curvature with quantum precision. Further, analysis of this expression reveals a new fundamental constant of nature S which is assigned the symbol θ_si not because it is a radian measure with respect to all frames of reference, but because it belongs to a class of constants whose value is the same regardless of the frame of reference. The value can be macroscopically measured as demonstrated by Shwartz and Harris in their experiments regarding the polarization of X-rays in certain maximal Bell states necessary for quantum entanglement. θ_si is known as the Planck momentum. And with respect to the non-discrete Target Frame of the universe - which has no external reference - θ_si has no units at all.

Such that Newton’s expressions are not as accurate, the two descriptions can be set approximately equal to give their relation.

Importantly, this quantum difference is not because either description is improperly implimented, but because of a new form of length contraction, not related to relativity. We call this effect the Informativity differential. It is a consequence of discrete measure as described with MQ. Because Newton has approaced gravity non-discretely using only two frames of reference (implicit), his expressions do not account for this effect.