First, a recap of the scenario at which we live in.

1) The structure of modern physics is built with a vital dependence about
the certainty of "universal properties" of three fundamental constants,
which are c, h and G.
Any failure of their universal character would completely ruin the physics
developments of the last 100 years, forcing to establish their reach as local.

2) So far, the known "visible" universe (Hubble's one) has a radius of about
13.5 bly (1.28×10^23 km) and involves a linear backward timeline of about
13,500 millions of years (1.35×10^13 years), all of this referenced to the
Earth. These are distances and age in the macro-cosmos (since us).

In the world of the micro-cosmos, depth challenging our observational
power, start at 10^-10 mt (used as average size of atoms), continues
down to 10^-15 mt (the only accepted size for the classical radius of
the electron, not the real as a particle), and goes down hundred of
thousand of times for "elementary particles and sub-particles".

3) The old methods for measuring the three constants have evolved
substantially in the last 100 years. Now, national organizations like
NIST at US, have developed techniques similar to those used in other
countries to measure them, and the results are accepted as universal
by a worldwide accepted organization BIPM (Bureau International des
Poids et Mesures), with more than 63 member states (like US).
The MKS system of units (SI) is maintained at BIPM, with member's
agreement.

Besides many other units of measures and values, values of constants
like c, h, e, k, NA, cesium clock preferred resonant frequency and many
others are displayed at the BIMP site for everyone who want to check them.

https://www.bipm.org/en/measurement-units/si-defining-constants

With the above background, now to the point.

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Chapter 1: the measure of the value of c.

The last (1983) and currently accepted value of c is 299792458 mt/sec,
with ZERO ERROR, as it was accepted to write it into stone.

And it has to be exact, with zero error, because the SI meter unit is valued
as the path traveled in euclidean space during 1/299792458 seconds.

Do you see a circular method here? In similar ways, other values of
constants in the MKS SI standard are developed.

Now, the preferred method to measure c is laser interferometry, measuring
null results of interferometry between two paths of a laser beam (one direct
and the other diverged and refocused using mirrors).
See https://en.wikipedia.org/wiki/Speed_of_light#Electromagnetic_constants

Now, the centuries old method of measure one way velocity, V=X/T, has been
abandoned in this method, as X is replaced by N wavelengths and T by the
multiple ticks of an atomic clock.

The problem here is recursion, and always has been. There are no independent
sources of length and time to measure c. Time unit of 1 second is tied to the
measurement of the frequency of a cesium atomic clock (10^-12 stability), but
there is not a source of higher quality to clock the frequency meter. So, a time
unit is WHAT IT IS, as defined at BIMP, and unquestionable by any mortal.

The problem with distance X is that its measurement is poisoned by the null
results at the detector in the interferometer. There is not a way to account
how many wavelengths have been skipped to get a null result, and the error
is contained in the range of one part in 10^10.
And I quote BIMP:

"The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s–1, where the second is defined in terms of the caesium frequency ΔνCs."

And this is a blatant recursion, a loop. The meter is defined by the speed of
light c, which is defined by the value of one meter, obtained by multiple wavelengths of a cesium clock, which is used to time the value of c, etc......

So, no direct and one-way measurement of the speed of light has been performed and its value is settled as exact, without chances to dispute it.

I wonder what would happen with a measurement made 1bly far away. Would
it give the same value? And 10 bly far away? And, also, how would we know
the results? Waiting billion of years till they arrive at Earth? Nonsense.

So, the unobservability of such UNIVERSAL CONSTANT put its value in the
realm of fairies and their tells.

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Chapter 2: the measure of the value of h.

The current accepted value of h is 6.62607015 x 10^–34 J/s (BIMP, NIST).

Leaving behind the century old value determined by Planck, relating it to a
relationship between NA and R (R is the Regnault’s constant), whom also
found the value of kB, the latest method involves several values of constants
within the MKS SI. Of course, c is one of them.

I quote, for the sake of brevity, this article:

Measurement of the Planck constant at the National Institute of Standards and Technology from 2015 to 2017
https://iopscience.iop.org/article/10.1088/1681-7575/aa7bf2

"This article summarizes measurements that were carried out with the Kibble balance, NIST-4, at the National Institute of Standards and Technology (NIST) from December 22, 2015 to April 30, 2017. A detailed description of NIST-4 and a first determination of the Planck constant h with a relative standard uncertainty of 34x10^{-9} can be found in [1]."
.....................
"The result is based on over 10,000 weighings of masses with nominal values ranging from 0.5 kg to 2 kg with the Kibble balance NIST-4.."
....................
"Common to NIST-1 through NIST-4 is that a wheel is used for both the balancing and moving mechanisms. The wheel pivots about a knife edge collinear with the wheel's central axis. A measurement coil and test mass are suspended from one side of the wheel while a tare mass is suspended from the other via multi-filament bands. The tare mass includes a small motor consisting of a coil in a permanent magnet system, similar in design but much smaller than the main magnet, for generating a force to rotate the wheel. The benefit of a wheel versus a traditional balance beam is that the former prescribes a pure vertical motion for the suspended coil whereas the latter traces an arc.

The measurement is performed in two modes: force and velocity mode. In force mode, a current I in a coil with a wire length l immersed in a radial magnetic field with magnetic flux density B is controlled such that the balance wheel remains at a constant angle chosen by the operator. While the balance wheel is servo controlled, a mass standard with a mass m, typically 1 kg, can be placed on or removed from the mass pan."
..........................
"Three mounting plates made from $25.4~$ mm thick aluminium, each supporting one interferometer and turning mirrors, were mated to the base plate through kinematic mounts."
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So, laser wavelengths, newtonian mechanics and maxwellian electromagnetic
forces and else are used in this complex arrangement.

Once again, recursive methods are at plain sight and the questions about how
it would perform very, very far from here are the same as with c.

Universal constants? I highly doubt it.

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Chapter 3: the measure of the value of G.

G and c are vital values for relativity. Any fail of its universal constancy makes
the theory collapse.

I'm using this article, very new, among many available:

Precision measurement of the Newtonian gravitational constant
https://academic.oup.com/nsr/article/7/12/1803/5874900

"The latest recommended value for G published by the Committee on Data for Science and Technology (CODATA) is (6.67408 ± 0.00031) × 10^−11 m^3 kg^−1 s^−2 with a relative uncertainty of 47 parts per million."
......................
"The Newtonian gravitational constant G, which is one of the most important fundamental physical constants in nature, plays a significant role in the fields of theoretical physics, geophysics, astrophysics and astronomy. Although G was the first physical constant to be introduced in the history of science, it is considered to be one of the most difficult to measure accurately so far."
....................
"To date, there is no quantitatively theoretical relationship between the Newtonian gravitational constant and other fundamental constants. Scientists can only measure the gravitational constant through Newton’s law of universal gravitation. One of the greatest difficulties in any G measurement is determining with sufficient accuracy of the dimensions and density distribution of the test mass and attractor mass."
.........................
"The phenomenon of inconsistent measurements of G makes many scientists puzzled [45–49]. It is most likely that there might be some undiscovered systematic errors in some or all the G measurements. Our group has been dedicated to the precise measurement of G for over thirty years. In 2018, G values measured with two independent methods, the time-of-swing (ToS) method and angular acceleration feedback (AAF) method, were obtained with the smallest uncertainty reported to date and both agreed with the CODATA 2014 recommended value to within two standard deviations [50]. The thirteen values of the Newtonian gravitational constant [30–44,50,51] measured after 2000 are listed in Table 3 and shown in Fig. 2."
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So, science doesn't know the real value of G and, even more, if it poses universal constancy (within error margins).

The same questions about its value very, very far from here, remains as with
the first two.

So, I wonder. How solid is the building of physics upon these facts of dubious
universality of the three major constants in physics?