What Real Experiments Explore the Speed of Gravity?

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The discussion centers on identifying real experiments that investigate the speed of gravity. A thought experiment is presented comparing scenarios with and without the Shapiro delay, highlighting the implications for light and gravitational wavefronts. The reference to Kopeikin and Formalont's work suggests a controversial approach to understanding gravitational wavefronts. Participants seek clarity on the nature of these wavefronts in relation to gravity's speed. The conversation emphasizes the need for empirical evidence to support theoretical claims about gravitational phenomena.
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Can you advice a good list of real experiments related to speed of gravity?

And here is simple thought experiment:

version 1 with Shapiro delay
.....................|
.....................|
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(source of gravitational and light wave)..>......(star)
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version 2 without Shapiro delay

As I understand wavefront of light would look like in version 1.
But which type of wavefront would have gravitational wave?
 
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Kopeikin and Formalont [http://arxiv.org/abs/astro-ph/03110632003] is one example. It is, however, controversial.
 
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Thread 'EPR revisited'

In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...
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