Kings had absolute power so they did not need to conspire to maintain their power. Exercising ruling class power within a democracy requires secrecy and generations of brainwashing. The 1% cannot control the 99% if the 99% know that the system benefits the few and not the many. The 99% are educated to see the “honor” in order, inequality, and blind obedience.
The easiest way to prove that the Empire exists is to use science. The Empire has published a lot of fake science that it cannot walk away from. Oil geology is an ideal target since no one has any emotional attachment to geology. The most profitable oil companies are using science which is absent from the scientific literature. Scientific literature that was produced by government organizations who had to know about that science in order to avoid publishing any data which might undermine or reveal the secret science. If you are protecting secret science then obviously you have to know what the secret is before you publish.
If a science organization censors or falsifies data to protect the secrecy of private science (knowledge held by a few) then it is guilty of conspiracy. American agencies like the US Geological Survey have lied.
American science is controlled for either economic reasons or to produce technology to defeat anyone who has a better form of government. The American people cannot embrace another form of government if there are no other surviving forms of government.
American science says something is black for the last 100 years and you prove it is white. American science has 100 years of papers which are lies. It is that simple to prove the existence of the Empire.