Elysia
First Landed 2128
Elysia started out as a company planet owned by REC, formally a British registered company (as all companies must be registered to a nation). All planetary settlements are expensive so they generally have to have an equally large benefit to be financed. For REC, it was seeking a secure location it could develop the Impossibility Engine and to minimise government interference, industrial espionage and general intellectual property theft.
Elysia was chosen due to its similarity to Earth in mass, year length and even its 25 hour day. It was otherwise hostile, with no oxygen and an average temperature of 80C, but if terraformed it would be very Earth-like. Unfortunately, terraforming was just a dream, and factored in as a gift for the future, but no one expected to see it in their own lifetime, never-mind 15 years. To establish a base in the horrendous environment, REC pursued an aggressive research program into exo-planet construction, which rapidly got renamed 'Double Diamond Dome' technology.
Much to their critics surprise, the REC supported the call from those seeking to gain independence under the Settlement Act 2109. Some people had thought that the REC would hold the population at 19,000 but REC kept building domes and encouraging scientists and their families to join the REC on this planet, rapidly pushing the population to over 22,000. The REC actively changed contracts that allowed the local security force to become a local Police force, they had hired ex-Policeones, and setup a Parliament lower house and a Senate upper house. As this was done prior to official recognition of independence, out of respect, the Astry did not send its usual fleet of HAAS NorAm Class ships to 'watch over' the transition process.
Independence was gained in 2132, a phenomenally short time but after that the REC plan became clear and it officially reregistered the company as Elysian. Cynics were disgusted, declaring that it was all just a 'money making political manoeuvring'. The REC gets highly annoyed with this tabloid journalism, especially the British Press that bemoaned a betrayal, as if the rest of humanity was less important than their readership. The REC frustration is born out of the silent implied second statement. It fully admits that yes, it was 'money making political manoeuvring' but that it was also 'a good thing'.
Government Business
The REC remains highly integrated into the Elysian economy, but with a more secure research base, a scientific population and a dedicated political body, the REC was free to develop the Impossibility Engine securely. Britain also remains the Earth hub for the REC, and a lot of the wealth generated was paid in tax to both governments, with Elysia putting the extra wealth into their own wealth fund. After all is done, the British are better off, the Elysians are happier and better off and the REC is richer. On top of that the entire human race benefits from the Impossibility Engine.
Terraforming
Elysia dome technology is high quality and viewed as completely reliable and safe. The REC and Regal Calculus are companies with very different philosophies and generally don't get on well. However, Regal Calculus was successfully and rapidly terraforming their company planet Initium Novum (also founded 2128) with Oxgae, although it still takes 10 years. Consequentially, the businesses agreed a technology swap that allowed both companies to develop their planets faster. The Rec got Oxgae while Regal Calculus got domes. Elysia is now a very Earth like planet.
EI Elysia
Elysia was founded with an EI that views the planet as its body. It is an integral part of Elysia and runs a lot of the civil service. The EI Prime also is based on Elysia but is an entirely separate person.