Well, despite what you think landing the rocket was a breakthrough. Sure it involved the application of standard techniques in the industry but a combination so executed becomes more than the sum of its parts.

If you want something where SpaceX has blazed trail in science as well as engineering then there's thir work on CFL and more importantly supersonic retro propulsion. It turns out that the bow shock created by the engines is enough to serve as an ersatz heat shield and it protects the rocket when it would otherwise be destroyed during reentry. NASA's studying the data they've recorded for the purposes of applying it to Mars EDL. It's given them a chance to investigate an entirely new EDL technique which is important seeing as the Low-Density Supersonic Decelerator seems to be going nowhere.

>What exactly is the breakthroughs/discoveries that Spacex have made that will justify the claim.

The breakthrough is actually doing it. A lot of space engineers were saying before Falcon 9 that what SoaceX were trying to do was impossible.

Hindsight is 20/20. It's easy to see now what steps were required to pull this off and that clearly those steps were possible. But if it's so clear, why wasn't it done before? The ottoman line is only Must and SoaceX were prepared to get the job done. Nobody else was even trying.

> Please note that landing the rocket does not count. Because I don't think it involved something new, some new technique that was unknown before.

"Answer my question despite my imposition of arbitrary criteria that intentionally make it unanswerable"

Landing the rocket is the first step in figuring out reuse. Its irrelevant that it probably did not involve some scientific breakthrough - in fact it makes it all the more sadder that no-one bothered to do it before. Same situation with Tesla. No breakthroughs there either. Now imagine all the things we can do right now but aren't because no-one is interested in funding it.

If you arbitrarily dismiss things because you "don't think it involved something new" that's a fairly random criteria.

Their unique breakthrough is relighting rocket engines in a hypersonic airflow. Everything else is shoulders-of-giants and design iterations and good project management, but relighting rocket engines like that was an unknown.

Landing is a critical prerequisite to reuse: we can't reuse what we discard.

But the important reusability breakthrough comes in a few months when they do the first reflight of an orbital booster.

Actually there was a lot of new stuff learned especially in the transonic regime.