The cosmic distance ladder is fascinating. At university, we had an astrophysics professor who said his secret worry is that something was broken about the ladder. If you have a wrong assumption close to the bottom, then the error would compound the more you go to larger distances. And you would not just have quantitative errors, such as mismeasured distances, but qualitative errors. The objects you think you are looking at might be something completely different. It is unlikely because the picture we have is consistent. But it could be also wrong and still consistent. The big open questions such as dark matter / dark energy could be the only hints we have that something is wrong.
I'm an experimental particle physicist by training and know that feeling. We never see the particles directly, but reconstruct them in a complex chain. Hits in a detector become tracks, tracks are assigned to particles according to our expectation of how those particles behave. Bunches of tracks are interpreted as decaying heavier particle. Sometimes I wonder if we missed something important in the early days of quantum mechanics and particle physics, and some of the things we think we are investigating don't actually exist, or are subtly different than we think. But we look at the data though our lens, and see what we are expecting to see. My gut feeling says everything is consistent, and experiments match the theory so incredibly closely that it can't be a coincidence, but I don't think there is a mathematical proof. It could be that our theory is just so flexible that it lets us see Higgs particles and top quarks, even though the actual entities are something different. Like when people thought planets move in epicycles.
I know it is likely nonsense, but it is what motivated me every now and then to go back and revisit the basics of our field, like how is a particle state defined in QM, how does it interact with the experiment, how do we reconstruct larger objects, and so on.
Luckily, the bottom rung of the distance ladder, parallax, is only dependent on geometry, and is therefore completely solid. With the Gaia space telescope, there are now parallax measurements almost to the center of the Milky Way.
Having parallax measurements to that distance helps to build multiple versions of the next rung in the ladder (such as Cepheids and the tip of the red giant branch).
i think one of the things astronomers were pleasantly surprised to see was that the Gaia results have indicated that other low rungs of the distance ladder were pretty well calibrated. Most of these are based in some way on stellar evolution, and given that stars can be kind of messy there was always a bit of nervousness that maybe our systematic errors are larger than we think. But the models turned out to be pretty good.
parallax is only perfectly solid before GR. once you accept that space can bend it becomes a lot more complicated (especially given that we currently think ~75% of mass is dark matter which could be bending light without being visible
General Relativistic effects are taken into account by Gaia, but they're dominated by Solar System objects. Space is very close to flat, unless you're close to a very massive object.
Even mathematical proofs don't have mechanized, verifiable proofs, so physics has a ways to go. Once most mathematicians are using formal tools like theorem provers, maybe they will be usable and general enough to trickle down to physicists, and you'll have a more verifiable chain of reasoning from top to bottom for machines and observations. It probably will turn up a few minor issues, but I wouldn't expect anything drastic.
I'm an experimental particle physicist by training and know that feeling. We never see the particles directly, but reconstruct them in a complex chain. Hits in a detector become tracks, tracks are assigned to particles according to our expectation of how those particles behave. Bunches of tracks are interpreted as decaying heavier particle. Sometimes I wonder if we missed something important in the early days of quantum mechanics and particle physics, and some of the things we think we are investigating don't actually exist, or are subtly different than we think. But we look at the data though our lens, and see what we are expecting to see. My gut feeling says everything is consistent, and experiments match the theory so incredibly closely that it can't be a coincidence, but I don't think there is a mathematical proof. It could be that our theory is just so flexible that it lets us see Higgs particles and top quarks, even though the actual entities are something different. Like when people thought planets move in epicycles.
I know it is likely nonsense, but it is what motivated me every now and then to go back and revisit the basics of our field, like how is a particle state defined in QM, how does it interact with the experiment, how do we reconstruct larger objects, and so on.