I left uni in 1975 so my knowledge of maths, physics and chemistry is dated as of that time.
Still, triangles are a definition, agreed between people who study Euclidean geometry. If you go one step further and assume that you only have curves between two points in space and/or your space has more than 3 dimensions then the triangle as we know it can't be defined in the same way. The way physics has developed in my time, it is very likely that we have more dimensions than space time.
Yes and no. This absolute zero is also an agreed hypothesis in thermodynamics based on our definition of enthalpy and entropy. We don't know for sure the structure of matter and what kinds of energy are left in matter at zero Kelvin. The science is still too young. One day we'll discover new subatomic particles and new fields that encompass the Higgs field, then the current theory on entropy, enthalpy will have to evolve.
this is only partially true, the lines vary with the atomic mass of the elements. I take it that you talk about spectra of hydrogen and elements that don't have isotopes. Further, they are only repeatable when acceleration is not present in your frame of reference, which restrict that 'truth' to earth-bound measurements.
the complexity of real systems will make everyone realize how little equipped we are to study these things, so we postulate and assume to simplify the number of variables, therefore we know in advance that whatever conclusion we come up with, the result of our experiments cannot be the whole truth.
My point is about there being absolutes. Agreed the triangle is an agreed definition, which then allows an entire logic structure to be built in it.
My point about absolute zero as a thermodynamic concept, does provide the validity for the 4K radio noise, and is independent of any internal atomic mechanisms which may require the concept to be further refined, not modified but refined e.g getting closer to a truth. Remember that absolute zero was an experimental measurement before it was a theoretical construct.
My choice of atomic spectra, was made in the knowledge that it encompassed both pure uncompressed gases, high pressure gases, isotopes, Doppler and gravitational shifts and multiple elements, all of which give us objective tools to investigate the universe.
I would agree with you about the difficulties of modelling even relatively simple systems, let alone those we find in the real world. You might however be pleasantly surprised by the advances in computational modelling of physical systems over the last few decades.. not my area, but for instance the reason why nuclear test ban treaties, have been successful is because the modelling of yields had become so accurate.
My point, which I am unwilling to concede easily is that there are objective truths, and by science we get a glimpse of some of these and we make ourselves closer and closer to these by intelligent experimenation.