SR and GR are valid to Pedro. Also, the principle of inertial motion, which is due as far back as Galileo, is NOT that there are no special or preferential frames, such as the CMB or other, but that there are no frames in inertial motion where the laws of physics are different to inertial observers.
Apparently, there are several Pedros nowadays in the world of physics and maths, including the well-known Pedro by Bernard d'Espagnat in quantum mechanics, all differing from one another on important or even minor views.
All, here, affirming the view that we live in a 3D world, and time is an independent variable. The consequence is the subject of this discussion, and how it can influence life.
Pedro called himself a die-hard pragmatist. The world he rightly saw was 3D and a passing reference, which he called time. Someone could call Pedro a "realist", even himself described him that way, many times, but others could equally well call him a "platonist".
The muon is an elementary particle similar to the electron, but with a much greater mass, that has a very short lifetime, far too short to reach the sea level. It exemplifies the discussion, as an example.
First, it is indisputable in life that muons, are produced too high to reach us, measured by their own lifetime, but we do see them at sea level.
IF the muon lives longer for maths reasons, as Pedro is at rest and we all live in 3D as Pedro insists, that is not physical. one can't use the word "remember" in that context when one sees a muon at sea level. They just seem to live longer if Pedro is at rest, it is an illusion. Nature is what Pedro sees as objective.
But, IF It makes sense to remember that muons do live longer to Pedro, albeit not to the muon, if Pedro is at rest, and for everyone? It is not just that some calculation says so, anyone can remember. Nature can also be intersubjective. What Pedro sees is then revealed as just subjective.
Then, 4D spacetime is just not an arbitrary math method, then we all live in 4D spacetime, times passes differently for Pedro at rest, than for the muon. That fact is in the future as anyone can remember, not just as one can calculate. Muons will arrive at sea level.
Pedro takes the first view, that 4D spacetime is not physical, just maths, not life. The muon, however, in life, arrives at sea level. We have memories of it, and other events that depend on 4D, such as movement at any speed v > 0.
NOTES
1. The CMB does not introduce new physics. The SR and GR do NOT work on the basis that there is no preferential or special inertial frame of reference.
According to the Lorentz ether (which is the only viable theory which is based on a 3D world with time as a parameter) the life time of a muon depends on its velocity. Thus, if their velocity is large enough, close enough to the speed of light, they can be found at sea level even if they are produced only very high. This effect is a physical one.
Your description confuses the position of the Lorentz ether (Pedro?) with those of the spacetime interpretation. Such things as "living longer for math reasons" sounds like part of relativistic reasoning, as well as the position that all has to be equal for Pedro and the muon. Roughly, you start with the assumption that there is no preferred frame, to show that 4D is necessary. Ok, if you start with this assumption, you get 4D. But those who believe in the Lorentz ether don't believe that all things are equal, they assume that there is a preferred frame, with the CMBR frame as the obvious candidate. Then, Pedro moves with much less absolute velocity than the muon, and therefore muon clocks are much slower.
The "fact is in the future as anyone can remember" sentence makes no sense at all.
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