[SR] Their proper times will necessarily be equal

Let us understand each other (a moment of optimism).
   The immense, the incomparable, the fantastic relativist theorist (that's me) wrote:
   "If two different observers travel an identical path in equal observable times,
then their proper times will necessarily be equal.
   The no less immense, incomparable, and fantastic international Python critic refutes.
   And yet, the idea is very simple.
   Let's set up a Galilean frame of reference, in which a Galilean mobile moves from left to right on the x axis.
   When it goes to O, in R, we click.
   When it passes x, let's say 12 al, we click.
   For example, we obtain To=12.915.
   Or a speed of Vo=x/To=0.9291c
   Tr=To.sqrt(1-Vo²/c²)=4.776
   Let us pose another body, but this time in uniformly accelerated motion, and whose speed will be specially chosen so that To=12.915.
   This means that in R, if they leave together, they arrive together (even if they do not have the same speed between them).
   This is where the problem lies with Mr. Python.
   He will immediately assert that the proper times will not be equal, and that to write this is to contradict the relativist concept, and, inevitably, to be mistaken.
   But let's take a moment at the level of mobiles.
   For the mobile at constant speed, the point to be joined, that is to say which will return to it,
is at x'=x.sqrt[(1+Vo/c)/(1-Vo/c)] and it moves with a speed of Vapp=Vo/(1-Vo/c).
   For the accelerated mobile, the acceleration is only constant in its frame of reference (it is he who accelerates)
and we have in each part of the path, dTr=dx'/dVapp' or dTr=dTo/sqrt(1-Voi²/c²)
   However, the integration of this, practiced at real speed, leads to Tr=To.sqrt(1+Vrm²/c²).
   That is to say again at Tr=To/sqrt(1-Vo²/c²) where Vo is the same speed as in the other Galilean frame of reference.
   We come back once again to:
   "If two different observers travel an identical path in equal observable times,
then their proper times will necessarily be equal.
   Jean-Pierre Python then asserts that this is absurd, because there is acceleration of one of the mobiles in relation to the other.
   Except that there is also an acceleration of the other in relation to the one.
   And when placed on the same equal footing, we cannot differentiate the total proper time of one from the total proper time of the other.
   The fact that different observers experience acceleration between them is not an admissible objection, because let us take the case of two mobiles each performing at the same speed over half a circumference,
one in hourly revolution, and the other in trigonometric revolution. It is quite obvious that the proper tenses will be equal to each other (otherwise it is immediately absurd) during their conjunction.
   And yet, constantly, they will have accelerated and decelerated between them, and at every point of their journey.
   It is the same thing with the proper times of two different observers, but covering equal portions in equal times.
   Their own times will be equal.
   The relativists' error consists of a poor understanding of the calculation of the proper times of objects
in accelerated movement. They then find a proper time that is too small, compared to the correct proper time.
   They then deduce that the proper times of the two observers described above will not be equal.
   Always, always, always the same error is reproduced among them, they consider observable speeds as real.
   It's passable in Galilean RR with the artifice of mass change, with the artifice of time skipping, and other useless and ridiculous joys.
   In accelerated benchmarks, continuing with the same falsified principles becomes cumbersome.
   Hence the last criminal proposition of the physicists: "Ah yes, but these frames of reference are more like special relativity, they are hyperbolic, geostrategic, Remanian physics,
and transcendental.
   It's not very serious when you scratch a little.
   It's even a very speech full of abstract religiosity.
   R.H.