Langevin's paradox again

Langevin's paradox.
The Langevin paradox is a very serious criticism against the theory of relativity. Unfortunately, the canonization and divinization of Albert Einstein as the new son of God on earth (it was excessive in both substance and form) completely obscured the problem, and we only saw dozens high-level theorists were right against him, and that their grievances were audible.
What was the grievance?
If the twin of the stars returns younger in the frame of reference of the twin who remained on earth, then the twin who remained on earth, if we apply the reciprocity of effects, and Doctor Richard Hachel says that we must use this notion of reciprocity, very basis of logic, comes back older than the other. Which is both logical and absurd.
No one has ever been able to answer the question correctly and perfectly (except Hachel), and if we look closely at the forums, articles, websites, books, publications, for 120 years, not everyone has There's nothing wrong with it, and everyone says anything to try to get back on their feet.
Only Doctor Hachel (what a man!) gave the perfect explanation, as on other points of the SR, because he uses appropriate and consistent relativistic geometry, and he KNOWS how to explain things clearly.
The great problem facing the world's physicists is a problem of confusion. They confuse two notions: the notion of relativity of measured times, and the notion of reciprocal relativity of chronotropies.
It's not the same thing.
Hence the impossibility for them all to explain things coherently.
The relativity of the measured times will show that over a journey of 24 light years, carried out at v=0.8c, Terrence will age by 30 years.
It's very simple: x=v.t, i.e. t=x/v and 24*0.8=30
But when Stella returns, she will only be 18 years old.
There is therefore an asymmetry, that is obvious, but it is on the explanation of the asymmetry that everyone sinks into complete ignorance.
Because we are confusing it with the notion of chronotropy, which is ANOTHER THING, and which can be defined by the internal functioning of watches. On this, yes, the effect is symmetrical, reciprocal; each watch, and throughout the entire journey, (including if I place a small half-turn phase on a semi-circle with a preserved tangential speed of 0.8c), beats faster than the other watch, and the equation is constant and reciprocal over the entire path: T2=T1/sqrt(1-v²/c²).
This is true.
But this only qualifies chronotropy, that is to say the internal mechanism of watches, it is not the whole of the relativistic effect.
This is not what we will ultimately measure.
I can't explain it more clearly.
Now, if you are curious, and truly in love with science, you try to understand what I am saying, without spitting, without mocking, and you refer to the little diagrams posted years ago already, which explain the things as we have never done before, notably with the logical notion of the elasticity of relativistic distances.
All of perfect theoretical and experimental beauty.
“I have told you all these things, so that when the time comes, you will remember that I said them.”
Jesus Christ knew that no one would believe him, and that Minerva's owl would not take flight until nightfall.
R.H.