Accelerated frame and Tau Ceti problem

We know the famous example of Doctor Hachel (that's me) entitled "the traveler of Tau Ceti".
The Tau Ceti traveler is characteristic of special relativity, and its simplicity of understanding
(but no resolution) is now famous throughout the world.
We imagine a young woman, named Bella, to differentiate her from Stella who is used to always traveling, in the examples, in uniform Galilean movement. Beautiful journey always in accelerated mode at 10m/s² (i.e. 1.052ly/year²) starting from the earth.
Physicists, because they are curious, and above all competent, will easily calculate how long the journey in the terrestrial frame of reference will last.
We will then place a watch on earth, a watch at 3 ly, a watch at 6 ly, a watch at 9 ly, and a watch at 12 ly.
The watches were previously tuned in the same place, and are remarkably atomic precise.
They are moved slowly to their position, to avoid any effect of dyschronotropia.
We ask Paul B. Andersen to please give the corresponding equation to use to know these times.
Paul B. Andersen gives To=(x/c).sqrt(1+2c²/ax)
Doctor Hachel, who is not an idiot (a doctorate, three Nobel prizes) validates Paul's equation, and considers it to be completely accurate.
We then measure the duration of the trip.
When we move to level 3 ly, the local watch marks: 3.8345 years
When we move to level 6 ly, the local watch marks: 6.8852 years
When we move to level 9 ly, the local watch marks: 9.9050 years
When we cross Tau Ceti (12 ly), the local watch says: 12.9156 years
We have therefore just verified experimentally that the equation is correct.
It seems very simple, but we now know Richard Hachel, and we know what kind of madness attacked his neurons.
We will then say: What is the observable time that exists between the passage in (3ly) and the passage in (6ly)?
Or again: And between the passage in 9 ly and Tau Ceti?
This is where everything descends into horror.
And there, it is all of humanity placed on the scale of a scale which will sink into stupidity and ignorance, and Hachel on the other, who will beg that we listen to him, and that we stop playing the little relativist idiots with the simple authorization that we are "in a pack" and that "if it wasn't like that, what we have to do, it would be known".
We just forget one thing.
A stupid thing to cry about.
R.H.