left:
A sends signal at 2.7, which returns at 37.3 with a timestamp from B reading Bt=10.
She calculates her clock read At=(37.3+2.7)/2=20 when Bt=10, in agreement with a td of 1/2. She calculates their separation at At=20 as .866*20=17.3.
That is all she knows 'now' at At=40, since the remaining events haven't happened yet for her.
Note that your calculations conclude something factual about At=20 even though she cannot actually perform those calculations until later at 37.3 which is well after At=20. Well my post was about concluding something factual about At=40, not making sure the calculations could be completed before that time.
So instead you should have said that A sends a signal at 5.4, which returns at 74.6 with a timestamp from B reading Bt=20. She would then calculate her clock must have read At=(5.4+74.6)/2=40 when Bt=20, in agreement with a td of 1/2. She can also calculate their separation at At=40 as .866*40=34.6.
right:
B sends signal at 1.6, which returns at 20 with a timestamp from A reading At=5.4.
He calculates his clock read Bt=(20+1.6)/2=10.8 when At=5.4, in agreement with a td of 1/2. He calculates their separation at Bt=10.8 as .866*10.8=9.2.
That is all he knows 'now' at Bt=20, since the remaining events haven't happened yet for him.
Or let B send a signal at 2.7, which returns at 37.3 with a timestamp from A reading At=10. He would then calculate his clock must have read Bt=(2.7+37.4)/2=20 when At=10, in agreement with a td of 1/2. He can also calculate their separation at Bt=20 as .866*20=17.3.
No matter what times we choose, this signal method only tells us what we already should have known just from the td of 1/2: When she is At years old she says he is At/2 years old, and when he is Bt years old he says she is Bt/2 years old, for the whole time they are in relative motion.
If we want to make some verifiable measurements and avoid the time delay in waiting for signals to travel, we can just let A have a partner called AA who is stationary with respect to her, located at x=34.6 and possessing a clock that is synchronised to hers. When B passes closely by AA, they both instantly record the respective times on their respective clocks as AAt=40 and Bt=20 which is an event that all reference frames must agree on. This confirms that when she is 40 years old and she says he is 20 years old, she is correct.
And we can also let B have a partner BB stationary with respect to him, located at x'=-17.3 and possessing a clock that is synchronised to his. When BB passes closely by A, they both instantly record the respective times on their respective clocks as BBt=20 and At=10 which is also an event that all reference frames must agree on. This confirms that when he is 20 years old and he says she is 10 years old, he is also correct.
Their 'nows' are simultaneous.
Their conclusions are based on historical events.
No, there is no universal now while the twins are in relative motion, because each one says the other is younger by 1/2 at any given time.
If one of them decelerates/stops so that they are stationary with respect to one another, then they can agree on now, and that is what my post was about. If he decelerates/stops at his own time Bt=20, then he will have to conclude she is At=40 instead of 10. But the reverse is also true, if, for example, if she instead accelerates to his speed at her own time At=10, then she will have to conclude that he is Bt=20 instead of 5.
