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I've heard that Mathematica uses a session ad hoc to process DynamicBox, but I don't know any detail. I am using DynamicBox in stylesheets and sometimes I can't understand its behavior: when it is updated, what difference can be produced when it's placed as CellFrameLabel etc.

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    $\begingroup$ This is entirely implemented by the front end and is so mostly undocumented, but basically there are two modes in which evaluation can occur: in the first the FE calls back into the kernel to run code and in the second it runs the code on its own. Whenever possible try to write your interface to do the second as that tends to perform significantly better. $\endgroup$ – b3m2a1 Jan 8 at 5:40
  • $\begingroup$ DynamicBox is what Dynamic is typeset to so the first question is, are you familiar with Dynamic documentation / tutorials? $\endgroup$ – Kuba Jan 8 at 8:19
  • $\begingroup$ @Kuba I've read the tutorials. However, when I tried to provide my example for the strange behavior of DynamicBox just now, I found a new interpretation which has nothing to do with DynamicBox. That's my fault. Leave this question alone. You can talk about the general properties of DynamicBox here and there isn't any specific trouble any more. $\endgroup$ – bcegkmqs23 Jan 8 at 11:52
  • $\begingroup$ @Kuba Finally, I think the trouble can be summarized as: DynamicBox with Refresh does not update CounterBox. It seems that the only thing can update CounterBox is any modification of cells. $\endgroup$ – bcegkmqs23 Jan 8 at 11:58