minkwe wrote:[...]
But first, what do you understand by "signaling"?
I snipped the previous part of your post because I think this last sentence covers the essence of it.
"Signaling" means that there is a procedure whereby someone with a hypothetical free will has some means to somehow change the physical configuration at another place in time and space (also known as "transferring information"). This should be interpreted in a way that also includes change in entropy; i.e. any transfer of information entropy counts as signaling. Thus any statistical procedure for transferring information will also count as signaling.
This is not a mathematical definition, because there is no unique mathematical definition. Since signaling is in its essence a physical process, any mathematical definition will necessarily be domain dependent. (The one that got closest to an all-encompassing definition was Claude Shannon.)
However, the definition above has the advantage of clearly placing the burden of proof: If someone claims that signaling is possible for a particular physical configuration, it is up to that person to provide a specific mechanism (or in the case of statistical data, an algorithm) whereby information can be transferred.
In the EPR experiment we are discussing here it is obvious that outcomes at the stations cannot be used to transfer information, since they are beyond the observer's control.