The most important factor to take into account, is the people making this decsion are part of the establishment. It always makes me chuckle when the likes of the Daily Mail talk about our liberal Judges in the Court of Appeal. I defy anyone who has been in front of the Court of Appeal, or had dealings with it, to characterise it in those terms. Its primary function is to uphold the decision of the court below and only a determination that is likely to bring the overall system into disrepute is tackled with any gusto.
The other point is that as people get older they become more conservative. This is (generally) as self-evident as the decline in penile function as we age. Supreme Court Judges are almost exclusively in their sixties and seventies - the demographic who ultimately determined the referendum vote. They are hardwired to maintain the status quo and not rock the boat from a legal perspective, unless given no other choice.
So that is the backdrop.
That said, ambition does strange things to people and Judges of the Supreme Court have reached their professional apogee. They have literally nowhere further to go in their careers; and so given the ladder of ambition has been climbed to its full extent, you are much more likely to get an intellectually honest determination from this tribunal than from the courts below, the Judges within which may be seeking one (or more) more leg- up(s) from those they are being asked to make judgments against, to climb further up the tree.
I've not heard enough of the evidence to form a view about how it will end, but whatever the decsion, it is bound to carry accusations of being political.
What I have no doubt about is the importance of the role of an independent judiciary in holding the executive to account, within certain limits, of course - but anyone taking that as a fait accompli in terms of these proceedings, or any other, is seriously deluded. The establishment tends to take care of its own, unless compelled to do otherwise.
Gina Miller has to overcome that aphorism, if her appeal is going to find favour with the Court.