Sticking strictly to the facts, all we know of the current situation is that Mrs May went to Brussels in the expectation of making a deal with Jean-Claude Juncker. That in turn would pave the way for the European Council to approve a mandate for Michel Barnier to move to phase two of the negotiations.
From that, the only thing we know for sure is that Mrs May didn't get her deal. After the meeting, both parties held a joint press conference during which they said very little. There were no questions and Mrs May left for a meeting with Donald Tusk to ask for extra time.
As to the reasons why there was no deal concluded, most of what we're getting is speculation, based largely on leaks to the media.
Their current narrative is that the UK government had been on the brink of an agreement in which it would accept "continued regulatory alignment" between the Irish Republic and Northern Ireland apparently based on a deal brokered between Whitehall and Dublin.
As the narrative has developed, it is asserted that the DUP intervened publicly, rejecting the Whitehall/Dublin deal. This led Mrs May to break off her meeting with Juncker to take a 'phone call from Arlene Foster, the outcome of which, it is said, was that attempts to conclude the deal with Brussels on the day were abandoned.
Foster's pitch, based on "speculation emerging from negotiations", was that Northern Ireland must leave the EU on the same terms as the rest of the UK. The DUP would not accept any form of regulatory divergence which separated Northern Ireland economically or politically from the rest of the UK. The economic and constitutional integrity of the United Kingdom would not be compromised in any way.
Crucially, we are told, Foster came away from her telephone discussion with Mrs May saying that the government understood the DUP's position. The prime minister had made it clear that there would be no border in the Irish sea and that the "territorial and economic integrity of the United Kingdom will be protected".
A popular media narrative
thus rests on the scenario that "Theresa May's desperate bid to break the Brexit deadlock and move on to trade talks was dramatically torpedoed in an eleventh-hour phone call with the DUP".
That said, there are some crucial, unresolved inconsistencies in this narrative to the extent that it hardly seems to hang together. First, and most important, it relies on the idea that Mrs May went to Brussels with a proposal that she must have known that the DUP would not accept and then had to be dragged out of her meeting with Juncker to be told this.
Now, over months that Mrs May has been prime minister, we have largely come to terms with her incompetence. But it is nonetheless difficult to believe that, with the well-known and frequently rehearsed position of the DUP, she could go to Brussels with a proposal she must have known would by rejected by this Northern Ireland party. This is carrying incompetence to a new level.
Secondly, while much has been said of the Whitehall/Dublin deal, as far as I am aware, the full official text has not been made public. All we have to go on is an "early negotiating text" leaked to RTÉ News
and "sight of a key phrase in the joint text".
This "key phrase" said that "in the absence of agreed solutions, the UK would ensure no divergence from those rules of the internal market and the customs union which supported North/South cooperation and the protection of the Good Friday Agreement".
And while there is also talk of "regulatory alignment", there are no indications as to whether that encompasses the full extent of the deal, or whether there was more to it especially in the small print.
Further, we do not know whether this deal, apparently agreed between the UK and the Irish Republic, was necessarily agreeable to Brussels. And nor do we know that Mrs May based her proposal on the exact deal that was agreed, or whether she changed some of the text, or even played around with the framing.
What we do know though is that the prime minister made it clear to Arlene Foster that "there would be no border in the Irish Sea and that the territorial and economic integrity of the United Kingdom will be protected".
This begets another major inconsistency. As it stands, there is no possible way that Brussels could accept a situation where there was a soft border between the Republic and Northern Ireland, with no controls over goods from the mainland UK. This would open a back door
into the Single Market which would be completely unacceptable to the remaining EU Member States.
This again is an issue of which Mrs May can hardly be unaware, which leaves one dubious at the prospect of her proposing something to Brussels that cannot ever have been acceptable.
This, then, leaves us with two implausible options. On the one hand, Mrs May went to Brussels with a proposal she knew the DUP could not accept, or she went with a proposal that the EU could not accept. And, from what we know, it could just as easily have been the case that she went with the second proposal her telephone conversation with Arlene Foster simply confirming something that was already in hand.
There is little doubt, however, that Mrs May did go to Brussels expecting a deal. She had booked time in Parliament today, asking the Speaker to clear "several hours" for a "major statement" on the outcome of her talks. This has now been cancelled.
Going for the other option, we have a statement from Leo Varadkar. Speaking yesterday, he claimed that the United Kingdom had agreed a text on the border that had met Irish concerns. He was, therefore, "surprised and disappointed that the British government now appears not to be in a position to conclude what was agreed earlier today".
This might be given credence by suggestions that Mrs May was relying on "creative ambiguity" in the Irish text, thinking that it would get the UK past this milestone and give her wriggle room when it came to filling the detail.
In this, May possibly banked on the full text not being published, except that most of the content was leaked by Belgian Green MEP Philippe Lamberts. He, with other MEPs had been meeting Juncker in the morning, emerging to tell journalists that the "Brits" had accepted "reality". This is said to have provoked Arlene Foster into action.
Either way, however, Mrs May's negotiation was doomed to fail as it always was. This is the epitome on the rock and the hard place
, where the only real option the "wet" border was never going to be politically acceptable to the DUP. If Mrs May didn't realise this, and thought she could get away with a fudge, then we have a very worrying situation.
One wonders, therefore, Mrs May was going through the charade of trying to make an unmakable deal, simply so that she could say that she had tried. But even that does not square with the indications that she believed she would conclude a deal.
And despite everything, that is still on the table. Mrs May is to return to Brussels on Wednesday for another round of talks, with Donald Tusk saying that there is "still time" before the 15 December, when the European Council must meet to determine the fate of the negotiations.
Whether the prime minister can pull it off remains to be seen. I suspect it will depend on whether Brussels prefers its fudge toasted or fried. For the moment, though, no deal means no deal the only thing clear about this episode.
For the rest, we're getting confirmation of that old saw about Irish politics: if you think you understand them, you haven't been listening.