Europe editor Katya Adler looks at whether the negotiations are over after months of shadow-boxing.

Katya AdlerEurope editor@BBCkatyaadleron Twitter
image copyrightPress Association
image captionBoris Johnson decided to walk away from negotiations last Friday
After months of wrangling and shadow-boxing, posturing and incomprehension of the bottom-line priorities of the other side – are the negotiations truly over?
Political Twitter is exploding with theories: that Prime Minister Boris Johnson never really wanted a deal in the first place, that the EU threw away its chances to make a deal with missteps at last week’s summit, or that the UK is overplaying its hand – expecting the EU to “cave in at 10 to midnight” in negotiations…
Certainly, the last 24 hours have not played out as many a seasoned observer of this by now very, very, very long Brexit process might have imagined.
Unlike Mr Johnson’s decision on Friday to walk away from negotiations. That was half-predicted, following the EU leaders’ summit.
The prime minister had set the summit as a deadline (the EU regarded it as an artificial one) by which time a trade deal should be on the table. If not, Mr Johnson had said, he thought there wouldn’t be an EU-UK trade deal and “we should move on”.
No-one I spoke to in EU circles in the lead-up to the summit took that ultimatum too seriously.
Instead they reeled off examples of promises and deadlines the prime minister had made and set and ultimately ignored in the past: walking away from negotiations this June if sufficient progress hadn’t been made, dying in a ditch last year rather than extend Brexit divorce talks and more.
media captionWhy is it so hard to reach a Brexit deal?
But I detected a slight unease in Brussels too.
“You never know with Boris Johnson. Might he do something radical? Something unexpected? I mean just look at the Internal Market Bill!” mused one Brussels contact on the eve of the summit.
The government’s Internal Market Bill published last month has provisions (the cabinet call them a safety net) to override parts of the divorce agreement pertaining to Northern Ireland – which was agreed and signed off by the EU and Mr Johnson last year. The EU was taken aback by the bill and started legal proceedings.
Yet on Friday, when the prime minister insisted there was no point carrying on with negotiations unless the EU fundamentally changed its position, there was a widespread assumption in Brussels and in parts of the UK that this was political posturing.
Yes, the government had clear frustrations with the EU in its approach to talks.
Yes, the EU was impatient with the UK because of a range of issues that came up in negotiations.
But – the theory went – the end stage of negotiations would naturally be when both sides would publicly flex their muscles most of all.
To show domestic audiences back home that they would fight their corner to the end… just before they agreed a compromise deal behind closed doors in the coming weeks.
We saw France’s Emmanuel Macron sweep into the EU summit last week sounding intentionally hardline about fish.
EU leaders’ written summit conclusions pointedly put the onus on the UK to make the compromises necessary to make a deal. And the prime minister responded that the EU had effectively ended negotiations, unless it changed its position.
Most commentators assumed talks would resume late this week after some diplomatic to-ing and fro-ing.
image captionMr Barnier has long been pushing EU coastal member states to allow him to start discussing compromises on fish
And bang on cue on Monday, EU chief negotiator Michel Barnier offered to intensify talks (a big UK complaint has been that the EU hasn’t complied with a promise to truly speed up talks this autumn).
He also spoke about getting to work on “legal texts”. Again, this was an overture to the UK, which has long grumbled that Brussels refused to start work on a joint legal text, despite the majority of the EU-UK deal already being agreed.
But instead of welcoming these moves – while maybe playing coy or hard-to-get till the end of the week (as it might have felt it too soon to “give in” after declaring talks over, such a short time ago) – Number Ten responded that, although welcome, the EU offer was insufficient.
Again came the demand for a “fundamental change of approach from the EU”.
This is far tougher to come back from than the bilateral fist-waving last week. The EU has already made its overtures. It’s unlikely to go much further unilaterally.
Depending, of course, what the UK means by “fundamental change of approach”.
If what the government is after is the EU dropping its insistence on agreed competition rules, or at least common “principles” aka the level playing field, then Downing Street must know that’s not going to happen – and negotiations are indeed over.
The UK says it no longer wants to be tied to “Brussels’ rules” but it’s not unusual to agree competition regulations with trade partners. The UK has a state aid agreement in its post-Brexit trade deal with Japan. It’s asking for level playing field provisions in a future deal with the US.
If pushed, the EU may well further water down its demand for what it calls “fair competition” rules – if, for example, it feels there is a robust dispute mechanism in place in the trade deal, that allows either side to take swift legal action, if they believe the other has broken their agreement.
Brussels has already budged on some of its competition demands, by the way, but it will never drop the ask altogether.
Protecting the single market is more important to the EU (and for German car manufacturers, as they’ve told us) than a trade deal with the UK.
And the EU does feel it must protect its market and businesses from potential “unfair competition” from post-Brexit UK.
But, if what the government wants is the EU admitting that it, too, must make compromises to reach a deal, not the UK alone, in order to return to the negotiating table, then that is certainly doable. German Chancellor Angela Merkel and Dutch Prime Minister Mark Rutte said as much last week.
The President of the European Commission, Ursula von der Leyen, who has in the past also spoken of bilateral compromise, could call Boris Johnson over the coming days.
Mr Barnier has long been pushing coastal member states to allow him to start discussing compromises on fish. Months ago, he openly admitted that the EU’s demand to keep pretty much the same fishing quotas in UK waters after Brexit as before was a “maximalist position”.
The EU’s negotiating team was keenly aware that it would be easier for Downing Street to discuss compromises on competition regulations – which are far more important to the EU as a whole than fish – after it became clear Brussels would give way on fishing quotas.
But coastal nations like Spain and the Netherlands – and especially France – insisted that they’d only start talking about quota compromises once the UK “seriously engaged” in discussions on the level playing field.
Most importantly, those countries wanted to be seen by the fishermen and fisherwomen at home to have been fighting hard for their industry in trade negotiations with the UK.
That they would have to compromise in the end is an open EU secret.
Bets are now on amongst Brexit commentators over whether EU-UK talks will resume, come the end of the week, or next week at the latest, or whether we’re indeed heading for no-deal.
In the knowledge that, as economically significant neighbours and trading partners, the EU and UK will end up back around a negotiating table at some point, whatever happens next.