Next week EU leaders will descend on Salzburg, the picture book city overlooked by the Alps, and studded with renaissance and baroque architectural jewels.

It is also the birthplace of Mozart, and in recent weeks there have been suggestions that an aria of goodwill would waft from the 27 leaders in Theresa May’s direction, signalling an ornate pirouette in the Brexit melody.

In the British press this is taken to mean a signal to Michel Barnier to relax his "dogmatic" negotiating stance and to unlock a deal on the Irish border.

UK negotiators, however, have been playing down expectations.

All the signals are that the most Theresa May can expect is some positive words, and at the very least, a hope that the EU27 won’t say anything that kills off her Chequers plan altogether.

So suggestions that in Salzburg the EU will change their negotiating guidelines – from which Mr Barnier derives his mandate – are false. 

Donald Tusk, the European Council President, has laid out three key issues for the agenda on Brexit. 

A reaffirmation of the need for the UK to agree a backstop, a discussion on a political declaration on the future EU-UK relationship (which will sit alongside the Withdrawal Agreement), and the issue of how the EU27 should prepare for the critical weeks ahead.

Although the EU’s chief negotiator will brief heads of government, and Theresa May is likely to put forward her own views, this is an informal summit. 

That means there will be no draft text, no formal conclusions and no updating of the guidelines.

The idea is rather to reacquaint leaders with where things stand after the summer, and to prep them for an intense two months ahead.

Dublin is confident that the resolve over the Irish backstop will not waver.

"There will be a resounding restatement of unity and support for Ireland," says one senior Irish figure, "no question of tinkering with guidelines, and a look forward to October."

But Theresa May will be desperate for some kind of affirmation.

When the House of Commons Brexit committee arranged a hearing in Brussels, leading eurosceptic MPs desperately tried to get Michel Barnier to trash Chequers, in the belief that that would bury it completely and leave a Canada-style free trade agreement as the only option.

However, Mr Barnier was careful to speak positively about aspects of the White Paper.

In Strasbourg this week the Commission president Jean-Claude Juncker did the same.

"Salzburg should be the same direction," says one UK source. "It’s not going to be a deal, but it’s all moving in the right direction. None of the mood music suggests they’re going to use Salzburg to kill Chequers."

Even at the next formal summit in October, it is unlikely that the negotiating guidelines will be opened up, and even if they are, there is very little chance the paragraph on avoiding a hard border in Ireland will change.

"Our existing guidelines on Ireland are short and still apply," says a senior EU official. 

"I can’t imagine a situation where they would reopen those guidelines. In every set of conclusions [of European summits] they stress the importance of coming to an appropriate arrangement [on Ireland]. But you don’t need to amend the guidelines to do that."

But Ireland is still the implacable obstacle to a successful Withdrawal Agreement.  "The only deal-breaker is Ireland," says the official.

To recap, the backstop comes into effect if a future trade relationship, and/or technology, fail to completely remove the need for customs and regulatory checks along the Irish land border.

It would mean Northern Ireland to all intents and purposes remaining in the single market and customs union.

The British side believes the backstop stand-off can be resolved through a Temporary Customs Arrangement, which would keep the UK as a whole inside the customs union until the future trade agreement, as envisaged in Chequers, takes over.

In that way, there would be no customs border between Northern Ireland and Britain even if the backstop kicked in, and the Facilitated Customs Arrangement contained in Chequers – a kind of dual-tariff system – would then remove long-term the need for customs checks either on the Irish Sea or on the island of Ireland.

Whatever about Chequers, the problem for the EU is that, by inserting that idea into the Withdrawal Agreement, it is too-clever a move by the UK to fast-track their way into a future relationship via the divorce.

EU sources say this is not just the European Commission being dogmatic. 

"The French and Germans are all over this big time," says one EU diplomat, "and they don’t like the UK-wide customs approach at all.  It’s a license to cherry pick.  It’s totally playing politics with this unique situation of Ireland."

British officials, however, argue that the European Commission Task Force on Brexit is already doing something similar with the draft Irish Protocol, which will contain the backstop in the Withdrawal Agreement.

They argue that in practical terms the Irish Protocol contains lists of things that are "kicked into a subsequent process," ie through annexes that are fleshed out later by joint committees involving UK and Irish officials.

"There is an acceptance," says one UK figure, "that you can’t pin it all down now."

In other words, London believes a Northern Ireland-specific backstop enshrined in the Withdrawal Agreement will only be fully realised at a later date, so therefore there should be no political or legal issue with a UK-wide backstop also in the divorce treaty if it’s viewed the same way.

In general, London wants to ensure there is no Northern Ireland-only backstop in isolation. 

Although nothing new is being tabled – and probably won’t be until after the Tory Party Conference – some ideas have been in the mix.

One is the so-called "conjoined twin", of which my colleague Peter Foster has written in the Daily Telegraph.

Under this idea, the UK would agree to a Northern Ireland-specific backstop in the Withdrawal Agreement, but the EU would simultaneously commit to creating a separate backstop for the rest of the UK as soon as trade negotiations open during the 21-month transition period.

This would be the "conjoined twin" of the Withdrawal Agreement backstop, but it would keep the UK in the same customs arrangement via a different route. 

This "parallel backstop" would have the effect of keeping the whole of the UK in the same customs arrangement, until such a time as a final trade deal is in place, at which both fall away.

Another idea would be for the UK to seek an extension of the 21-month transition, but only for the parts relating to the EU customs union rulebook.

"They may be thinking," says one source close to the negotiations, "of a sort of customised extension of the transition where they keep the customs union bit.  But that’s very difficult because the whole virtue of the transition is it’s a wholesale extension of the status quo. 

"It’s quite difficult to cherry pick."

These are all fiendishly complicated ways of trying to square the backstop circle, and the prospect appears remote that both sides can come up with something that fulfills both Theresa May’s avowed rejection of anything that will give rise to customs checks on the Irish Sea – because she has interpreted it as an assault on UK sovereignty – and the need to avoid checks along the Irish border.

"Because the UK has decided to take this stance on sovereignty," says an EU official, "it’s very difficult to climb down from that branch.  I don’t know how you get out of that situation, for both sides, that kind of works."

For the EU Task Force and the Irish Government, the way to get out of it is to continue the mantra of "de-dramatisation".

"Dedramatising the backstop," says one Irish figure, "means approaching it in a sober factual way, not regarding it as a proxy for mad constitutional agendas.  It is about building on controls and checks that are already there on the Northern Ireland-Britain side.

"The EU is willing to adapt the protocol. The objective is to avoid a hard border, with a backstop that is all weather, which is there unless and until something else is agreed, and which is legally operable."

Irish officials points out that the EU’s Union Customs Code is littered with examples where member states have quirky customs and transit arrangements for various geographical and historical reasons, such as in the Canaries, Heligoland, a German archipelago in the North Sea, in northern Italy and even on Mount Athos in Greece.

Finding pragmatic solutions that do not threaten the constitutional integrity of the UK should be possible, they say.

But this may be easier than it sounds. 

The Withdrawal Treaty is a legal text which will bring with it new legal realities (as does, of course, Brexit).

"De-dramatisation can go a long way in making everything seem low key and unobtrusive," says one source close to the negotiations. "The question is not how you name it, but what the reality of it is."

That will be the real negotiating battleground after Salzburg.

There is also the question of the political declaration that accompanies the Withdrawal Agreement.

It will sketch out what the future relationship will be, and it will most likely take up most of the October summit (with a mid-November summit becoming the new Withdrawal Agreement deadline). 

Dublin and Brussels have seen it as a way of providing the kind of reassurance London wants that the backstop will only be used if the agreed future symbiosis does not eliminate the need for customs and single market compliance checks and controls.

Both the divorce treaty and political declaration are closely linked, but the latter is not legally binding.

For that reason London is digging in its heels on a UK-wide customs backstop to be enshrined in the Withdrawal Agreement. 

UK sources say whereas a Northern Ireland-only backstop would be legally binding in the Withdrawal Agreement, a UK-wide customs backstop would only be "a vague promise" in the political declaration.

The problem, officials say, is that customs is a binary issue, while there is more scope for creative drafting on continued regulatory alignment as regards the single market. 

You are either in one customs regime or you aren’t.

However, the EU applies the same logic. 

The Union Customs Code is an internationally recognised entity which sets a common external tariff around the perimeter of the EU, and allows goods to circulate inside that perimeter once the common tariff has been met by importers buying goods from third countries.

It means a single trade policy which the Commission pursues on behalf of members.

If the UK wants it to apply during the transition and beyond in some ambiguous, staggered fashion, in order to accept the backstop, then the EU will probably only permit that if London abides by those same rules, the ones which are, of course, anathema to Brexiteers.

The final weeks will therefore be a bruising contest over Ireland.

The UK will uphold its depiction of the backstop as a constitutional threat and will press the EU to push its rulebook on customs to the limit – and perhaps beyond – while Dublin and the Commission will push for what they see as a pragmatic approach which builds on differences between Northern Ireland and the rest of the UK that already exist.

The UK is effectively saying it cannot accept a Northern Ireland-only backstop with only the promise of it never coming into effect; Ireland is saying it cannot rely on the future relationship as a guarantee of avoiding a hard border.

For both Theresa May and Leo Varadkar, the domestic repercussions of how this plays out could not be more stark.

"What it boils down to," says Paul McGrade, a consultant with Lexington Communications and a former Foreign Office official, "is this - who is prepared to bear the legal risk, and who bears the political risk."

So this is the context as we head towards Salzburg. 

It is salutary to remember that, aside from the associations of classical harmony, the city’s name in German means "Salt Fortress…"