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Brexit is just over a month away and despite repeated claims by the government that progress is being made on changes to the withdrawal deal that might somehow make it acceptable to MPs, theres still no evidence to suggest thats actually the case.

In a speech in Strasbourg the president of the European commission, Jean-Claude Juncker, demanded operable proposals, in writing, from the UK on replacing the Irish backstop and warned a no-deal exit was now a palpable risk.

Finland, which holds the rotating presidency of the Council of the European Union, and France said whatever Britain did come up with would have to be tabled within a fortnight so it could be properly discussed by the EU27 before next months summit.

But it emerged that Boris Johnson had been taken aback during his meeting with Juncker last week at the scale and complexity of the potential problems on the border, and the extent to which Britains sketchy ideas have failed to address them.

In a speech in Madrid that went down like a lead balloon, Brexit secretary Stephen Barclay said the purist EU would have to take risks with the Irish border for a deal to be struck, demanding more flexibility and compromise from the bloc.

The government said it would present its plans when it was ready, and then angered the EU27 by insisting that the papers it finally submitted dismissed in Brussels as still very far from what was required must not be circulated.

The EUs chief negotiator, Michel Barnier, later described the British solution for replacing the backstop as unacceptable, adding that the UK governments position would have to change for there to be any hope of success.

Meanwhile, the supreme court heard arguments in London for and against Johnsons decision to suspend parliament until 14 October, including allegations that the mother of parliaments had been shut down by the father of lies and that the governments stated reasons for the prorogation were misleading.

No 10 said it could not rule out proroguing parliament again if it loses the potentially explosive case, while the judges were urged to encourage the speakers of the Commons and Lords to reconvene the parliamentary session. The verdict should come on Tuesday morning (see below).

As the prime minister headed to a UN climate summit in New York, where he was due to meet European leaders saying he was cautiously optimistic he could negotiate a deal with EU leaders, Labour continued to tear itself to pieces over its Brexit policy.

Jeremy Corbyn wanted to stay neutral and let the people decide in a referendum; activists pushed for a campaign to remain; the party conference was plunged into Brexit disarray and then into downright chaos.

In the end, Corbyn won: delegates rejected a motion that would have obliged Labour to adopt an out-and-out remain position before a general election.

In the short term, all eyes are on the supreme court, whose verdict on whether Johnsons decision to prorogue parliament for five weeks was lawful or not is expected on Tuesday morning.

A ruling against the government could trigger a constitutional eruption of volcanic proportions, one legal expert said, with much depending on how the court framed such a decision particularly if it determines that Johnson misled the Queen.

Past that, the crucial problem facing the prime minister is whether or not he can solve the riddle of the Irish backstop and thus wring a deal from the EU (he would then have to get it through parliament, of course, but thats for another day).

At the moment the two sides have starkly different visions of what the withdrawal agreement and the Irish protocol need to guarantee.

Britain has proposed Northern Ireland stays under EU rules for agri-food but that otherwise there be two regulatory zones on the island, with some checks on goods necessary albeit facilitated by technology. The EU wants to secure full frictionless trade across the island in order to maintain the status quo.

At present, there is little sign of any meaningful rapprochement.

In the Guardian, Jonathan Lis argues that the language of Brexit betrayal is poisoning politics:

Our fundamental problem is we have lost the ability to distinguish between compromise and betrayal. We now confront a situation in which language proves as dangerous as policy.

Politicians can no longer merely disagree. They must be acting in bad faith, or subverting democracy, or betraying the electorate. This finds its extreme form in the word treason, which now peppers and pollutes the language of rightwing politicians and commentators. But it has also insinuated itself into the way we address Brexit altogether.

The essential toxin here is the requirement for political purity. This is partly driven by the increasing radicalism of our mainstream political parties and partly by the appetite for nationalism unleashed by the referendum and now rapidly advancing.

Britain is no longer just riven politically and economically, but fully entrenched in a culture war which demands rigid and extreme conceptions of identity. This new polarisation necessitates an all-or-nothing stance not just on Brexit, but on politics altogether. When we join battle on those lines, we leave no room for anything in between or any obvious route to heal afterwards.

A left-leaning journalist despairs at Labours Brexit policy contortions:

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Brexit weekly briefing: no evidence of progress on deal despite claims - The Guardian