What a difference a by-election makes. A bracing dook in the Rutherglen & Hamilton West ice bath appears to have snapped the SNP out of its internal debate on the constitution.

After years of conferences specialising in gimmicks to make Indyref2 seem imminent, the party has drawn a line under ‘process’ and pivoted to bread-and-butter policies.

Well, according to Humza Yousaf, that is. How long he will keep framing the narrative is unclear and the ‘process’ is expected to return for the Holyrood election in 2026. 

However the SNP has at least settled on a plan for the general election next year - regarding winning a majority of Scotland’s seats as a mandate for independence talks.

With Labour breathing down the party’s neck and independence no shield against defeat in Rutherglen, Mr Yousaf wants to talk about the cost-of-living instead of navel-gazing.

With four options for defining that mandate before them on Sunday, delegates at the SNP conference in Aberdeen could have gone against his majority threshold plan.

But after a long afternoon, they overwhelmingly fell in behind their new leader on the issue closest to their hearts, despite some colourful holdouts, including Helensburgh activist Graeme McCormick, who said it was all “flatulence in a trance” or vague and windy nonsense.

After the worst period in the modern SNP’s history, it was not surprising that a sort of peace broke out in Aberdeen as delegates came together in the face of adversity.

But there were other undercurrents at play. 

Although Nicola Sturgeon’s name did not come up, the independence strategy debate was also about killing off another part of her legacy.

It was her idea to use the election as a ‘de facto referendum’.

Mr Yousaf brutally rejected that, earning applause for saying: “Let’s not fall into the trap of setting ourselves a bar that no other party sets itself to win.”

The former First Minister is becoming an unperson in the SNP.

Another sign of that was the return and rehabilitation of SNP MP Joanna Cherry KC.

In years gone by, Ms Cherry was treated like a leper by the party leadership. 

On Sunday, after talks with Mr Yousaf, she dropped an amendment that could have cut across his plan in the spirit of compromise and was cheered for doing so.

“I want to pay tribute to Humza,” she said, adding: “The new leadership of this party are returning our party to its tradition of respectful and reasoned debate.”

With that officially sanctioned burial, the Sturgeon era is well and truly over.

But it wasn’t all good news for Mr Yousaf. 

The more open debate also highlighted the strain and self-doubt currently afflicting the SNP.

Multiple speakers brooded over what would happen when Westminster, whether under Labour or the Tories, inevitably said No to the SNP’s latest demand for independence.

For a party which won 48 MPs in 2019, setting the threshold for claiming a mandate at 29 MPs was a tacit admission it expects to go backwards next year.

Even that target is a hostage to fortune. It will become the minimum Mr Yousaf can achieve and still hold his head high as SNP leader. If he falls short, he will be grievously wounded.

Some delegates scolded their comrades for lacking faith in the party’s ability to win big, even to win a majority of votes. Without self-belief and vision, it couldn’t sway the public to its cause, they argued.

So while it was a decent day for Mr Yousaf, there remain rumbling problems for the SNP.

His party is jumpy, spooked at its electoral mortality, up against a viable Labour party for the first time in decades and outstaying its welcome in power for increasing numbers of voters. 

Labour and Tory opposition to independence is also unchanged, so the debate over SNP mandates cannot shake off its other-worldly air. Labour's message is far simpler - vote for us to oust the Tories.

Mr Yousaf concluded by hammering home the message of having “unity” within the SNP and using it to secure independence. But in truth neither is within his grasp.