Mr Blanch found Folbigg, who had not given evidence at trial, had been “untruthful, unbelievable and made deliberate attempts to obscure the fact that she committed the offences of which she was convicted.”

That inquiry was conducted at a cost of $2.4 million, launching three years after Folbigg’s lawyers petitioned for the case to be re-examined in light of a report they commissioned from forensic medical investigator Professor Stephen Cordner, which cast doubt on the medical evidence presented at the trial.

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Mr Blanch, a former Supreme Court Justice and Chief Judge of the NSW District Court, was not persuaded by the medical evidence presented at the inquiry that it raised a reasonable doubt as to Folbigg’s guilt.

New evidence that arose after the inquiry’s conclusion – of a genetic mutation affecting Sarah and Laura that could have triggered Sudden Infant Death Syndrome – was addressed in an addendum, with Mr Blanch again finding it did not change the outcome.

In the Court of Appeal judgment delivered on Wednesday, Justices John Basten, Mark Leeming and Paul Brereton wrote that Mr Blanch’s 2019 conclusion was not at odds with the scientific evidence, which had “raised a theoretical possibility that there were innocent explanations for the deaths of the two girls.”

Despite the existence of the CALM2 genetic mutation in Ms Folbigg and the two girls, “their circumstances departed from the reported cases of deaths associated with CALM abnormalities,” they wrote.

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“The girls’ deaths were thus ‘outliers’ when compared with those reported in the literature. Further, the boys’ genomes provided no common cause.”

When weighed alongside Ms Folbigg’s diary entries and “her evidence in seeking to present innocent explanations” for them, “there was an ample basis, consistent with the scientific evidence, for the judicial officer to conclude that there was no reasonable doubt as to Ms Folbigg’s guilt.”

Folbigg’s long-time friend and supporter, Tracy Chapman, said “today wasn’t our day” but that she and Folbigg were “content that we respectfully challenged the system” and the decision “only strengthens our resolve to keep going”.

Ms Chapman said the medical evidence has grown since the inquiry, and “many more Australians are rightly asking why Kath’s still in prison after 18 years when there’s mounting scientific evidence relating to her innocence.”

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There is just one final slice of hope left for the woman once dubbed “Australia’s most hated” and her growing army of supporters, which now includes dozens of eminent scientists.

Last month, a 14-page petition containing the signatures of 90 medical and science leaders – among them, Australian Academy of Science president John Shine, AC, 2009 Nobel laureate Emeritus Professor Elizabeth Blackburn, AC, and former chief scientist for Australia, Emeritus Professor Ian Chubb, AC – was presented to the Governor of NSW calling for Folbigg’s immediate pardon and release from jail.

A spokesperson from Government House in Sydney said the matter had been referred to NSW Attorney-General Mark Speakman and the Governor would await his advice.

Mr Speakman declined to comment on the outcome of the appeal on Wednesday, saying it would be inappropriate as the petition “remains under consideration.”

Folbigg will be eligible for parole in 2028.