The hospital where terminally ill Alfie Evans is on life support has insisted it has not "given up" on him.
The statement from Alder Hey Hospital said its neurologists had "made every effort" to cure the 22-month-old's degenerative brain condition.
The hospital defended itself after online criticism during a long legal battle to move him to end-of-life care.
It said experts in Manchester, London, Stoke, Rome and Munich all agreed there was "sadly no hope of recovery".
Alfie's undiagnosed condition was described as a "progressive neuro-degenerative disease" which causes "regular seizures, particularly when exposed to light or touch".
Parents Tom Evans and Kate James want doctors to keep their son alive so they can take him for treatment in Rome and possibly Munich.
A High Court judge ruled in the hospital's favour last month, the Court of Appeal upheld the decision, and on Tuesday the Supreme Court denied the parents permission to take the case there.
They are now deciding whether to appeal to the European Court of Human Rights.
Alder Hey Hospital, in Liverpool, answered 14 "frequently asked questions" in the statement after the Supreme Court decision.
It said: "We haven't 'given up' on Alfie. We have a team of the very best neurologists who have made every effort to find a way to treat Alfie.
"Sadly, the vast majority of neuro-degenerative diseases are irreversible and have no treatment or cure.
"All the experts are agreed that Alfie's condition is untreatable and that there is no benefit to him of further investigation."
It added: "We understand that this decision is very distressing for Alfie's family at this very difficult time and we will continue to work with them to agree the most appropriate palliative care plan."
The hospital has been criticised on the Alfie's Army Facebook page, which calls for Mr Evans and Ms James to have control of his care.
Mr Evans responded to the "light and touch" claim by posting a clip of Alfie remaining still as he flashed a light on him and touched him.