The claim under examination: Jesus was crucified, died, and was later raised, and his earliest followers encountered him alive.
Standard · preponderance of the evidence, not proof
The verdict
The core facts, the death, the early appearance-belief, Paul, and James, are strongly supported. The resurrection is the strongest single explanation of them and fits better than any one natural alternative, but it is not laboratory certainty, and a principled naturalist can still withhold. We follow the evidence; we do not use the word proven.
If you read nothing else
He was crucified, as solid as ancient history gets. Very soon after, people who had every reason to give up were insisting he was alive, and two of them had been on the other side. Natural explanations each take a bite; none swallows the whole thing cleanly. The resurrection is the best explanation on offer. Not proven. Just, on the evidence, the way I would bet.