AP: We may wonder why there are reasonable doubts concerning the historicity of specific details surrounding the crucifixion. Generally speaking, doubts arise about specifics. We are talking about things like whether the nails pierced Jesus' wrists or his palms, whether or not Jesus said certain things while he was on the cross, how they drew lots for Jesus' clothes, whether a spear was thrust into Jesus' side, etc. And what's the reason for all this doubt? It's because the allusions and quotes from Psalm 22 are omnipresent. It makes us ask to what degree is the Psalm responsible for shaping the way the narrative is constructed.
On the other hand there are details for which there can be no doubt regarding their historicity. They are, in my opinion, the following: the titulus crucis (the inscription fixed to the cross that indicates the cause behind Jesus' crucifixion ["King of the Jews"]) has the highest overtones of being authentic. Pilate probably had it done to warn other would-be rebels in the empire, letting them know that they would suffer the same fate if they acted in a like manner. The restless Jewish people should know that the crimes of "treason" that is, against the constitution of the empire or against the power and the figure of Emperor would not go unpunished.
And here we can see how the Gospel of John dramatizes and exaggerates the episode: the text was trilingual; Pilate argues with the chief priests about the accuracy of the title "King of the Jews"; it is Jesus who says so, argued the elders; but it's not true, it is argued; the prefect, skeptical as he is, does not know what the truth is (John 18:38), but he imposes his will upon the Jews. But despite the dramatization, it is important to note how all the evangelists agree in substance: the charge against Jesus is that he proclaimed himself the "King of the Jews," which refers to the Davidic messianic claims of Jesus, at least according to his entry into Jerusalem.
Given "death by crucifixion" was not something that happened every day, even in a place like Judea, and it was Pilate's custom to inform the emperor of things that happened in his government, he presumably sent a report to Rome informing them of this event with Jesus, which was received and filed.
This could explain the text of Tacitus in his Annals XV 44.3: "This name [Christians] comes from Christ, who was executed under Tiberius by Pontius Pilate." To this adds José Montserrat, in the book ¿Quién mató a Jesús?, that in the manuscript (unfortunately the only one) of the Annals of Tacitus the word written is chrestiani not christiani. Our illustrious colleague argues that the fact of the mention of the crucifixion of Jesus by work of Pontius Pilate (not to mention the Jews!) was due to a "philological" desire for accuracy by Tacitus: the Roman people mistook the name that referred to the alleged cause of the fire in Rome as a chrestiani and not christiani. And he, Tacitus, put the right way (chri)- and identified the one who killed him as Pontius Pilate. Therefore, the text of Tacitus is not a gloss of a Christian scribe. It shows that at the beginning of the 2nd century this fact was well-known in Rome–if imperial files were consulted–that Jesus had died on the orders of Pontius Pilate.