Was Jesus crucified?

Question
Was Jesus of Nazareth crucified on a Roman cross? Was he lifted up on wooden beams (or a wooden beam, we don't meant to debate here its configuration) for the purpose of executing Jesus in an excruciating way, as instigated by Roman authorities?
1. Christopher Bryan (NT Professor at Sewanee): “Jesus was crucified under Pontius Pilate. That, as a matter of history, is just about as certain as anything in antiquity.” [The Resurrection of the Messiah (Oxford, 2011), 3.]

Historians

See quotes from historians saying Jesus specifically died by crucifixion. Included are quotes from Paul Maier, Luke Timothy Johnson, John Crossan, Craig Keener, Raymond Brown, and Gerd Lüdemann. They each say it is essentially an indisputable fact granted by all parties across the theological spectrum.

“Yes, after all…

Early Christians said Jesus was crucified
- (AD 33) The 1 Corinthians 15 creed (apostles) says Jesus was crucified.
- (AD 40-50) Paul was saying Jesus was crucified.
- (AD 40-90) The Gospels say Jesus was crucified.¹
- (AD 70) Acts of the Apostles says Jesus was crucified.²
This is relevant because there are no exceptiosn or instances where Christians doubted Jesus's crucifixion. There are also many reasons to think this is not the sort of things Christians would invent. (It was rather humiliating in general for one's leader to be excuted like this by Roman enemeis, but all the more for the prophesied Messiah to be so humiliatingly destroyed by the very people [Romans] he was supposed to deliver them [Jews] from.)
1. Mt 27:32-56 (see v. 35, 50), Lk 23:26-46 (see v 33, 46), Jn 19:17-30 (see v. 18, 30).
2. Acts 2:23; Acts 13:29,

Early non-Christians said Jesus was crucified
- (AD 55) Thallus's 3rd volume of his history book says Jesus was crucified.
- (AD 93) Josephus's ‘Jewish Antiquities’ 18 says Jesus was crucified.
- (AD 150) Justin Martyr's ‘Dialogue with Trypho’ says Jesus was crucified.
- (AD 165) Lucian's book, ‘The Death of Peregrinus’ says Jesus was crucified.
- Talmud b. Sanhedrin 43a. “On the eve of the Passover Yeshu [Jesus] was hanged [or crucified]. … Since nothing was brought forward in his favor he was hanged on the eve of the Passover.”