Again, Jerusalem was razed to the ground by order from Vespasian. It was rebuilt. It was razed again in 136, following the Bar Kochba revolt. A new city Aelia Capitolina, was built on the ruins. The likelihood of the Empress Helena finding the actual sepulcher, the cross (which would probably have been destroyed by then in any case) and the titulus (which may be a complete fabrication) are nil. As to any Roman records that might have survived, feel free to produce them. Remember that, in the eyes of the Roman officials, Jesus was just one more local trouble maker, like Judas the Galilean and Theudas.
This supposed report by Pilate is, along with the Acta Pilati (Acts of Pilate), a Christian fabrication. As we go from the earlier gospels to the later, Pilate is increasingly vindicated and even sanctified, just as the Jews are increasingly demonized. Ths is particularly true of the Gospel of John.
As to the Titulus, all Mark says about it is (Mk. 15:26):
And the inscription of the charge against him read, "The King of the Jews."
Matthew elaborates a bit on this (Mt. 27:37):
And over his head they put the charge against him, which read "This is Jesus the King of the Jews."
Luke simplifies this description somewhat (Lk. 23:38):
There was also an inscription over him, "This is the King of the Jews."
In all three of these descriptions, the context of the soldiers mocking Jesus is such that it's reasonable and plausible to assume that these same soldiers had written the Titulus as further mockery. It's only in John that Pilate personally writes the Titulus in a much more elaborate passage (Jn. 19:19 - 22):
Pilate also wrote a title and put it on the cross; it read, "Jesus of Nazareth, the King of the Jews" Many of the Jews read this title, for the place where Jesus was crucified was near the city; and it was written in Hebrew, in Latin and in Greek. The chief priests of the Jews the said to Pilate, "Do not write, 'The King of the Jews,' but, 'This man said, I am the King of the Jews.' " Pilate answered, "I have written what I have written."
This account is highly implausible. It's unlikely Pilate would have bothered writing the Titulus. Also, the author of the Gospel of John, writing in Greek, seems to have thought that the Jews of that day were speaking and writing in Hebrew; when, in fact, they were reading and writing in Aramaic. So, to believe John's account, we have to accept that not only that Pilate would bother to personally write the Titulus; but that he not only knew Latin and Greek, which is reasonably plausible, but that he knew and could write Hebrew - by that time only a liturgical language - as well.
The depiction of Pilate in the gospels, particularly John, is at varience with what we actually know of him. Josephus portrays him as quite brutal, and he seems to have been removed from office by the Romans for his excessive brutality. Remember that he was a protoge of Lucius Aelius Sejenus, the captain of the Praetorian Guard who was de facto ruler of the Roman Empire while Tiberius secluded himself on the isle of Capri. Sejenus was overthrown and executed when his plot to assassinate Tiberius and make himself emperor in name as well, was discovered. Those who remember the PBS series I, Claudius will recall that Patrick Stewart played Sejenus, portraying him with a certain genial malice.
The only evidence we have, outside the gospels, is a statement by Tacitus, in The Annals of Imperial Rome, written early in the second century, that Pilate crucified Christ for sedition.
In a word, no, I don't know anything of the kind. Helena's pilgrimage was made after her son Constantine had made Christianity, de facto, the state religion (IIRC Theodosius made it official). The city of Aelia Capitolina was then being reconfigured not only back to Jerusalem, but to a specifically Christian version of Jerusalem. The "reports" Helena was using as a guide were Christian writings.
Perhaps I overgeneralized. So, let's look at Jewish burial practices in the first century, the effects of repeated sackings and the antiquities market:
In the first century, bodies were laid out on a rock platform inside the family sepulcher in a funeral shroud, and allowed to decay and desiccate. Months later, the relatives of the deceased opened the sepulcher, collected and cleaned the disjointed bones and placed them in a limestone box called an ossuary. These boxes are about three feet long or less, IIRC. The relatives then placed the box in a niche and closed the sepulcher.
If the sepulcher was a free standing structure, it was likely to have been flattened in the year 70, when Vespasian razed Jerusalem. If it was dug into a hillside it would be more likely to survive. We do indeed have have some of these intact. We also have some intact ossuaries, though most of these are empty.
Another hazard faced by those sites that survived repeated razing and burial in rubble is that, once unearthed, they are vulnerable to grave robbers intent on selling materials from them on the antiquities market.
Assuming any sepulcher survives all this, given that the names given in the gospels were all common Jewish names - including Jesus (i.e. Yeshua) - it would be unlikely that we would be able to prove that the sepulcher in question was the family crypt of Joseph of Arimathea.
