First off, pertaining to the specific issue of Jesus' resurrection, there's an important distinction between "historical evidence for the resurrection" and "historical evidence for the belief in the resurrection." Scholars of early Christianity universally acknowledge that some of the earliest followers of Jesus came to believe that Jesus was resurrected, and even had what can be described as resurrection "experiences" (whether these are considered to be real experiences of actual events or merely subjective spiritual experiences).

1 Corinthians 15:3-8, as the original comment mentioned, is indeed an important part of this evidence.

But when it comes to assessing the historicity of the resurrection itself, things are quite a bit different. This isn't just a "purely historical" thing in the way people might think of it. Mainly because there is no such thing; all historical analysis like this necessarily encounters a bunch of philosophical and methodological problems, with no consensus at all about how to resolve them.

So we can look at individual claims and data and work with these a bit; but in terms of putting them together into some sort of synthesis that should lead us to either accept the historicity of Jesus or reject it, there's no consensus whatever, and all ways forward are uncertain.

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Getting into the actual comment.

First, there are problems with

Also, the early proclamation in Jerusalem is strong evidence that the tomb was empty. Why? Because Jesus' crucifixion was a public event with many witnesses and certainly people would have known the location of his tomb and whether it was empty or not. The apostles could not have claimed Jesus rose from the dead in Jerusalem if the location of the tomb was known and not empty.

If we're reading the gospel of Mark—which is all but unanimously thought to be the earliest New Testament gospel, upon which at least the gospels of Matthew and Luke are literarily dependent—Joseph of Arimathea has to personally request the release of Jesus' body from Pilate's custody, of his own initiative. And Mark 15:47 seems to make a point of only two others being aware of where Joseph lays Jesus' body: "Mary Magdalene and Mary the mother of Joses."

Later, these two will visit the tomb to perform an anointing ritual—which they'll find already open, with an angel who tells them that Jesus has risen.

Similar to Mark, when we get to Matthew, we also find that "Mary Magdalene and the other Mary" go to visit the tomb. But framing this event in Matthew, as it were, is an additional story that wasn't in Mark: that after Joseph had requested Jesus' body from Pilate, "the chief priests and the Pharisees" also go to Pilate, and request that they supply them with Roman soldiers to guard Jesus' tomb, under the stated pretense of preventing Jesus' disciples from stealing his body and just saying that he had been resurrected.

One big problem, though, is that most scholars acknowledge that this story in Matthew appears to be an apologetic fabrication designed to counter a Jewish rumor that the disciples took the body themselves. (You can find discussion of this in all major commentators on Matthew: Allison and Davies; Luz; Gundry; Nolland. See in particular Matti Kankaanniemi's monograph on this, and also Raymond Brown's massive commentary on the passion narratives.)

Not to mention that it plainly contradicts the other gospels: as mentioned earlier, in Mark, the tomb was already open when the two Marys arrived; yet in Matthew, the tomb isn't open when they arrive—and in fact isn't opened until an angel descends from heaven and rolls the stone back in front of them! (I've defended this interpretation in exhaustive detail here.)

Luke follows Mark, against Matthew, in having the women arrive to an already open tomb. Luke only adds one other witness to this whose presence isn't mentioned in Mark or Matthew: the women who visited to tomb tell the apostles about their discovery, and then "Peter got up and ran to the tomb; stooping and looking in, he saw the linen cloths by themselves." (One wonders why this detail wasn't included in Mark, if he was indeed "a scribe of Peter," as claimed in the original quoted comment.)

For the sake of space I won't cover what's said in the gospel of John.

Needless to say though, a lot of what I've mentioned problematizes the idea that Jesus' tomb was widely known to the wider Jewish and Roman populace, or was even directly seen by many of Jesus' own disciples.

Moving on:

At least some of the disciples were martyred for their belief and there is no evidence any of them recanted. Luke, Clement of Rome, Igantius of Antioch, Hegisippus, and others all refer to their martyrdoms. The five best-attested martyrdoms are Peter, Paul, James the Just, James the brother of John, and Thomas.

I think it's always important to note here that the apostles and disciples don't appear to have been killed specifically for their belief in the resurrection, but for other aspects of their broader religious and political ideology.

Now, for those who actually had resurrection experiences themselves, or who were close to those who had experienced them, this obviously played an important part in their conviction in Jesus. But again, there's a distinction between historical evidence for the resurrection and historical evidence for belief in the resurrection; and all we can really here is that the followers of Jesus—those who had personally had a resurrection experience and who would later be killed for their Christian faith—believed in the profundity of their experiences. So this may be evidence; but it's not quite the evidence that people may think it is.

The conversion of Paul and James, two former skeptics and individuals hostile to the church. What would cause Paul to become the greatest evangelist ever in history? Why would James suddenly go from being skeptical to becoming a leader of the Jerusalem church and dying for the cause?

This is precisely one of those things that starts to get far beyond mundane historical analysis. Neither Paul nor James is held to have actually seen the empty tomb—in fact, nowhere in Paul's epistles does he actually mention a tomb in particular, though he does mention Jesus' burial—so we're basically stuck debating the validity of the supernatural revelations ascribed to them.

The break with previous Jewish traditions. Why would they move the Sabbath to Sunday, or do away with animal sacrifice, when doing so could mean death by stoning?

Really, here, we're starting to get far beyond the issue of resurrection itself. Really now we're just talking about the strength of Jesus' followers convictions in generally. Incidentally though, the Maccabean martyrs died for their refusal to transgress the Mosaic Law, in light of their conviction of its absolute authority and eternal validity. So I don't think we can do very much with this in terms of Jesus' resurrection.

The historical accuracy of the book of Acts. Time and time again, historical and archeological discoveries have supported the claims made by Luke and he performs admirably in his reporting of the early Christian movement.

This is definitely one of the most contentious and misunderstood claims. Certainly there are those scholars who've pointed to the accuracy of certain historical verisimilitudes in Acts: authentic "local color" and so on (see for example Hemer's The Book of Acts in the Setting of Hellenistic History). But this doesn't necessarily translate to a wider historical accuracy. And in fact, a large number of scholars see Acts as in many ways a work of hagiography, or in any case a very creative or "rewritten" history of the earliest Christian movement—one that was almost certainly more unified and rosier than it actually was.

The early dating of the Gospels and Acts. There are multiple pieces of internal and external evidence that support an early dating (prior to 70 AD) for the Gospels and Acts, such as the statements by early church fathers that Mark was a scribe of Peter

Here's something that really starts to push up against mainstream academic views.

Granted, there have been perfectly respectable scholars—even non-Christian scholars, like James Crossley—who've suggested early datings for one or more gospels. Ironically though, at the same time as this person appeals to early church tradition about the Petrine associations of Mark and so on, these same traditions specify that Mark only published his gospel after Peter had died—which already brings us to the mid-60s CE!

And once we also consider the literary dependence of Matthew and Luke upon Mark—and even a probable literarily dependence of Luke upon Matthew (and don't forget Acts being written after Luke, too!)—we're clearly getting way past 70 CE for these latter gospels.

Which ties into

the statement by Luke that he knew people "from the beginning that were eyewitnesses to the word"

Of course, it's always been wondered why, if Luke is so adamant about having directly sought out eyewitness testimony, does he copy so much of the text of Mark's gospel nearly verbatim (and without attribution, at that)?

For that matter, if Luke was indeed consciously aware of the gospel of Matthew, it becomes very interesting precisely where Luke apparently diverges from Matthew—which, to reiterate, has also traditionally been held to be the eyewitness testimony of the apostle Matthew himself—in ways that appear irreconcilable.

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not a historian, but hopefully the mods will let me add a historical source.

There is no record of anyone surviving a Roman crucifixion

there is, in fact, a record of someone surviving a roman crucifixion:

And when I was sent by Titus Caesar with Cerealins, and a thousand horsemen, to a certain village called Thecoa, in order to know whether it were a place fit for a camp, as I came back, I saw many captives crucified, and remembered three of them as my former acquaintance. I was very sorry at this in my mind, and went with tears in my eyes to Titus, and told him of them; so he immediately commanded them to be taken down, and to have the greatest care taken of them, in order to their recovery; yet two of them died under the physician’s hands, while the third recovered.

The Life of Flavius Josephus, 76.