The 14th century theorem has long been debunked, as the Pray-codex https://en.m.wikipedia.org/wiki/Pray_Codex contains strong evidence that the shroud was already known in the 12th century.
The 14th century radio carbon dating is still by far the most accepted dating. Even the wikipedia article you linked describes the Pray-cosex as not being definitive.
IMO a plausible theory here is that imagery of Jesus's death with those "distinctive features" was already popular at the time and both artifacts are representative of that imagery.
The best explanation to what the codex depicts, is the shroud. Which could be a copy of an older shroud e.g., but the C14 dating has its flaws (burnt material etc.).
The Pray codex is listed under “fringe theories” in the Wikipedia Shroud entry. That certainly make it wrong, but it does make it a little more suspect than the c14 dating criticism. The c14 contamination arguments seem more than adequately addressed in the entire last 3rd of the article.
Yes, the wikipedia article makes an argumentation error. Even if the Pray Codex doesn't show the shroud, it contains a very unique depiction of a nude Jesus. So the painter of the codex with high probability have seen the exact same picture as what is on the Shroud now. This doesn't prove that the shroud is earlier than the Pray codex, but this is something an unbiased scientist have to try to answer. I find it very annoying that all these very scientific-looking articles never try to explain how the hell is it possible that the Pray codex contains a depiction of the dead Jesus in a way, of which the first known depiction is from a century later in a photonegative form. Not to mention the other ridiculous arguments, that the shroud is one from the enormous amount of medieval forgeries. Where are all the other photonegative shrouds and pictures. I personally don't think that a supernatural creator omniscient etc god would create a photo of his resurrecting son, but I am really annoyed by all that bad science around the shroud. Ok, the C14 is real, because they told so (yeah, science never tries to find contradicting evidence, never challenges previous knowledge or belief...) but then you could still use Occam's razor to find simple explanations for like the Pray Codex depiction. At least please try to explain, why the drawing there is so different to all other drawings of Jesus in that era.
'Cause A caused both B and C? If you see the codex and the shroud contain the "same" information, doesn't it seem reasonably likely they got it from the same place? And people weren't bad at copying back then, so the "same place" could really be all over.
I don't think you can "debunk" something merely with strong evidence.
Besides that, I wasn't aware of this codex, so I'm glad you shared it. Has anyone suggested that (assuming there is a relationship) the arrow of causality might go the other way? That perhaps this image was a reference for the shroud itself?
The C14 dating is one evidence, and there are plenty of contradicting evidence for the 14th century dating. But my main point is that there is at least doubt for the 14th date, and any proper scientific approach should at least mention the codex.
IMO a plausible theory here is that imagery of Jesus's death with those "distinctive features" was already popular at the time and both artifacts are representative of that imagery.