The latest analysis has all but confirmed the recently announced “Gospel of Jesus’ Wife” is a modern forgery. See Mark Goodacre’s summary in Jesus’ Wife Fragment: Further Evidence of Modern Forgery or go look at Andrew Bernhard’s latest analysis directly: How The Gospel of Jesus’ Wife Might Have Been Forged: A Tentative Proposal. Bernhard is the renowned author of Other Early Christian Gospels: A Critical Edition of the Surviving Greek Manuscripts (2006).
Very early on several scholars pointed out that all the words in the fragment come from the late Coptic text of the Gospel of Thomas, and suggested this indicated forgery because such an agreement would be improbable. But in fact those agreements were not established as improbable; almost all consisted of single words, not phrases, and none of any extended length, and dependency on or similar origin to GThom could have been at play. Indeed this could even be a fragment from a redaction of GThom. In Bayesian terms, critics were saying this feature was improbable (had a low likelihood, or consequent probability) on the hypothesis of authenticity, but the fragment’s content was probable on a hypothesis of forgery. (And the prior probability is always dangerously high, owing to the fact that biblical and apocryphal texts, especially on recently fashionable subjects like whether Jesus was married, are prime targets for forgery, and like most forgeries, this fragment’s exact provenance was unknown or unverifiable).
However, this estimate of improbability (of a low likelihood) was not soundly based. Moreover, there are improbabilities also on the forgery hypothesis: forgers would more likely have attempted to create a Greek fragment to market it as earlier and more authoritative (and thus more valuable); would more likely have made the text clear rather than ambiguous; the forgery is in most respects physically excellent; etc. Whereas the fact that it had words shared by GThom is not sufficient to lower its consequent probability, because of the danger of the multiple comparisons fallacy: of all Coptic texts one could find such a match with given such a small scrap of so few words, what are the odds one will match by accident? Probably not as low as you think [as Timo Pannanen demonstrated by parody]. So the critics did not yet have a good argument for forgery. They established only its possibility, not its probability.
However, a new analysis just came out that shows features that actually are very improbable on any other hypothesis but forgery, and in this case that conclusion is self-evident even before we attempt any kind of exact mathematical calculation. These features include the repetition of typos and other mistakes from an online edition of the Gospel of Thomas in Coptic, which are extraordinarily unlikely, unless the text was being reproduced using that online resource (which would date the forgery to after 1997, when that resource first appeared online). Defenders of authenticity (if there even are any left at this point) have not yet responded to this evidence. But I think the odds of authenticity are pretty low at this point. The only way it can be rehabilitated is if proponents can show the coincidences with the online source are highly probable, or at least not very improbable, and I cannot presently imagine how they could do that.
There is one last question. Chemical tests on the ink are still underway. And whether those could be fooled will depend on exactly which tests are done (and no one has specifically said). A mere chemical composition assay could presumably be fooled by a forger simply composing a realistic ink. But isotopic tests can more likely establish a post-Hiroshima date, since any biological materials in the ink, such as oil, gall, or soot, will carry trace signatures from nuclear fallout. Only inks that set before 1945 will lack those trace signatures. (And an ink made without biologicals will fail to pass a standard assay, since no such ink would be realistically ancient.) Carbon dating would be fruitless in this case since an actually-ancient scrap of blank or washed papyrus was most likely used. Faded ink on the reverse, which does not align with the formatting on the front, is in fact already suspicious. It has been suggested that the ink on the back was washed off and reused on the other side to produce the forgery, and if that’s the case, it’s possible even an isotopic test could be fooled.
When the results of the promised chemical tests are announced I’ll add an update here and in comments below. But in the meantime, the authenticity of the fragment is already highly doubtful.