O’Connor et al. 2020 are not giving up without a fight.
Now they are arguing against a published objection (Li et al. 2020) to their interpretation of Oculudentavis as a strange tiny bird encased in Early Cretaceous Burmese amber. Citation and excerpts are below. You have to admire their courtesy while defending their hypothesis with every weapon they have… except the correct one.
From the O’Connor et al. abstract:
“We welcome any new interpretation or alternative hypothesis regarding the taxonomic affinity of the enigmatic Oculudentavis khaungraae. However, here we demonstrate that Li et al. have failed to provide conclusive evidence for the reidentification of HPG-15-3 as a squamate. We analyse this specimen in a matrix that includes a broad sample of diapsid reptiles and resolve support for this identification only when no avian taxa are included. Regardless of whether this peculiar skull belongs to a tiny bird or to a bizarre new group of lizards, the holotype of Oculudentavis khaungraae is a very interesting and unusual specimen, the discovery of which represents an important contribution to palaeontology.”
‘Regardless’ indeed, as a scientist it’s your job to figure this out. This time it’s not either this or that… it’s something else, a third alternative nobody wants to talk about.

FIgure 1. CT scan model from Li et al. 2020, who denied the presence of a quadratojugal and an antorbital fenestra, both of which are present. Arrow points to antorbital fenestra Colors applied here. In the LRT Oculudentavis nests with Cosesaurus, a pterosaur precursor. See figure 2.
Interesting that O’Connor et al. bring up taxon exclusion,
yet keep excluding the taxa that would resolve this stand-off, members of the Fenestrasauria (Peters 2000). The O’Connor et al. taxon list was ‘broad’, but not broad enough.

Figure 2. Cosesaurus flapping animation. This sister to Oculudentavis in the LRT was a flapping lizard and a pterosaur precursor provided with locked down coracoids, a aternum, strap-like scapulae, an antorbital fenestra a large orbit and bulbous cranium.
From the O’Connor et al 2020 introduction.
“We welcome any new interpretation or alternative hypothesis regarding the taxonomic affinity of the enigmatic Oculudentavis khaungraae.”
No they don’t! They were sent an alternative hypothesis the day after publication. (Not whining. Just stating fact in the face of all their righteous signaling).
“Several of the squamate morphologies described by Li et al. were noted by ourselves in the original manuscript (e.g., pleurodont dentition, morphology of the eye)1. However, we will argue that other features which Li et al. describe as unusual for archosaurs are not incompatible with our original interpretation.”
The solution continues to be the third choice, which both sides continue to overlook (= taxon exclusion).
From the O’Connor et al. text,
“Li et al. criticize our phylogenetic analysis yet provide none themselves.”
Good point! A phylogenetic solution is paramount. Otherwise you’re “Pulling a Larry Martin” trying to make your argument with possibly convergent traits, not last common ancestry, which, when done right, is irrefutable.
The O’Connor et al. text continues,
“However, this does highlight a weakness of a majority of phylogenetic analyses utilized to describe new taxa. If a new specimen is identified as a bird it is analysed in a matrix targeted at birds; if the specimen is identified as a lizard, it is analysed in a matrix targeted at lizards. Descriptions of new taxa rarely include phylogenetic datasets targeted at higher level relationships such as all of Reptilia or Amniota that would be capable of testing alternative placements.”
Another excellent point! That’s why the large reptile tree (LRT, 1697+ taxa) is online and available for anyone to use, precisely for problem taxa, like Oculudentavis.
O’Connor et al. report,
“However, removal of all avian taxa results in Oculudentavis being resolved among squamates.”
That’s interesting! (and supports Peters 2007). By the way, such a phylogenetic leap rarely happens in the LRT. Removing large proximal clades usually results in the next closest clade nesting the enigma taxon.
O’Connor et al. conclude:
“Oculudentavis may represent an outstanding case of convergent evolution between squamates and birds, the likes of which biologists have rarely seen before.”
Well, yes, if you’re referring to flapping, flying lizards (aka ‘pterosaurs’; Peters 2007). This citation is rare due to academic suppression.
Unfortunately, O’Connor et al. are still missing the headline of this story: Oculudentavis is a late-surviving member of the Middle Triassic radiation that produced pterosaurs. The arose from an overlooked third clade of Lepidosaurs, some on which became protorosaur mimics. Others became archosaur mimics.
“However, regardless of whether this peculiar skull belongs to a tiny bird or to a bizarre new group of lizards, the holotype of Oculudentavis khaungraae is a very interesting and unusual specimen, the discovery of which represents an important contribution to palaeontology.”
It won’t be ‘bizarre’ once you understand what Oculudentavis is: a sister to the lepidosaur tritosaur fenestrasaur Cosesaurus. Just expand that taxon list and come to an agreement.
Again, when someone uses the word “bizarre” they have not included all the pertinent taxa. It’s sign they are giving up. Nothing is bizarre in the LRT. All enigmas are nested. No taxon stands alone.
This is what citation avoidance and suppression results in. Neither party understands what they have here. We looked at this exact problem yesterday.
We looked at the Oculudentavis controversy
earlier here, here, here, here and here. And the story has yet to reach a conclusion.

Figure 3. The origin of pterosaurs now includes Kyrgyzsaurus, nesting between Cosesaurus and Sharovipteryx.
Postscript:
The post-crania of Oculudentavis remains unknown. It could resemble anything from Cosesaurus (Fig. 3) through pterosaurs, given its Early Cretaceous age and the variety we already find in the clade Fenestrasauria, from which it arose.
References
Li Z, Wang W, Hu H, Wang M, Y H and Lu J 2020. Is Oculudentavis a bird or even archosaur? bioRxiv (preprint) doi: https://doi.org/10.1101/2020.03.16.993949 (Not cited in O’Connor et al. 2020)
O’Connor J Xing, Chiappe L, Schmitz L, McKellar R, Li G and Yi Q 2020. Reply to Li et al. “Is Oculudentavis a bird or even archosaur?” bioRxiv 2020.06.12.147041 (preprint)
Peters D 2000. A Redescription of Four Prolacertiform Genera and Implications for Pterosaur Phylogenesis. Rivista Italiana di Paleontologia e Stratigrafia 106 (3): 293–336.
Peters D 2007. The origin and radiation of the Pterosauria. In D. Hone ed. Flugsaurier. The Wellnhofer pterosaur meeting, 2007, Munich, Germany. p. 27.
Xing L, O’Connor JK,; Schmitz L, Chiappe LM, McKellar RC, Yi Q and Li G 2020. Hummingbird-sized dinosaur from the Cretaceous period of Myanmar. Nature. 579 (7798): 245–249.