Lophiodon and Eolophiodon move to Amynodon as basal Perissodactyla

The mammal subset
of the large reptile tree (LRT, 2340 taxa) continues to be difficult to fully resolve. That is caused by corrections that still need to be made.

Progress continues.

Recent corrections
to Amynodon [now Sharamynodon] (Fig 1) a traditional rhinoceros now nests it with overall similar Lophiodon and Eolophiodon (Fig 1). Now all three are basal perissodactyls (odd toed ungulates) with four fingers (2–5) and three toes (2–4).

Even so finger 3 and toe 3 are the most robust.

These taxa share
a tall, narrow skull, small canines and lophiodont molars. Though these taxa are considered perissodactyls, I have not seen a published study that compares them to each other as close relatives. Lophiodontidae are traditional chalicothere relatives within Ancylopoda = ungulates with claws. Amynodontidae are traditional hornless rhinos.

In the LRT chalicotheres nest with elephants and astrapotheres basal ungulates derived from large adapids, among the most primitive primates.

In the LRT perissodactyls arise from the most primitive artiodactyls, pigs and pre-pigs like Ancodus = Bothriodon. These retain 5 fingers and 4 toes.

Amynodon advenus
(Marsh 1877; 1m in length; Oligocene-Eocene, 40-23 mya) was originally considered an aquatic rhino. Here it nests with Lophiodon and Eolophiodon. The long neck and other traits are more horse-like than rhino-like. Manual digit 5 was retained. The skull was narrow and deeper as in basal forms like Hyracotherium.

Lophiodon ballardi
(Cuvier 1822, Holbrook 2009, originally Tapirotherium Blainville 1817, Eocene) is traditionally considered a chalicothere or a tapir. Here it nests with Eolophiodon and Amynodon. Note the four fingers and three toes. The dentary tip rises. The skull length is equal to the neck length. The limbs are short and robust.

This appears to be a novel hypothesis of interrelationships.
If not, please provide a citation so I can promote it here.

References
Cuvier G 1822. Recherches sur les Ossemens Fossiles (Nouvelle Edition)2(1): Chez G. Dufour et E. D’Ocagne, Paris, France.
Holbrook LT 2009. Osteology of Lophiodon Cuvier, 1822 (Mammalia Perissodactyla) and its phylogenetic implications. Journal of Vertebrate Paleontology 29(1):212–230.
Marsh OC 1877. Notice of some new vertebrate fossils. American Journal of Arts and Sciences 14:249-256
Vautrin Q et al. 2020. New remains of Lophiaspis maurettei (Mammalia, Perissodactyla) from the Early Eocene of France and the implications for the origin of the Lophiodontidae. Journal of Vertebrate Paleontology.40(6) e1878200.

wiki/Sharamynodon
wiki/Lophiodon
wiki/Amynodontidae
wiki/Lophiodontidae
wiki/Ancylopoda
wiki/Perissodactyla