Elephant tusks are canines, not incisors

Traditionally elephant tusks
(Elephas Fig 1, Loxodonta Fig 2) have been considered hyper-enlongated incisors, round in cross-section, different from all other mammals with oversized incisors.

According toWikipedia-Elephant
“Tusks, which are derived from the incisor teeth, serve both as weapons and as tools for moving objects and digging.”

After further examination
incisors are absent in elephant (Figs 1, 2) and pre-elephant skulls (Fig 3). Instead, hyper-elongated canines form the tusks. The premaxillae wrapped around the underlying maxillae holding the tusks, creating the illusion that the tusks were incisors arising from the premaxillae. The bit of overlooked maxillae surrounding the tusks peeks out from around the alveoli.

Elephant ancestors
in the large reptile tree (LRT, 2340 taxa) retained large canines (Fig 3) and lost the incisors. The premaxillae were in-between the maxillae without overlap in Astraponotus and Numidotherium.

Perhaps the reason for the ‘incisor hypothesis’
is the overlap of the premaxillae laterally over the maxilla, wrapping the canine tusks in two laminated layers of bones – increasingly needed as the canine tusks grew larger and larger. The maxilla wrapped the canines, as in other tetrapods. The premaxillae wrapped the distal maxillae in elephants alone. That wrap provided a new and prominent premaxilla/maxilla suture (Figs 1, 2).

Unfortunately, the invalidated incisor hypothesis
led to the previously invalidated hypothesis that linked sirenians (= manatees) to hyraxes andelephants in traditional and genomic cladograms.

This appears to be a novel observation and hypothesis.
If not, please provide a citation so I can promote it here. Phylogenetic analysis sooner or later tells you where the mistakes appear in your scoring matrix.

Phylogenetic analysis is a powerful and authoritative tool. Embrace it.

References
Ameghino F 1901. Notices préliminaires sur des ongulés nouveaux des terrains crétacés de Patagonie [Preliminary notes on new ungulates from the Cretaceous terrains of Patagonia]. Boletin de la Academia Nacional de Ciencias de Córdoba 16:349-429.
Blumenback JF 1799. Handbuch der Naturgeshichte, 6th ed xvi, 708pp, Dietrich, Göttingen.
Brookes J 1828. A catalogue of the anatomical & zoological museum of Joshua Brookes. Esq. FRS, FLS ec. Part 1 76 pp. R Taylor, London.
Burmeister 1879. Description physique de al République Agentine, T. III 1879:517. 
Hatcher JB 1901. Report of the Princeton University Expeditions to Patagonia 1869-1899. Mammalia of the Santa Cruz Beds. IV. Astrapotheria. Scott WB ed. Vol. 6, Paleontology 3. Princeton, NJ Stuttgart 1909-1928.
Linnaeus C 1758. Systema naturæ per regna tria naturæ, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis. Tomus I. Editio decima, reformata.

wki/Astrapotherium
wiki/Astraponotus
wiki/Elephant
wiki/Mammoth – Mammuthus