Many online sources state categorically that ordinary (non-deponent, non-defective) Latin verbs have four principal parts. It is often also implied that they have a fixed order (1st pers. sgl. present active indicative, infinitive, 1st pers. sgl. perfect active indicative, and the supine). Many sources also state that the four principal parts are given in all dictionaries.
But some sources omit the infinitive or place it last. Notably, Lewis & Short lists the principal parts like this: ămo, āvi, ātum, 1. Now, you may say that the 1 effectively tells us the infinitive, and that's true - even so, a conscious choice has been made not to list all the principal parts. And more to the point, the Elementary Lewis & Short lists the forms like this: amō āvī, ātus, āre. In other words, it puts the infinitive last - so the forms aren't in (what is widely considered) the canonical order. ( https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0060%3Aentry%3Damo ) Similarly, if you visit https://logeion.uchicago.edu/amo and tab across to Gaffiot 2016 (a French dictionary of Latin), the principal parts are given as ămō, (6) āvī, ātum, āre - the standard four but in a less usual order.
I know that the canonical order for cases differs between authorities (it was traditionally nom-gen-dat-acc-voc-abl, but many recent grammarians have preferred a different ordering) but I haven't found anything about disputes over (or changes in) the canonical order of the principal parts.
But what is perhaps more surprising is that some sources add an extra principal part. So, if you look in Ernout & Meillet, Dictionnaire étymologique de la langue latine, you see: amo, -ās, -āuī, -ātum, -āre. A fifth principal part (the 2nd p. present singular active indicative) has been added. And this is true of verbs in general; "amo" is merely my example, not a unique case.
Now, English Wikipedia states as fact that Latin verbs (other than deponents etc) have four principal parts, with no indication that there is any dispute or anyone who thinks differently. But if you consult the Italian Wikipedia, it is stated equally categorically as fact that Latin has five principal parts ( https://it.wikipedia.org/wiki/Paradigma_(linguistica) ):
in latino, il paradigma è composto da cinque forme:
- prima persona singolare dell'indicativo presente attivo
- seconda persona singolare dell'indicativo presente attivo
- prima persona dell'indicativo perfetto attivo
- supino attivo
- infinito presente attivo
Any idea where the perceived need for the fifth principal part (the second person singular present active indicative form) comes from, or why the ordering varies (has the infinitive historically come second or last, or does it vary wildly)?