Cut halfpennies and farthings on Numista - different coins, different variants or not different?

A large number of medieval coins were cut - both at the mint and during transactions - to provide fractional denominations. In England, this was done for the best part of 500 years, from Saxon times until Edward I introduced round farthings and halfpennies. My question is - should 'cut halfpennies' and 'cut farthings' (as they're described by dealers) be recorded on Numista separately from the uncut versions?

They're clearly struck in the same way as the complete versions, and all halves and quarters would exist of one whole. However, they were intended to be cut, and were cut at the mint. They're certainly different in terms of shape, size, weight and 'face' value (not that the value is written on them, even on the whole coin). So does this make them different coins, given they were different denominations once the production process was complete?

On Numista, the problem with ignoring the fact that they're cut is that the values and prices displayed are not for like coins - some are literally half or quarter of others. It also means you have to record that you have e.g. a Henry III penny when, in fact, you have a farthing. (I don't think the recipient in a swap would be pleased to get a VF cut half instead of a VF whole).

If they were recorded separately, that could either be done with each as a separate page, or as a different 'variety' on the same page.

I can only find one example on the site presently, and that is a different page for the coin (which doesn't look as if it was cut at the mint):
https://en.numista.com/catalogue/pieces109847.html