How can an HP 4100N detect non-standard cartridges?

Probably because of the electronic sensors (Chips) that are built into the cartridges. It is set up to expire when the cartridge becomes empty. So, when it is refilled, the chip still recognizes it as being empty

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RE:

How can an HP 4100N detect non-standard cartridges?

I have an HP 4100N printer. I also have a standard HP made, 61x toner cartridge. However because the HP cartridges are outrageously expensive, this particular cartridge was refilled by a professional agency. Yet the printer detects it as a "Non HP Cartridge"

How can it tell? After...

There is a small electronic chip on the cartridge, typically a small looking circuit board type card about 1/2" to an inch long & about 3/8" wide that is mounted on the top of the cartridge with copper electrical contacts on it that the printer used to detect that an appropriate cartridge is installed. The chip also carries the information about the manufacturer & if it's not an HP chip it will show on the printer display. The printer is supposed to still work even with non-HP cartridges, just try pressing the Go or Ready button to bypass the message.

The chip on the cartridge tells you that it is empty.

The printer will work just fine with out the chip.