Wouldn't the minimum discrete unit be something that is capable of recording the ID? Or, if not, space somewhere would need to identify that that atom has this

Wouldn't the minimum discrete unit be something that is capable of recording the ID? Or, if not, space somewhere would need to identify that that atom has this ID, which would take at least as much space. In other words, the act of 'assignment' presupposes some mechanism of assignment, and at a certain level of granularity the information needed for that mechanism to function is greater than the information the system can store. It would be like assigning each byte in a stick of ram a 32 bit random access ID, and trying to store the assignments in the same memory space. Memory addressing only works because we assume a linear, unchanging order.