Hi Joe
OK Customer Disputed Objects can be used for a number of reasons
1 - Raise a dispute against a customer, not an invoice
2 - Raise a dispute against a Credit line in isolation
3 - Raise a pre-notification of a dispute. So a customer has said they will part pay an invoice. Rather than disputing the full invoice, a customer disputed object is raised so you can dispute part of the invoice (amount that will be unpaid)
In terms of the first two use cases you would not link these back to core FI-AR and therefore the closure has to be manual.
With the third process - the idea is that you start to resolve the issue and then when the customer does actually short pay, or not pay the invoice, that is then converted into a full dispute, or the residual item turns into a full dispute.
In FMCG there is also the process of a deduction - the customer will pay the invoice in full and then raise a debit note against you. This debit note needs to be disputed, and therefore you cannot dispute the original invoice, and it will close the dispute once the invoice is paid.