What are the proofs for the permissibility of offering a fidyah for delaying a compensatory fast without a valid excuse, and what are the proofs for its impermissibility?

It was previously mentioned that the evidence for the obligation of the fidyah (definition) (expiatory payment) on one who delays making up missed fasts without a valid excuse until the next Ramadan (definition) begins is well-established. Those who argue against the fidyah contend that making up fasts is always obligatory on an extended basis (i.e., not immediately due), and that the obligation of fidyah was not proven from the Prophet, peace and blessings be upon him. However, the view that the fidyah is obligatory when delaying making up fasts without a valid excuse is stronger because it is the view of a group of Companions, and no dissenting opinion from them is known.