How PUT state idempotency works after DELETE

is the following a correct way to see how Idempotent works for a REST PUT

Given X is a request

Context_N indicates information about the context in which the operation is execute, but do not influence the state

• e.g. Device/user information

State_XN is the state after executing an operation

• Resource/Entity State as use in Real world

Meta_XN is the metadata captured or internal information in the system generated by the operation

• For example

- Audit AuthZ claims- Path or ID of record in storage- Timestamp when record     is applied in the system    initially recorded

initial state    = (X, void, void )           // X Does not existsPUT(X,Context_1) = (X, State_X1, Meta_X1) PUT(X,Context_2) = (X, State_X2, Meta_X2) Delete(X)        = (X, void, void )           // X Does not exists   PUT(X,Context_3) = (X, State_X3, Meta_X3)

Based on idempotency the following MUST be true

State_X1 == State_X2 == State_X3 

But might

Meta_X1 <> Meta_X2 and Meta_X1 <> Meta_X3