Planning and budget documents naming the function, approval matrices showing your authority, leadership materials, contracts you signed, decisions recorded in ordinary correspondence, and organizational charts drawn accurately. Performance targets the function sets for others also help, as do records of who executes the underlying work.
Prefer records made for other reasons
Documents created in the normal course of business are harder to dismiss than material assembled for a file. Gather signature authorities, purchase approvals, project charters and the message where you redirected a workstream. Include the counter-evidence too: if a colleague approves your spending above a threshold, the reviewer will discover it.
Advisers can organize this into a coherent set, while sufficiency remains a judgment for licensed counsel. Include the unfavourable records deliberately rather than hoping they go unnoticed. If spending above a threshold is approved elsewhere, if a hiring decision needs another signature, if the function's budget is set by a committee, those facts form part of the picture, and a file omitting them reads as constructed rather than described.
The stronger approach shows the boundary first and then what sits inside it, since real authority is always bounded somewhere. Hypothetical example: a dredging contractor's operations lead approves equipment spending up to a set limit and refers larger purchases upward, and the file states the limit, evidences six approvals made under it, and describes the referral rule — which carries more weight than an unqualified assertion of complete authority ever would.