Most credibility problems are definition problems
Procurement reports a number. Finance cannot find it in the accounts. Both are right, because they are measuring different things and neither has said so out loud.
Procurement is usually reporting annualized run-rate value against a negotiated baseline. Finance is looking for a reduction in actual spend inside the fiscal year, at the cost centre level. Those are different numbers about the same event, and the gap between them is where trust goes to die.
Agree it in advance or argue about it later
This is the cheapest credibility procurement will ever buy, and the timing is the whole point. Definitions agreed before savings are claimed are a standard. Definitions negotiated during the argument about a number are a retreat.
The standard covers seven terms: negotiated, realized, cost avoidance, cost reduction, run-rate, in-year and working capital. It states plainly which of them belong in the P&L and which are tracked separately. Cost avoidance is real value and deserves to be reported. It is not a saving finance can bank, and saying so out loud is what makes the rest of the report believable.
Baselines decide most disputes
The rule that settles the majority of them: baseline is the last twelve months of actual spend, at the price actually paid, for the same specification. Not list price. Not budget. Not the first quote received.
And volume is held constant. Value that comes from buying less belongs to the budget owner who decided to buy less, not to procurement.
Once the definitions are agreed, the realized savings tracker is where the numbers live, and the value leakage checklist is how you find out why some of them never arrived.