The University's policy must be that all transactions are required to be properly recorded. The policy isn't that "most are properly recorded", or the "large transactions are properly recorded." All are expected to be properly recorded and, "to the best of their knowledge and belief," deans and department heads should ensure that all transactions are recorded properly, incorporating any specific guidance received from the Campus Controller.
To answer the question directly, there is no bright line "materiality threshold" for deans or department heads as it may relate to the activities discussed in the fiscal closing certification letter. In a decentralized environment, judgment decisions related to what is, or is not, material must not be made at a department level. Judgment decisions with respect to individual transactions may seem to be immaterial, but in the aggregate may become material. In general, however, items are considered material, regardless of size, if they involve an omission or misstatement of accounting information that, in the light of surrounding circumstances, makes it probable that the judgment of a reasonable person relying on the information would have been changed or influenced by the omission or misstatement. The Campus Controller may communicate certain materiality thresholds for various transactions in conjunction with fiscal closing instructions. The dean or department head must comply with this guidance.
Notwithstanding the above, in a practical sense, given the millions of transactions in the year, it is recognized that it is not possible for every transaction to be recorded properly. So the certification doesn't imply that the dean or department head is providing absolute assurance that all transactions in their area, regardless of dollar amount, are properly recorded. They are only asserting that "to the best of their knowledge and belief," they aren't aware of any transaction that isn't properly recorded, regardless of the dollar amount, or if they are aware of a transaction that isn't properly recorded, they have disclosed it to the Campus Controller for evaluation.
We are not asking for information on items such as expense reports that relate to business conducted in June, yet are completed and processed in July. We are, however, asking whether significant revenue has not been recorded, such as grant or auxiliary enterprise revenue, large donations, etc. or whether large expenses that were incurred in the current fiscal year were mistakenly processed and recorded in the next fiscal year.
There is also no bright line "materiality threshold" with respect to instances of communications from regulatory agencies regarding noncompliance, fraud that hasn't been reported to the appropriate authorities, funds that are being used in a non-compliant manner, etc. The Campus Controller (and Campus Counsel or the Office of the General Counsel) must be made aware of any such circumstances so they can then evaluate that information within the context of their responsibilities for accurate financial reporting and the management representations they must make to the external auditors.