What is a Return? What proof do I need of deductions?

Technically, a return is any taxpayer verification of income and deductions and an agreement with the IRS, or at least no contest from the IRS. So, a "return" that everyone files every year is one definition of a return, but it is not the only one.

Since the attestation clause is a sworn statement, the taxpayer verifies the truthfulness of the return under penalty of perjury. If a taxpayer has no records of income they are required to reasonably estimate the amount. Similarly, a taxpayer must also reasonably estimate all deductions to which they are entitled. So, it would be erroneous to require a taxpayer to honestly reveal his or her income to the best of their knowledge without simultaneously allowing reasonable deductions off that income, despite a lack of hard evidence.