How accurate is the three month treasury?

A silly question, maybe. What happens on a 3 month basis? Institutions make their quarterly ledger entries for  government.

So both the  term and the rate are set by fiat.   Fiat in the sense that government creates synchronizes the short term volatility to three month periods.

But term and rate are slightly in error when compared to an alternative approach.  If business and individuals were honest, and reported to government only when they make compliant changes to restore reserves. Move toward the sandbox concept of honest contracts reporting asynchronously as needed. We get asynchronous, adaptable interest charges, sandbox style.  Fixed term rates set by insurance companies, smart contract style.

The asynchronous system  still generates something around the three month rate.  Government really needs to know when stuff is out of variance, it uses periodic reporting for convenience. There is a natural yield curve, the terms and interest charges market determined according to the depreciation cycle of rel goods. The posted, periodic curve is a good approximation, but will have measurable error bounds.