President who signed bill is not identified

[GPHemsley]

When a bill is signed by the President, it appears like this:

Exactly who the President is at the time of the bill being signed does not appear to be specified anywhere, and must be inferred from the date. This is particularly concerning for browsing historical bills (like the example here from 2012), and even moreso when the President might have a legislative history worth reviewing (as would be the case for e.g. President Biden).