No takings clause issue with Eldred Petition

Eugene Volokh points to Texaco, Inc. v. Pond, a 1982 Supreme Court case, specifically held that the government may indeed require that owners of old property interests (there, mineral rights) periodically register their claims, and if they don't register them, the interests would be forfeited. This seems quite analogous to Larry's proposal:

We have launched a petition to build support for the Public Domain Enhancement Act. That act would require American copyright holders to pay $1 fifty years after a work was published. If they pay the $1, the copyright continues. If they don’t, the work passes into the public domain. Historical estimates would suggest 98% of works would pass into the pubilc domain after 50 years.

Petition for the Eldred Act: save the public domain | Lessig Q&A