Where in the Constitution does it say that when a Territory enters the Union to become a State that the Federal Government gets to claim any part of it as Federal Land?
The way it is supposed to work is the Government is to deal with the State government who represent the citizens of the new state to work out Federal claims on plots of land (For Federal Buildings and such). There has long been a claim the Feds fudged that part of the deal on many of the Western states when they were brought into the Union.
There is one school of thought this was done so that the Politiclowns of that time could deal out land for votes/campaign contributions/graft to Railroads/Big Money interests and the like.
As of March 2012, out of the 2.27 billion acres in the country, about 28% of the total is claimed by the Federal government according to the Interior Department (including over 80% of the State of Nevada ).
If what you say is the correct understanding of the intent of the framers of the Constitution, the Federal government been violating it for over a hundred years with the complicity of the states.
Although my research is just know getting to this point in history, you conclusion is essentially correct.
From what I've read so far, what happened is the Territories became States with the proviso of them becoming States is that they turn around and ceed any claims over massive amounts of land to the federal government once they became States. Several bills in the Library of Congress show the feds were selling the States the land back....piecemeal.
What better way to plump the federal coffers? As long, of course, you can ignore the fact it violated more than one provision in the Constitution and that pesky little 'under duress' thing.