United States Senate blocks seating of Constitutionally Qualified Senator

The United States Senate has determined that the Constitutionally appointed Senator Burris does not meet their standards.
However, The United States Constitution has spelled out the necessary qualifications in Article I Section 3:

No person shall be a Senator who shall not have attained to the Age of thirty Years, and been nine Years a Citizen of the United States, and who shall not, when elected, be an Inhabitant of that State for which he shall be chosen.

Mr Burris is 71 years of age.
Mr Burris is a citizen of the United States.
Mr Burris is an Inhabitant of The State of Illinois.

So far Mr Burris has met all qualifications.

The Senate is not basing their standards on The United States Constitution.
While it is true that

Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members

Those qualifications are fully met, as we have already seen.

The Senate is basing their standard on a technicality that is in The Senates rulebook. They require the Secretary of State of The Senator's State to sign his credentials.
A seemingly reasonable point considering that each State of the Union has such a requirement to legally determine their own elections.
One thing, though, is very different here. Senator Burris was not elected. Senator Burris was appointed to The Senate in full accord with Illinois State law and The 17th Amendment to The United States Constitution

When vacancies happen in the representation of any State in the Senate, the executive authority of such State shall issue writs of election to fill such vacancies: Provided, That the legislature of any State may empower the executive thereof to make temporary appointments until the people fill the vacancies by election as the legislature may direct.

Illinois State law does not require any Secretary of State signature, nor does The United States Constitution.

There is absolutely no Constitutional basis for the exclusion of Senator Burris.