stipulate to means to agree to something. This sense of the word is often used by lawyers in litigation when agreeing to accept a fact without requiring it to be established by proof.
We will stipulate to the fact that my client signed the agreement if you will stipulate to the fact that your client received the contract before 31 May 2010.
to demand, require or to specify a requirement, often as part of an agreement
The parties stipulated that their briefs would be filed by March 31.
to specify, often used regarding the terms or conditions of an agreement or statute
The contract stipulates that payment must be made by 31 December 2010.