The state university system’s Board of Governors will be asked Wednesday to sign off on the bonds, after the Florida State University Board of Trustees meets earlier in the day on the issue.The hospital is planned to be finished by December 2027 and would open with 80 beds, according to documents prepared for Wednesday’s board meetings. The university would enter a long-term lease and management agreement with Tallahassee Memorial HealthCare to operate the facility under the “FSU Health” brand.