An Open-Label Pilot Study of VTX2735 in Recurrent Pericarditis

This is a study to understand if taking VTX2735 is safe and effective in participants diagnosed with Recurrent Pericarditis (RP). Cohort A will include approximately 10 participants and will consist of the following: * A 30-day Screening Period (to see if a participant qualifies for the study) * A 6-week Open Label Treatment Period - participant receives VTX2735 Dose A * A 7-week Extension Treatment Period (if a participant meets criteria for extension treatment) - participant receives VTX2735 Dose A * An 11-week Once Daily Treatment Period (if a participant meets criteria for this treatment period) - participant receives VTX2735 Dose B * A 14-day Follow-Up Period Cohort B will include approximately 20 participants and will consist of the following: * A 30-day Screening Period (to see if a participant qualifies for the study) * A 6-week Open Label Treatment Period - participant receives VTX2735 Dose B or C * An 18-week Extension Treatment Period (if a participant meets criteria for extension treatment) - participant receives VTX2735 Dose B or C * A 14-day Follow-Up Period Cohort C will include approximately 20 participants and will consist of the following: * A 30-day Screening Period (to see if a participant qualifies for the study) * A 6-week Open Label Treatment Period - participant receives VTX2735 Dose D or E, and B * An 18-week Extension Treatment Period (if a participant meets criteria for extension treatment) - participant receives VTX2735 Dose B * A 14-day Follow-Up Period