Added a DiscontinuityIndex property to ScheduleEntry and related DTOs to track the cumulative number of discontinuities in live streaming. Updated the LiveWindowCalculator to utilize this index for generating accurate EXT-X-DISCONTINUITY-SEQUENCE values, ensuring compatibility with ffmpeg-based players. Enhanced the WriteEntriesAsync method to calculate and persist the discontinuity index during entry creation. Updated relevant tests and documentation to reflect these changes, improving the reliability of live streaming functionality.