Live game snapshots become version 2 with the clock and each move's time left. On restore the running clock goes on from the start of the turn, so downtime is not charged; version 1 snapshots get a new clock. Saved games keep the initial time (migration 002_clock) and each move's time left.
GameClockScheduler checks every live game once a second and ends those whose running clock has reached zero, whether or not anyone is connected. The clock replaces the offline turn timeout and the inactivity rule, so both are removed with the offline times they used.
Each player starts with GAME_CLOCK_MS (5 minutes). A move deducts the turn's time from the mover; a move that arrives after the time has run out is not played and the opponent wins on time. Every ending stops the clock, and clients get the clock and the server time with each game message.
GameClock and optional clock fields on live games, end messages, move records and finished games; getClockTimes, ClockSync, getClockAtMove and formatClock with tests.
Each player has 5 minutes; the server keeps the time and a scheduled service ends games whose running clock reaches zero. Replaces the offline turn and inactivity rules.
