Generic manager (rank 0) loop for dynamic-assignment manager-worker MPI parallelism.

RunManagerLoop<TaskT, ResultT> uses credit-based dispatch: each worker announces its capacity (number of tracking threads) at loop start via TAG_CAPACITY; the manager keeps up to that many tasks outstanding per rank, dispatching a new task each time a result arrives. Workers are told to stop by receiving a sentinel task, sent only once that rank has zero tasks outstanding.

Requirements:

• TaskT must be Boost.MPI-serializable
• ResultT must be Boost.MPI-serializable
• sentinel must be a TaskT value that workers can detect via is_sentinel() (or be a dedicated out-of-band value)

For Phase 1 (before-EG), TaskT = std::size_t (path index) with sentinel = std::numeric_limits<std::size_t>::max().

For Phase 2 (during-EG), TaskT = Phase2Task<ComplexT> with sentinel constructed via Phase2Task<ComplexT>::sentinel().