## What changed
Add `history_initialization` to `x-codex-turn-metadata`, distinguishing `new`, `cleared`, `cold_resume`, `warm_fork`, `cold_fork`, and `supplied_history`.
Classify forks by whether the source runtime is loaded and has not shut down. Preserve the classification for the runtime's lifetime, including warm resumes and compaction. This records how history was initialized; it does not establish whether tool metadata is missing. Reserve the field against client-supplied overrides.
## Testing
Extend coverage for warm and cold forks, cold resumes, warm reconnects, supplied history, WebSocket metadata serialization, and reserved-field filtering.
GitOrigin-RevId: 468153512a84d0f4d4ea742198a29e0fa3873a72
