Migrate Formula Alpha Search control state to the shared MCTS kernel

[proerror77]

Parent\n\n#184\n\n## What to build\n\nMove the Formula Alpha Search controller from its private factor-name visits/reward/backpropagation state onto the existing shared MCTS kernel while preserving Formula candidate identity and the causal time-series evaluator. Existing Alpha Search artifacts become read-only projections of that Formula adapter checkpoint.\n\n## Acceptance criteria\n\n- [ ] Formula candidate identity, parent lineage, reward, budget, selection, and resume are owned by the shared kernel.\n- [ ] The existing Formula evaluator remains the sole producer of Formula reward; prediction settlement evidence is never accepted.\n- [ ] mcts-state and expansion-plan artifacts derive deterministically from the Formula adapter checkpoint and contain no independent UCT update path.\n- [ ] Invalid legacy Alpha Search state is rejected with an explicit version diagnostic; it is never silently reinterpreted.\n- [ ] Focused counterexample tests cover deterministic resume and rejection of a forged/mismatched artifact identity.\n\n## Out of scope\n\nPrediction checkpoint artifact publication (#202), collector/snapshot changes, evaluator metric redesign, cloud result publication, Paper/Live, OMS, and RiskGate.\n\n## Blocked by\n\n#185\n\n## Rollout / rollback\n\nPublish the new projection beside the legacy artifact for parity. Rollback selects the previous Formula image and checkpoint schema; mixed checkpoint writers are forbidden.