Switch monday-prediction-research to the shared MCTS controller

[proerror77]

Parent

#184

Depends on

#197, then #198.

Change contract

Make the official monday-prediction-research entrypoint use the shared kernel for budget, iteration ledger, selection/backpropagation, checkpoint/resume, and terminal outcomes, while the existing prediction evaluator remains the domain evaluator. Preserve an explicit legacy-controller selector for rollback; do not translate partial checkpoints.

Acceptance evidence

• Baseline-only missions with zero search budget still run exactly one deterministic evaluator pass and make no LLM call.
• Search missions resume from the shared checkpoint and select the same next candidate after process restart.
• The exact selected candidate and immutable snapshot identity reach the evaluator.
• Held-out evaluation occurs only after candidate selection and cannot feed back into the search checkpoint.
• Markov, Formula, or probability-blend model choices are evaluator/candidate configuration, not alternate loop controllers.
• Existing prediction result/evidence identity remains bound to mission, snapshot, evaluator policy, candidate, and checkpoint.

Out of scope

Deleting legacy state code, changing evaluator metrics, Alpha Search artifact format, collector/snapshot work, result publication, or execution.

Dependency / merge order

Merge #197, then #198, then this issue.

Rollout/rollback

Keep the legacy controller available as an explicit selector. Rollback selects the old entrypoint without translating a partial new checkpoint.