Extract a domain-neutral UCT kernel from continuous Formula MCTS

[proerror77]

Parent

#184

Change contract

Extract deterministic UCT tree mechanics from the existing continuous Formula MCTS into one shared research-core module, while keeping Formula candidate generation and continuous evaluation behavior unchanged.

Acceptance evidence

• The shared kernel owns node visits/rewards, UCT selection, deterministic RNG state, backpropagation, and checkpoint validation.
• The existing Formula MCTS delegates those mechanics through a Formula adapter.
• Fixed-seed propose/observe/checkpoint/restore parity tests prove the same next Formula candidate and node metrics before and after extraction.
• Invalid/cyclic/mismatched checkpoints remain fail-closed.
• The PR stays below the scope guardrail or documents a mechanical-move exception before review.

Out of scope

Prediction-market code, LLM proposals, evaluator changes, collector/snapshot work, cloud execution, and checkpoint deletion.

Rollout/rollback

No schema cutover. Revert restores the current Formula-local implementation.