feature: add verifier-guided ReMoM pruning and adaptive breadth

Summary

Improve ReMoM candidate quality and compute efficiency with deterministic evidence retention, verifier-guided round pruning, adaptive breadth, and convergence stopping.

Parent hardening tracker: #2336

Blocked by: #1456, #2855, #2856, #2857, #2858, #2861

Current behavior and gaps

ReMoM executes each configured breadth round in parallel, builds the next round's synthesis prompt from retained previous responses, and appends an implicit final synthesis round. Concrete quality/cost risks include:

• length sorting followed by deterministic shuffle can make max_responses_per_round drop useful evidence arbitrarily;
• retained trace cardinality and next-round synthesis input are coupled;
• if final synthesis fails, fallback prefers the longest publishable prior response rather than the best-supported candidate;
• breadth is static even when candidates agree, duplicate one direction, or fail verification;
• there is no shared outcome verifier or explicit convergence criterion;
• repeated same-model samples can share correlated blind spots.

Proposed phases

Deterministic quality fixes

• Separate full usable candidate state, synthesis-selected evidence, and externally included trace.
• Remove random truncation before synthesis selection.
• Replace longest-answer fallback with a configured deterministic selector and explicit low-confidence state.

Verifier-guided pruning

• Normalize/cluster answers and, where available, reasoning directions.
• Score candidates through #2857 using deterministic/trusted-context verifiers first, then calibrated outcome judges.
• Preserve minority/dissenting directions; do not equate cluster size with truth.
• Feed top/diverse supported candidates into the next synthesis prompt.

Adaptive breadth and stop

• Stop when answer/support convergence meets a calibrated condition.
• Increase or redistribute the next round only when disagreement or verifier uncertainty justifies it.
• Reserve each next round against #1456/#2861.

Research context

• NeurIPS 2025 DORA shows solution-level allocation over-spends on duplicated reasoning directions.
• ICML 2025 verifier research supports outcome ranking but warns that generic LLM critique is weak for process search.
• NeurIPS 2025 overthinking results favor multiple bounded paths over unconditionally extending one trajectory.

Non-goals

• Do not implement full MCTS/beam/KV search in ReMoM.
• Do not hard-filter candidates solely by peer consistency.
• Do not change default breadth without matched-budget benchmark evidence.

Acceptance criteria

• Synthesis evidence selection is deterministic and independent of trace display limits.
• Final-round failure uses a quality-aware typed fallback, not answer length.
• Candidate answer/direction clusters and verifier scores are replayable.
• Pruning preserves configured diversity/minority constraints.
• Adaptive breadth and convergence stop respect hard token/cost/call/wall budgets.
• Breadth ablations and fixed-budget comparisons cover same-model and mixed-model pools.
• E2E covers convergence stop, verifier failure, final fallback, budget exhaustion, and multi-round usage.