feature: add adaptive-N allocation and staged early stopping

Summary

Allocate candidate sampling compute per request and stop staged generation when additional samples are unlikely to justify their cost.

Parent research tracker: #2337

Blocked by: #1456, #2855, #2858, #2861, #2862

Motivation

Fixed-N sampling wastes compute on easy/high-agreement requests and may under-spend on difficult/high-entropy requests. Sequentially generating one sample at a time can save tokens but harms latency and GPU batching. The Router has request-level complexity and decision-confidence evidence, while a Best-of-N runtime will provide answer agreement and verifier outcomes; these should drive bounded staged allocation.

Research context

• ACL 2026 Seer Self-Consistency uses cheap System-1 answer entropy to allocate parallel System-2 samples in advance, reporting lower token use and latency.
• ICLR 2026 Best-of-Infinity adapts N from answer agreement and extends weighting across multiple models.
• NeurIPS 2025 Every Rollout Counts (DORA) shows allocation by individual candidate count over-invests in duplicated reasoning directions.
• NeurIPS 2025 Does Thinking More Help? supports parallel paths over blindly extending one chain.

Proposed rollout

Phase 1: agreement-based staged sampling

• Start with a small parallel batch.
• Normalize/cluster answers and compute agreement with a confidence interval.
• Stop when the configured posterior/agreement criterion is met; otherwise reserve and launch the next bounded batch.
• Never exceed #1456/#2861 budgets.

Phase 2: advance allocation

• Use immutable Router evidence such as complexity and decision confidence.
• Optionally run a cheap non-reasoning/System-1 probe to estimate answer entropy.
• Allocate the System-2 batch size before parallel dispatch, preserving latency efficiency.

Phase 3: direction-aware allocation

• Cluster candidates by answer and reasoning direction.
• Spend additional rollouts across distinct promising directions rather than overrepresented duplicates.

Each phase requires a separate benchmark result and can land behind an explicit experimental mode.

Non-goals

• Do not add online model training or change Router signals during Looper execution.
• Do not implement global batch/capacity scheduling in the per-query router.
• Do not bypass fixed hard budgets when confidence is low.
• Do not enable adaptive allocation by default based only on smoke tests.

Acceptance criteria

• Adaptive policy consumes the typed evidence/budget contracts from #2861.
• Fixed-N remains available as the deterministic baseline.
• Every extra batch is reserved before dispatch and has a replayable allocation reason.
• Stopping criteria are calibrated on held-out data and avoid zero-as-missing confidence semantics.
• Fixed-average-budget evaluation shows quality equal to or better than fixed-N with lower tokens or latency.
• Easy/hard, low/high disagreement, and same/mixed-model slices are reported separately.
• Fallback behavior is deterministic when normalization, entropy probing, or verification fails.
• E2E covers immediate stop, maximum-N exhaustion, timeout, and hard-budget refusal.