LLM backtest auditing is a calibration problem: a useful auditor must identify methodology flaws without falsely accusing matched clean strategies. We construct a 96-item paired benchmark in which every flawed backtest has a clean control that holds the strategy, dates, code style, labels, and reporting scaffold fixed while changing one methodology detail. The benchmark covers eight flaw classes, three difficulty strata, prose and code surfaces, and 1,440 cached audits from four smoke-tested text endpoints. A deterministic scorer separately evaluates flaw classification, clean-control false positives, evidence localization, and fix relevance. The primary auditor reaches 100.0% closed and clean-aware code recall, yet open prompts falsely flag 93.8% of clean code controls. A clean-aware warning reduces its code false-positive rate from 20.8% to 0.0% while preserving 100.0% recall, although clean-aware all-three specificity remains 87.5% because some proposed fixes are incomplete. Model behavior differs sharply under the same clean-aware prompt: some models produce no clean false positives, while another flags 38/48 clean controls despite retaining high recall. Reporting recall alone would therefore hide large differences in practical audit quality. The benchmark does not certify live trading systems; it isolates whether an LLM can identify a planted flaw without manufacturing one in a clean counterpart.

Modern coding agents pair LLM generators with various tools, including cheap diagnostics and expensive verifiers. The tool-use decisions are typically governed by orchestrators that often use fixed rules and ignore uncertainty. We formulate orchestration as cost-sensitive sequential hypothesis testing: a Bayesian controller maintains a belief over candidate correctness and dynamically decides whether to gather more evidence, refine the candidate, verify it, or stop. Across six generators and nine coding benchmarks, Bayesian control proves to be most valuable when verification is costly and critics are informative but imperfect. Beyond control, the belief state yields an interpretable correctness score that outperforms token-probability and raw tool-success baselines for uncertainty quantification.

Test-time compute (TTC) scaling has emerged as a powerful paradigm for improving large language model (LLM) reasoning by allocating additional compute during inference, e.g., via multi-sample generation and verifier-based reranking. Existing TTC scaling strategies and reasoning scorers remain fragmented, evaluated under inconsistent protocols, and are rarely analyzed through the lens of quality-cost trade-offs. We introduce ThinkBooster, a unified framework for seamless test-time compute scaling of LLM reasoning, which consists of (i) a modular Python library implementing state-of-the-art TTC scaling strategy and scorer families, (ii) a benchmark that jointly evaluates performance and computational efficiency, and (iii) a deployable OpenAI-compatible proxy service that enables drop-in integration of adaptive reasoning into real-world applications. We further provide a demo visual debugger for inspecting the reasoning trajectories, intermediate selection decisions, and alternative reasoning paths. Empirical results on mathematical and coding tasks reveal the performance-compute trade-offs of TTC scaling strategies and scoring methods and demonstrate that ThinkBooster provides practical gains in real-world tasks. The code is available online under an MIT license.