Despite the adoption of Large Language Models (LLMs) in legal AI, automated contract revision remains impeded because generic models often treat strict legal constraints as mere suggestions. To address this safety gap, we introduce the Risk-Constrained Bilevel Stackelberg Framework (RCBSF), modeling high-stakes revision as a rigorous strategic interaction rather than an open-ended conversation. RCBSF establishes a hierarchical Leader-Follower structure: a Global Prescriptive Agent (GPA) leader imposes definitive risk budgets, while a follower system—comprising a Constrained Revision Agent (CRA) and a Local Verification Agent (LVA)—iteratively optimizes the output within these strict boundaries. We theoretically prove this bilevel formulation converges to an equilibrium yielding strictly superior utility over unguided methods. Empirically, RCBSF achieves state-of-the-art performance, surpassing iterative baselines with an average Risk Resolution Rate (RRR) of 84.21% and enhanced token efficiency. Our code is available at https://github.com/xjiacs/RCBSF .

Retrieval-augmented generation (RAG) substantially extends the knowledge boundary of large language models. However, it still faces two major challenges when handling complex reasoning tasks: low context utilization and frequent hallucinations. To address these issues, we propose Self-Correcting RAG, a unified framework that reformulates retrieval and generation as constrained optimization and path planning. On the input side, we move beyond traditional greedy retrieval and, for the first time, formalize context selection as a multi-dimensional multiple-choice knapsack problem (MMKP), thereby maximizing information density and removing redundancy under a strict token budget. On the output side, we introduce a natural language inference (NLI)-guided Monte Carlo Tree Search (MCTS) mechanism, which leverages test-time compute to dynamically explore reasoning trajectories and validate the faithfulness of generated answers. Experiments on six open-domain and multi-hop QA datasets demonstrate that our method significantly improves reasoning accuracy on complex queries while effectively reducing hallucinations, outperforming strong existing baselines. Our code is available at https://github.com/xjiacs/Self-Correcting-RAG .

While chain-of-thought prompting and scratchpads are frequently conceptualized as external memory for reasoning tasks, this perspective breaks down when a final answer must be generated from a bounded, jointly retained state. We formulate this limitation through a minimal constraint-satisfaction model in which an agent must exactly output N independent binary constraints using a shared internal and external memory configuration yielding at most 2^B distinguishable states. Under this framework, we mathematically prove a tight phase law:

p⋆(N,B)=min{1,2^B-N}.

This Joint Memory Budget Theorem establishes that each independent constraint exceeding the retained memory budget exponentially halves the probability of exact success. We further generalize this limit with adversarial robustness and a min-entropy extension that separates raw prompt length from effective independent information. To empirically test the qualitative predictions of this theory, we introduce a two-call retention protocol that forces large language models to reconstruct constraint hands solely from their bounded written representations. Comprehensive evaluations across modern long-context and reasoning models reveal sharp, capacity-dependent performance cliffs. While variables such as scratchpad formatting, effective task entropy, and answer-time external access can shift this phase boundary, they do not eliminate it. Ultimately, we demonstrate that long-context and scratchpad reasoning are fundamentally bottlenecked not by nominal context length, but by the independent information jointly available at the time of answer generation.