Discover, audit, narrow, and lock a high-value research direction through iterative dialogue, systematic literature retrieval, mathematical formalization, novelty and feasibility audits, boundary analysis, kill criteria, and pivot planning. Use when a user wants to choose or refine a research topic, test whether an idea is novel and feasible, formalize a research question, prepare a research prospectus, build a long-term research plan, or red-team an existing direction. Do not use to promise publication or dress up an unimportant problem with complex methods.