Research Brief

Produce an actionable brief that treats serious progress as attainable and preserves the user's exact mathematical target.

Build the brief

• Reuse the user's definitions, current results, scope, budgets, and working files. Resolve substantive ambiguity before spending research effort; ordinary implementation choices do not need another approval.
• State the theorem or counterexample sought, including load-bearing hypotheses, quantifiers, and degenerate cases. Separate the target from assumptions permitted in a proof.
• Specify what establishes completion. Distinguish a useful lemma, an equivalent reformulation, a finite check, and a complete resolution. If the assignment is a partial theorem or an audit, use that actual assignment as the completion condition.
• Name the immediate mathematical bottleneck and a genuinely diverse initial portfolio. Let the executing agent adapt its route rather than prescribe a fixed agent allocation.
• Give direction with confidence: pursue promising constructions fully, diagnose failed steps concretely, and continue to the next useful attempt. A problem's open status alone is not a stopping argument.
• For a prove-or-disprove assignment, keep both outcomes available. A solvability assumption may frame search, but it is never a premise proving the theorem and does not authorize inventing a result.
• Include the user's pause and budget boundaries and a precise checkpoint on interruption. Never substitute endless activity for a mathematical completion condition.

Use the launch template when a full launch prompt is requested. Adapt it to the problem and omit irrelevant parts. For a requested goal, use the one-line goal template; return one physical line and one paragraph. Drafting a goal is not authorization to activate it. Use the host's goal tools only on an explicit request.

Keep the output direct and pasteable. Do not describe confidence as a guarantee of success or spend the response explaining why the problem is hard.

Consult the workflow map only to choose a next skill. The map is not an instruction to load the whole package.