Research Closeout

Close the authorized work calmly and preserve its mathematical value. A request to wind down narrows the active work; it is not a request for a fresh research campaign.

Finish the bounded work

• Inventory live tasks and the user's finishing allowance. Finish only already authorized bounded items that fit it. Stop or narrow further agent work; a discovered new route becomes a checkpoint item.
• Integrate complete results under their exact hypotheses. Keep candidate arguments and open steps identifiable. Do not repeat settled checks without a new issue.
• Update the existing checkpoint with the achieved results, unresolved target, active resources, exact next mathematical step, relevant source versions, and checks actually performed. Use state examples if a format is needed; prefer the project's existing format.
• Distinguish the task's pause from completion of the mathematical objective. Follow the host's goal lifecycle tools only when a goal exists and the user's instruction authorizes the transition. Never mark an unresolved objective complete to end a session.

Prepare a manuscript when requested

Use the supplied author identity and preserve existing attribution. Lead with the concrete theorems and their meaning. Remove internal coordination prose; replace local bibliography paths with verified public, preferably version-specific sources. Keep legitimate original results distinct from imported results and conjectural implications.

Prepare one coherent edit before proportional validation. Compile when the edited document requires it, and inspect affected PDF pages when layout matters. A successful compilation is not a proof audit. External acceptance, formalization, and a literature-priority comparison are distinct from a complete written argument.

If publication advice is requested, assess the actual manuscript and choose one of:

• Publish now: a coherent and accurately scoped preprint is ready to share, with its substantive contribution explained.
• Ready, but wait: the document is usable, but a specific contribution comparison, proof repair, or focused rewrite would materially improve the release.
• Do not publish this version: a fundamental unsupported claim or unfit presentation requires repair first.

Give concrete reasons, not a blanket rule requiring journal acceptance before a preprint. When originality matters, use contribution-review for the targeted comparison, not an unlimited new literature project.

A recommendation or publication-ready file is not authorization to publish, push, send, or submit. End with what was achieved, what was verified, and the next step for a future authorized restart. Acknowledge good mathematical work enthusiastically without claiming the main problem solved.

Use the closeout template when the user asks for an instruction to another research agent rather than edits in the current workspace.

If Lean work exists, preserve the pinned environment, exact declarations, successful check evidence, transitive-axiom output, and outstanding formal goals in the checkpoint. Record analytical proof status separately. Do not start new formalization or install tooling during a pause.