idea-formalizer

Provide the approved idea.md for the branch and run the formalization step, which writes perspective_M/idea_N/setting.md with a Basic setup, Technical assumptions with stable assump:<slug> ids, and one Goal statement. The output follows the shared setting template exactly.

The only required input is perspective_M/idea_N/idea.md. Optional inputs include workflow_feedback.md, LITERATURE_SURVEY.md, prior same-perspective setting.md and proof_review.md files, and any existing setting.md draft for checkpoint reruns.

It identifies the semantic delta between the prior same-perspective idea and the current approved idea, preserves still-valid formalization choices from the previous setting.md, and rewrites only the modified or invalidated parts. Target-preserving repairs keep the prior theorem target; target-changing repairs are made explicit.

No. Every theorem-critical assumption must be primitive, checkable, and supported by literature, standard facts, or verification examples recorded in idea.md. If a needed assumption lacks recorded support, the workflow routes back to idea generation instead of adding it silently.

Exact-goal mode states the final theorem claim precisely when it is already known. Target-spec mode defines the target quantity, claim type, active regime, and success criterion when exact rates or constants are not yet known, without guessing unsupported sharper statements.