Proof Cooker

Proof Cooker

Overview

Use this skill after proof-material contains enough indexed material to justify reusable categories. The job is synthesis: cluster source-local items, identify transferable proof shapes, merge or distinguish near-duplicates, and write concise cooked entries into proof-usage.

Do not copy every material item into proof-usage. Prefer fewer, clearer entries that a future proof agent can actually find and adapt.

Pipeline Position

proof-cooker is the synthesis stage:

proof-material -> proof-cooker -> proof-usage

Its job is judgment. It reads source-indexed evidence, decides which items share a reusable proof shape, preserves differences that matter, and updates the final playbook without erasing material IDs.

Inputs And Outputs

• Input: one or more proof-material/references/<source-slug>.md files plus the material index.
• Output: proof-usage/references/index.md, category files, and proof-usage/references/source-map.md.
• Reference templates: references/taxonomy-template.md and references/cooking-checklist.md.

Cooking Workflow

1. Load candidate material.
   • Read the relevant material files and their local indexes.
   • Track each source ID that may become part of a cooked entry.
2. Cluster by transferable shape.
   • Compare proof object, assumptions, mathematical mechanism, failure modes, and adaptation path.
   • Keep source-local differences visible when they matter.
3. Decide taxonomy placement.
   • Use local-moves/ for reusable lemmas, estimates, inequalities, localization steps, and parameter balances.
   • Use strategies/ for macro proof decompositions, auxiliary models, algorithm-analysis templates, or multi-phase arguments.
   • Add a new category only when existing files would make discovery worse.
4. Write cooked entries.
   • Use the cooked entry contract from references/taxonomy-template.md.
   • Include Material sources with stable IDs and Public attribution.
   • State assumptions and failure modes explicitly.
5. Update discovery aids.
   • Add task-shape, assumptions, desired-move, tag, and source-ID routes to proof-usage/references/index.md.
   • Update proof-usage/references/source-map.md so every cooked entry can be traced back to material IDs.
6. Preserve legacy value.
   • If old techniques.md or strategies.md entries are superseded, leave a compatibility note or link them from the source map.
   • Do not delete useful old cards unless their replacements are already indexed.

De-Duplication Rules

• Merge items only when they share the same reusable proof shape and compatible assumptions.
• Split items when the same high-level idea has materially different prerequisites, rates, objects, or failure modes.
• Compare near-duplicates in the entry instead of forcing one source to fit another source's conditions.
• Keep source attribution public and compact.

Quality Bar

• A cooked entry must be usable without reopening the original paper for the first adaptation attempt.
• A cooked entry must still let a future agent reopen source material when details matter.
• The final proof-usage index must support search by task shape, assumptions, tags, desired proof move, and material ID.
• Public files must not contain private paths, account names, raw transcripts, or unpublished project details.