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r-irber-irbe/proof-skills/skills/lean-research/SKILL.md

lean-research

Skill3 starsChanged 24 days agoApache-2.0View on GitHub

USE FOR: per-question Lean 4 research: picking a research method (Mathlib grep / Web / repo grep / sub-agent). DO NOT USE FOR: full council convocation (@research-council). TRIGGERS: research, mathlib lookup, find lemma, theorem search, Loogle.

The file

We split this skill into the rules it gives an agent

5 rules. About 0 are common, 3 are distinctive, and 2 are very specific to this project.

  • ≈0

    Common · estimate

    Many files like this have a rule of this kind.

  • ≈3

    Distinctive · estimate

    This author's own choices. Worth a look.

  • 2

    Very specific

    Tied to their project's names, files or tools. Probably skip.

  • Common
  • Distinctive
  • Very specific
  1. Very specific:

    Run the discovery ladder in references/discovery-ladder.md whenever the answer depends on an existing theorem, package, or literature …

    line 59
  2. Distinctive:

    If the question is typed, switch to the typed protocol (handbook Part 9: M = Mathlib, T = Tactic, L = Literature, S = Strategy, D = Domain, …

    line 63
  3. Distinctive:

    STOP if findings contradict the Rumsfeld matrix classification (handbook Part 5) — re-classify the question first.

    line 69
  4. Very specific:

    STOP if Mathlib version drift is suspected — re-verify symbol existence at the current pin per the verification discipline memory.

    line 71
  5. Distinctive:

    STOP before calling a negative theorem/package result exhaustive unless the discovery ladder's required rungs and query variants are …

    line 74

≈ “Common” is an estimate: at least 1 in 5 of the 350,495 skill files we read have a rule of the same kind, not the same words. “Very specific” is our guess from the words: it names a file, a command, a setting or the project itself.

Keep what fits and drop the rest. Your version, ready for your agents.
Files
SKILL.md

Lean 4 Research Skill

Systematic methodology for investigating proof strategies, API availability, tactic behavior, and academic connections during Lean 4 formalization.

Routing

  • USE FOR / DO NOT USE FOR / TRIGGERS — see the description field in the YAML frontmatter above. Same dispatch contract is restated here for in-skill discovery.
  • USE FOR: per-question Lean 4 research — picking a research method (Mathlib grep / Web / repo grep / sub-agent), running the discovery ladder for Mathlib/Loogle/Reservoir/GitHub/literature lookups, choosing depth (Shallow / Standard / Deep / Exhaustive), emitting a findings + recommended-strategy + Zettel triple, integrating with the Rumsfeld epistemic matrix and the review council, running a typed protocol (M / T / L / S / D / X / E).

Workflow

  1. Classify the research trigger (handbook Part 1) — confirm research is warranted vs proceeding with current evidence.
  2. Pick a method (handbook Part 2), a depth level (handbook Part 4), and the applicable discovery-ladder type: Symbol, Package, Literature, or Strategy.
  3. Run the discovery ladder in references/discovery-ladder.md whenever the answer depends on an existing theorem, package, or literature anchor. Record misses with the negative-result block from that reference.
  4. If the question is typed, switch to the typed protocol (handbook Part 9: M = Mathlib, T = Tactic, L = Literature, S = Strategy, D = Domain, X = Cross-domain, E = Empirical).

Recovery & STOP

  • STOP if findings contradict the Rumsfeld matrix classification (handbook Part 5) — re-classify the question first.
  • STOP if Mathlib version drift is suspected — re-verify symbol existence at the current pin per the verification discipline memory.
  • STOP before calling a negative theorem/package result exhaustive unless the discovery ladder's required rungs and query variants are recorded.

Handoffs

  • Predecessors: agent:gateway, skill:lean-proof, skill:lean-proof-review, skill:lean-specification, skill:lean-blueprint.
  • Successors: skill:lean-zettelkasten, skill:research-council, skill:research-synthesis-engine, skill:lean-package-research, skill:lean-proof, skill:lean-proof-review.

Detailed reference

Full encyclopedic reference, decision trees, and lookup tables live in references/lean-research-handbook.md .

See also

  • ../../references/lean-research-handbook.md -- Complete lean-research Handbook
  • ../lean-gateway/SKILL.md -- Top-level skill router

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