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r-irber-irbe/proof-skills/skills/lean-nested-learning/SKILL.md

lean-nested-learning

Skill3 starsChanged 24 days agoApache-2.0View on GitHub

USE FOR: Formalize and extend nested learning theory in Lean 4. DO NOT USE FOR: proof tactics (@lean-proof); Lyapunov-only proofs (@lean-math-dynamical). TRIGGERS: nested learning, LaSalle invariance, learning hierarchy.

The file

We split this skill into the rules it gives an agent

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

  • ≈0

    Common · estimate

    Many files like this have a rule of this kind.

  • ≈0

    Distinctive · estimate

    This author's own choices. Worth a look.

  • 3

    Very specific

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

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

    STOP if the question is general nonlinear dynamics — delegate to @lean-math-dynamical.

    line 42
  2. Very specific:

    STOP if the spec is informal — delegate to @lean-specification.

    line 43
  3. Very specific:

    STOP if Mathlib lacks the needed primitive — escalate to @lean-research.

    line 44

≈ “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

SK-32: Lean Nested Learning Formalization

Routing

  • USE FOR: Formalize and extend nested learning theory in Lean 4. Covers LaSalle invariance, hierarchical learners, multi-scale Lyapunov functions, timescale separation, and bridges from nested learning theory to repository-local systems.
  • DO NOT USE FOR: proof tactics (use @lean-proof); Lyapunov-only proofs (use @lean-math-dynamical); review (use @lean-proof-review).
  • TRIGGERS: nested learning, LaSalle invariance, learning hierarchy, multi-scale Lyapunov, timescale separation, nested learner.

Workflow

  1. Identify the learning object: LaSalle invariance set, hierarchy level, multi-scale Lyapunov function, or timescale-separated subsystem.
  2. Pick the encoding from the body (nested-learning schema, hierarchy-level mapping, scale-separation argument).
  3. Produce the Lean statement; verify Mathlib dynamics primitives at the pin.
  4. Hand off: to @lean-proof for the proof, to @lean-proof-review for review, to @lean-zettelkasten.

Recovery & STOP

  • STOP if the question is general nonlinear dynamics — delegate to @lean-math-dynamical.
  • STOP if the spec is informal — delegate to @lean-specification.
  • STOP if Mathlib lacks the needed primitive — escalate to @lean-research.

Handoffs

  • Predecessors: agent:gateway, skill:lean-research.
  • Successors: skill:lean-proof, skill:lean-proof-review, skill:lean-zettelkasten.

Detailed reference

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

See also

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

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