lean-math-dynamical
Skill3 starsChanged 24 days agoApache-2.0View on GitHub
USE FOR: nonlinear dynamical systems, Lyapunov stability, bifurcation theory, catastrophe theory, control theory. DO NOT USE FOR: stochastic dynamics (@lean-math-stochastic). TRIGGERS: Lyapunov, stability, bifurcation, cusp catastrophe, attractor.
In this repository65 other files it gives its agents.
- AGENTS.mdAGENTS.md
- ai-guard-judge-evalSkill
- applied-data-information-securitySkill
- applied-engineering-disciplinesSkill
- applied-legal-reasoningSkill
- epistemic-discovery-engineSkill
- epistemic-mappingSkill
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- itp-cross-portingSkill
- lean-ai-formalizationSkill
- lean-applied-reasoningSkill
- lean-axiom-closureSkill
- lean-bigraph-modelingSkill
- lean-bisectSkill
- lean-blueprintSkill
- lean-buildSkill
- lean-causal-reasoningSkill
- lean-competitive-mathSkill
- lean-convergence-verificationSkill
- lean-core-onlySkill
- lean-dag-visualizerSkill
- lean-deep-auditSkill
- lean-doc-feedbackSkill
- lean-doc-improvementSkill
- lean-doc-requirementsSkill
- lean-enforcementSkill
- lean-formalization-breakdownSkill
- lean-gatewaySkill
- lean-integration-protocolSkill
- lean-knowledge-formalizationSkill
- lean-math-analysisSkill
- lean-math-discreteSkill
- lean-math-foundationsSkill
- lean-math-optimizationSkill
- lean-math-stochasticSkill
- lean-mweSkill
- lean-nested-learningSkill
- lean-package-researchSkill
- lean-pedagogical-expositionSkill
- lean-proof-refactorSkill
- lean-proof-repairSkill
- lean-proof-reviewSkill
- lean-proofSkill
- lean-prSkill
- lean-quality-engineSkill
- lean-replay-verificationSkill
- lean-reportSkill
- lean-researchSkill
- lean-retroactive-auditSkill
- lean-retro-methodologySkill
- lean-review-councilSkill
- lean-security-formalizationSkill
- lean-setupSkill
- lean-specificationSkill
- lean-tautology-triageSkill
- lean-upstream-portingSkill
- lean-vendor-substrateSkill
- lean-zettelkastenSkill
- math-product-managementSkill
- The first 60 shown.
The file
We split this skill into the rules it gives an agent
2 rules. About 0 are common, 0 are distinctive, and 2 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.
2
Very specific
Tied to their project's names, files or tools. Probably skip.
- Common
- Distinctive
- Very specific
- Very specific: line 41
STOP if the proof depends on a manifold or smooth-structure API not in Mathlib at the current pin — escalate to @lean-research.
- Very specific: line 44
STOP if a stochastic perturbation enters the model — re-route to @lean-math-stochastic.
≈ “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.
Files
Lean 4 Nonlinear Dynamics & Stability
Guide to formalizing dynamical systems, stability theory, and bifurcation in Lean 4.
Routing
- USE FOR: nonlinear dynamical systems, Lyapunov stability, bifurcation theory, catastrophe theory, control theory, phase-portrait analysis, attractor classification, and any deterministic system with state evolution over time in Lean 4.
- DO NOT USE FOR: stochastic dynamics (delegate to
@lean-math-stochastic); pure analysis / topology (delegate to@lean-math-analysis); optimization-only control problems (delegate to@lean-math-optimization); writing one specific proof (delegate to@lean-proof).
Workflow
- Classify the system (Part 1) — discrete-time, continuous-time, gradient, conservative, controlled.
- Pick the appropriate technique below (Lyapunov, contraction, bifurcation-normal-form, catastrophe-classification).
- Handoff to
@lean-prooffor the concrete proof; if it bottoms out in a derivative / measure step, handoff to@lean-math-analysis.
Recovery & STOP
- STOP if the proof depends on a manifold or smooth-structure API not in Mathlib at the current pin — escalate
to
@lean-research. - STOP if a stochastic perturbation enters the model — re-route to
@lean-math-stochastic; this skill covers only deterministic dynamics.
Handoffs
- Predecessors:
agent:gateway,skill:lean-proof(mid-proof stability goal),skill:lean-research(catastrophe-theory result survey). - Successors:
skill:lean-proof(apply the dynamical pattern),skill:lean-proof-review(audit Lyapunov candidate),skill:lean-math-analysis(continuous-derivative or contraction reduction).
Detailed reference
Full encyclopedic reference, decision trees, and lookup tables live in
references/lean-math-dynamical-handbook.md .
See also
../../references/lean-math-dynamical-handbook.md-- Completelean-math-dynamicalHandbook../lean-gateway/SKILL.md-- Top-level skill router
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