Generate structural V3 and/or V4 of a document from plain text input.
npx skills add https://github.com/bneb/perqed --skill geometric-flow-homotopy
Please help me install this Agent Skill. Skill: geometric_flow_homotopy Source: https://github.com/bneb/perqed/tree/main/.agents/skills/geometric_flow_homotopy Command: npx skills add https://github.com/bneb/perqed --skill geometric-flow-homotopy
Deform geometric objects continuously or via a PDE-driven flow (Ricci flow, mean curvature flow) to canonical forms, enabling rigorous proofs of topological or geometric theorems by studying the flow's long-time behavior.
Describe a Lean 4 proof skeleton that demonstrates a homotopy between two maps using the provided templates.
High-intent search queries and answers about installing and using this skill.
You formalize a homotopy equivalence in Lean 4 by applying continuous deformation templates to construct explicit homotopies between maps, verifying topological invariants through deformation retracts and fundamental group analyses.
Ricci flow in Lean 4 acts as a PDE-driven process that deforms geometric objects into canonical forms, allowing rigorous proofs of topological theorems by analyzing the flow's long-time behavior and simplifying complex geometries.
Yes, you can apply mean curvature flow templates to continuously deform geometric objects into canonical forms, facilitating the analysis of deformation retracts and fundamental groups for formalized geometric theorem proofs.
You apply Seifert-van Kampen style reasoning in Lean 4 by using the provided geometric-flow templates to satisfy explicit homotopy construction requirements, enabling fundamental group analyses through continuous deformation of spaces.
Explicit PDE-driven flows are not strictly required for all topological proofs in Lean 4, as the templates also support continuous deformations and explicit homotopy constructions, but PDE flows like Ricci flow help synthesize canonical forms for complex geometries.
The best way to simplify complex geometries in Lean 4 is to apply geometric-flow templates, such as Ricci flow or mean curvature flow, which continuously deform geometric objects into canonical forms to reveal underlying topological properties.
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