sheaf-cohomology
Čech cohomology for local-to-global consistency verification in code structure and data schemas.
npx skills add majiayu000/claude-skill-registry --skill sheaf-cohomology-plurigrid-asi-2 --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Sheaf Cohomology Skill: Local-to-Global Verification **Status**: ✅ Production Ready **Trit**: -1 (MINUS - validator/constraint) **Color**: #2626D8 (Blue) **Principle**: Local consistency → Global correctness **Frame**: Čech cohomology with descent conditions --- ## Overview **Sheaf Cohomology** validates that locally consistent data/code patches glue correctly into globally consistent structures. Uses: 1. **Čech cohomology**: H^n(U, F) obstruction classes 2. **Nerve of coverage**: N(U) simplicial complex from open cover 3. **Descent conditions**: Cocycle conditions for morphisms 4. **tree-sitter integration**: AST-level local consistency **Correct by construction**: If local patches satisfy cocycle conditions, global structure is guaranteed. ## Core Formula ``` H⁰(U, F) = ker(d⁰) # Global sections (agree everywhere) H¹(U, F) = ker(d¹)/im(d⁰) # Obstruction to gluing H²(U, F) = ker(d²)/im(d¹) # Higher obstructions ``` For code verification: ```ruby # Three patches (files/modules) are consistent iff: # On U_ij ∩ U_jk ∩ U_ik: g_ij ∘ g_jk = g_ik (cocycle condition) cocycle_satisfied?(patch_i, patch_j, patch_k) == (compose(g_ij, g_jk) == g_ik) ``` ## Why Sheaf Cohomology for Code? 1. *
- Overview
- Core Formula
- Why Sheaf Cohomology for Code?
- Gadgets
- 1. ČechCoverVerifier
- 2. NerveConstructor
- 3. DescentVerifier
- 4. TreeSitterSheaf
- Commands
- API
- Integration with GF(3) Triads
- Mathematical Foundation
- Čech Complex
- Differential Maps
Verify sheaf consistency just sheaf-check Check specific coverage just sheaf-coverage src/ Compute cohomology obstructions just sheaf-h1 Integration with tree-sitter just sheaf-ast src/*.clj
What does the sheaf-cohomology skill do?
Čech cohomology for local-to-global consistency verification in code structure and data schemas.
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill sheaf-cohomology-plurigrid-asi-2 --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.