Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add plurigrid/asi --skill sheaf-cohomologygit clone --depth 1 https://github.com/plurigrid/asiWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/plurigrid/asi/sheaf-cohomology)<a href="https://agentmods.dev/skills/plurigrid/asi/sheaf-cohomology"><img src="https://agentmods.dev/badge/skills/plurigrid/asi/sheaf-cohomology/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/plurigrid/asi/sheaf-cohomology"><img src="https://agentmods.dev/badge/skills/plurigrid/asi/sheaf-cohomology.svg" alt="Reviewed on agentmods" width="80" height="20"></a>- NVIDIA SkillSpector pass
What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00024 | $0.01615 |
| Opus 5 | $0.00012 | $0.00807 |
| Sonnet 5 | $0.00005 | $0.00323 |
| Haiku 4.5 | $0.00002 | $0.00161 |
Grade A, and why
sheaf-cohomology scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 8d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 211 lines — stays where its author put it; the contents beside it link to each section on GitHub.
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:
- Čech cohomology: H^n(U, F) obstruction classes
- Nerve of coverage: N(U) simplicial complex from open cover
- Descent conditions: Cocycle conditions for morphisms
- 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:
# 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?
- Module boundaries: Each module is an "open set"
- Import/export: Transition functions between patches
- Type consistency: Cocycle = type compatibility
- Refactoring safety: H¹ = 0 means safe global transform
Gadgets
1. ČechCoverVerifier
Verify local consistency across code patches:
verifier = SheafCohomology::CechCoverVerifier.new(
coverage: [:module_a, :module_b, :module_c]
)
verifier.add_transition(:module_a, :module_b, transition_ab)
verifier.add_transition(:module_b, :module_c, transition_bc)
verifier.add_transition(:module_a, :module_c, transition_ac)
verifier.cocycle_satisfied? # => true if g_ab ∘ g_bc = g_ac
verifier.h1_obstruction # => 0 if globally consistent
2. NerveConstructor
Build simplicial complex from coverage:
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 8d ago First seen · 211 lines · 24 tokens per session scan A 57633a06840c
sheaf-cohomology is a skill published in the GitHub repository plurigrid/asi (62 stars, last pushed 2mo ago), licensed MIT. It adds 24 tokens to every session and 1,615 once invoked, about $0.0001 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-09-03.
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