# Sheaf Glue

> Exact CSP for a capability sheaf. Accept iff every local section is good and every restriction agrees. Relative H¹ is ranking/diagnostic only — never the decision. Analog of meta-review in the sheaf-* family. Use when local skills report success and you need to know whether they form a global section. Trigger on "sheaf glue", "exact CSP", "global section", "Φ(c)", "restriction mismatch".

- Skill: `manutej/sheaf-glue` (Agent Skill)
- Install (CLI): `npx skillmds@latest add manutej/sheaf-glue`
- Raw SKILL.md: https://api.skillmd.com/api/skills/manutej/sheaf-glue/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Docs & Writing
- Author: manutej (https://skillmd.com/u/manutej)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/manutej/sheaf-glue

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# sheaf-glue

Decision skill. Occupies **V** (verification stalk) and evaluates Φ on the whole
sheaf.

## Predicate

Φ(c) = ∧_v [s_v ∈ G_v] ∧ ∧_{e=vw} [ρ_v s_v = ρ_w s_w]

Also report:

- mismatch ledger (edge, field, left, right)
- whether the linearized relative class vanishes

## Hard rules

1. Never accept on vanishing H¹ alone.
2. Never let a soft score override a restriction failure.
3. If the class vanishes and Φ fails, name it: linearization missed a discrete
   type mismatch (string path vs integer handle, etc.).
4. Verification still **executes** tests. This skill is not a substitute for
   running the oracle.

## Requires

`sheaf-localize` and `sheaf-preserve` have filled L, C, O, P. Kernel graph present.

## On failure

Hand the mismatch ledger to `sheaf-repair`. Do not patch fields in this skill.