MultiPhysicsVault/skills/fem-theory-query/SKILL.md

name, description

name	description
fem-theory-query	Use when answering finite element method, structural analysis solver, element formulation, residual/tangent, constitutive integration, contact, dynamics, eigenproblem, or verification questions from a configured FEM wiki vault.

FEM Theory Query

Use this skill as a portable domain router for finite element method and structural solver theory questions. Ground answers in a configured FEM wiki vault, then compose sibling skills instead of reimplementing their workflows.

FEM Vault Resolution

Resolve the FEM wiki vault in this order:

1. Skill-local config file: vault-path.txt in this skill folder. Read the first non-empty, non-comment line as the vault root path.
2. Current project instructions: AGENTS.md, CLAUDE.md, or an equivalent section named FEM Solver Theory Wiki.
3. Environment variable: FEM_THEORY_WIKI_VAULT.

If no valid vault is found, ask the user for the vault path. A valid vault must contain wiki/hot.md or wiki/index.md.

Keep vault-path.txt PC-specific. When the vault moves, update that file instead of editing this skill body.

Companion Skill Protocols

This skill is an orchestrator. Do not reimplement sibling skills. Use the sibling skill instructions as authoritative when available.

Companion skill path resolution

After reading vault-path.txt, call that value FEM_VAULT_ROOT. Resolve companion skill files from that absolute vault root:

• FEM_VAULT_ROOT\skills\think\SKILL.md: use for non-trivial FEM formulation, solver architecture, ambiguity, tradeoffs, verification design, or gap assessment.
• FEM_VAULT_ROOT\skills\wiki-query\SKILL.md: use for normal wiki-grounded answers from the configured FEM vault.
• FEM_VAULT_ROOT\skills\autoresearch\SKILL.md: use only when the user explicitly asks to research, find sources, update the wiki, or fill missing wiki coverage.

If the runtime provides a skill activation mechanism, activate the companion skill by name. If not, read the absolute companion SKILL.md path constructed from vault-path.txt and follow its workflow. If an absolute companion path does not exist, tell the user which path is missing and ask them to fix vault-path.txt.

Relative paths inside companion skills

When a companion skill refers to another file by a relative path, resolve that path from the absolute directory of the companion skill file under FEM_VAULT_ROOT, not from the caller project or current working directory. Normalize .. segments after joining paths. Keep the resolved path inside FEM_VAULT_ROOT unless the companion skill explicitly requires an external path.

Examples from FEM_VAULT_ROOT\skills\autoresearch\SKILL.md:

• ../wiki-cli/SKILL.md resolves to FEM_VAULT_ROOT\skills\wiki-cli\SKILL.md.
• ../../wiki/references/transport-fallback.md resolves to FEM_VAULT_ROOT\wiki\references\transport-fallback.md.
• references/program.md resolves to FEM_VAULT_ROOT\skills\autoresearch\references\program.md.

If a resolved companion-relative path is missing, report the missing absolute path and ask the user to fix vault-path.txt or install the full skills/ bundle.

How to use think

Use think as a compact internal preflight before answering FEM solver questions.

Do:

• Identify the user's real question: theory derivation, implementation design, verification, comparison, or missing source.
• Check whether you are relying on memory instead of wiki evidence.
• Decide whether the answer can be handled by wiki query or needs autoresearch.
• For complex questions, surface the reasoning structure briefly in the answer.

Do not:

• Print all 10 stages for routine factual questions.
• Use think as a substitute for reading wiki sources.
• Skip the ACCEPT step when the wiki has insufficient coverage.

How to use wiki-query

Use wiki-query for the default answer path.

Follow this order:

1. Resolve the FEM vault path.
2. Read wiki/hot.md.
3. If needed, use wiki-retrieve when provisioned: python scripts/retrieve.py "<question>" --top 5.
4. If retrieval is not provisioned or fails, read wiki/index.md.
5. Read 3-7 relevant wiki pages.
6. Synthesize with Obsidian wikilink citations.

Do:

• Cite every core claim with [[Page Name]].
• Prefer vault evidence over model memory.
• Say clearly when the wiki lacks enough evidence.

Do not:

• Answer a vault-specific question from training data alone.
• Open many pages when 3-7 are enough.
• Write to the wiki unless the user explicitly asks.

How to use autoresearch

Use autoresearch only for explicit research or wiki-expansion requests.

Trigger examples:

• "Find sources and strengthen this wiki coverage."
• "If the wiki does not cover this, research it."
• "Research and file this topic."
• "Create source and concept pages for this topic."

Before starting:

• Tell the user it will use web search/fetch and write new wiki pages.
• Mention that fetched content is subject to the autoresearch web egress hygiene rules.
• Ask for approval unless the user already gave explicit approval in the same request.

Do:

• Read FEM_VAULT_ROOT\skills\autoresearch\SKILL.md and FEM_VAULT_ROOT\skills\autoresearch\references\program.md.
• File results into the configured FEM vault, not the caller project.
• Use wiki locks and transport rules from the sibling skill.

Do not:

• Run autoresearch for ordinary Q&A.
• Fetch web sources silently.
• Write into .raw/ or wiki/ without explicit user intent.

Answer Contract

Answer in the user's language. For Korean questions, translate the section headings naturally.

Use this structure unless the user asks for another format:

• Summary conclusion
• Formulation
• Solver implementation view
• Verification and benchmarks
• Evidence
• Wiki gap

Every core technical claim should trace to wiki evidence. Use Obsidian wikilinks such as [[Finite Element Method]], [[Solid Element Stiffness Integration]], or the relevant source page. If the wiki does not cover a point, label it as a gap instead of presenting model memory as vault knowledge.

FEM Query Expansion

When a user asks a short FEM question, expand the retrieval intent before searching:

• Element formulation: shape functions, DOFs, Jacobian, B matrix, integration, load vector, result recovery.
• Nonlinear solve: residual, tangent, Newton update, convergence norms, load/time increments, cutback policy.
• Constitutive update: stress update, material tangent, state variables, return mapping, history evolution.
• Dynamics/eigen: mass, damping, time integration, modal extraction, normalization, residual checks.
• Contact/constraints: gap, normal/tangential law, penalty or multiplier enforcement, search, tangent contribution.
• Verification: patch tests, convergence, benchmark problems, matrix checks, residual norms, source-solver comparison.

Keep expansion internal unless showing it helps the user understand the answer.

Deployment Notes

Distribute this skill with the whole skills/ bundle so sibling paths remain valid. After installing or symlinking the bundle into another agent, update vault-path.txt for that PC or set FEM_THEORY_WIKI_VAULT.