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---
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name: fem-theory-query
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description: 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.
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description: Use when the user requests a finite-element structural-analysis answer grounded in a configured FEM wiki vault, or asks to identify a gap in that vault.
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---
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# FEM Theory Query
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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.
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Answer from configured vault evidence and clearly separate vault knowledge from gaps. Do not activate for ordinary FEM questions that do not request or require vault grounding.
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## FEM Vault Resolution
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## Inputs
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Resolve the FEM wiki vault in this order:
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- User question and explicit need for configured-vault evidence
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- Resolved vault root, index, relevant pages, and optional companion-skill instructions
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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.
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2. Current project instructions: `AGENTS.md`, `CLAUDE.md`, or an equivalent section named `FEM Solver Theory Wiki`.
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3. Environment variable: `FEM_THEORY_WIKI_VAULT`.
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## Vault Resolution
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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`.
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Resolve the first valid root containing `wiki/hot.md` or `wiki/index.md`:
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Keep `vault-path.txt` PC-specific. When the vault moves, update that file instead of editing this skill body.
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1. `FEM_THEORY_WIKI_VAULT` environment variable
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2. A `FEM Solver Theory Wiki` path in project instructions
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3. Optional skill-local `vault-path.txt`
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## Companion Skill Protocols
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`vault-path.txt` is a machine-local, untracked override created from `vault-path.example.txt`; never commit a workstation path. If no root resolves, report the missing configuration and ask for a path rather than answering as though it came from the vault.
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This skill is an orchestrator. Do not reimplement sibling skills. Use the sibling skill instructions as authoritative when available.
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## Workflow
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### Companion skill path resolution
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1. Read `<vault>/wiki/hot.md`; use the vault retrieval command when its own instructions provide one, otherwise read `wiki/index.md`.
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2. Read the smallest sufficient set of relevant pages, normally three to seven.
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3. For nontrivial derivation, solver design, ambiguity, or verification design, follow `<vault>/skills/think/SKILL.md` when present.
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4. Follow `<vault>/skills/wiki-query/SKILL.md` when present. Resolve its relative links from that companion skill directory and keep them inside the vault.
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5. Synthesize in the user's language with `[[Page Name]]` citations on core technical claims. Label inference and missing coverage explicitly.
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After reading `vault-path.txt`, call that value `FEM_VAULT_ROOT`. Resolve companion skill files from that absolute vault root:
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Use `<vault>/skills/autoresearch/SKILL.md` only when the user explicitly requests external research or vault updates. That work may use the web or write to the vault only within the user's authorization and the companion skill's safety rules.
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- `FEM_VAULT_ROOT\skills\think\SKILL.md`: use for non-trivial FEM formulation, solver architecture, ambiguity, tradeoffs, verification design, or gap assessment.
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- `FEM_VAULT_ROOT\skills\wiki-query\SKILL.md`: use for normal wiki-grounded answers from the configured FEM vault.
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- `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.
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## Output
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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`.
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Lead with the conclusion, then include only relevant formulation, implementation implications, verification, evidence, and vault-gap sections. Short factual questions do not require every section.
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### Relative paths inside companion skills
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## Evidence
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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.
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Every core claim traces to a vault page. Cite conflicting pages and explain the conflict; do not silently replace vault evidence with model memory.
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Examples from `FEM_VAULT_ROOT\skills\autoresearch\SKILL.md`:
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## Boundary
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- `../wiki-cli/SKILL.md` resolves to `FEM_VAULT_ROOT\skills\wiki-cli\SKILL.md`.
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- `../../wiki/references/transport-fallback.md` resolves to `FEM_VAULT_ROOT\wiki\references\transport-fallback.md`.
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- `references/program.md` resolves to `FEM_VAULT_ROOT\skills\autoresearch\references\program.md`.
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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.
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### How to use `think`
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Use `think` as a compact internal preflight before answering FEM solver questions.
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Do:
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- Identify the user's real question: theory derivation, implementation design, verification, comparison, or missing source.
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- Check whether you are relying on memory instead of wiki evidence.
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- Decide whether the answer can be handled by wiki query or needs autoresearch.
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- For complex questions, surface the reasoning structure briefly in the answer.
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Do not:
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- Print all 10 stages for routine factual questions.
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- Use `think` as a substitute for reading wiki sources.
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- Skip the `ACCEPT` step when the wiki has insufficient coverage.
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### How to use `wiki-query`
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Use `wiki-query` for the default answer path.
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Follow this order:
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1. Resolve the FEM vault path.
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2. Read `wiki/hot.md`.
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3. If needed, use `wiki-retrieve` when provisioned: `python scripts/retrieve.py "<question>" --top 5`.
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4. If retrieval is not provisioned or fails, read `wiki/index.md`.
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5. Read 3-7 relevant wiki pages.
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6. Synthesize with Obsidian wikilink citations.
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Do:
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- Cite every core claim with `[[Page Name]]`.
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- Prefer vault evidence over model memory.
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- Say clearly when the wiki lacks enough evidence.
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Do not:
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- Answer a vault-specific question from training data alone.
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- Open many pages when 3-7 are enough.
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- Write to the wiki unless the user explicitly asks.
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### How to use `autoresearch`
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Use `autoresearch` only for explicit research or wiki-expansion requests.
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Trigger examples:
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- "Find sources and strengthen this wiki coverage."
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- "If the wiki does not cover this, research it."
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- "Research and file this topic."
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- "Create source and concept pages for this topic."
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Before starting:
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- Tell the user it will use web search/fetch and write new wiki pages.
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- Mention that fetched content is subject to the `autoresearch` web egress hygiene rules.
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- Ask for approval unless the user already gave explicit approval in the same request.
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Do:
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- Read `FEM_VAULT_ROOT\skills\autoresearch\SKILL.md` and `FEM_VAULT_ROOT\skills\autoresearch\references\program.md`.
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- File results into the configured FEM vault, not the caller project.
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- Use wiki locks and transport rules from the sibling skill.
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Do not:
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- Run autoresearch for ordinary Q&A.
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- Fetch web sources silently.
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- Write into `.raw/` or `wiki/` without explicit user intent.
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## Answer Contract
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Answer in the user's language. For Korean questions, translate the section headings naturally.
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Use this structure unless the user asks for another format:
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- Summary conclusion
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- Formulation
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- Solver implementation view
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- Verification and benchmarks
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- Evidence
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- Wiki gap
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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.
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## FEM Query Expansion
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When a user asks a short FEM question, expand the retrieval intent before searching:
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- Element formulation: shape functions, DOFs, Jacobian, `B` matrix, integration, load vector, result recovery.
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- Nonlinear solve: residual, tangent, Newton update, convergence norms, load/time increments, cutback policy.
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- Constitutive update: stress update, material tangent, state variables, return mapping, history evolution.
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- Dynamics/eigen: mass, damping, time integration, modal extraction, normalization, residual checks.
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- Contact/constraints: gap, normal/tangential law, penalty or multiplier enforcement, search, tangent contribution.
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- Verification: patch tests, convergence, benchmark problems, matrix checks, residual norms, source-solver comparison.
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Keep expansion internal unless showing it helps the user understand the answer.
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## Deployment Notes
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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`.
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Do not modify the vault during ordinary queries, invent a configured path, force-load every companion skill, or present external research as existing vault knowledge. A missing companion skill limits that mode but does not block direct read-only vault synthesis when the index and relevant pages are available.
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KOKO\Mimi