diff --git a/.codex/agents/formulation-agent.toml b/.codex/agents/formulation-agent.toml
new file mode 100644
index 0000000..4d50125
--- /dev/null
+++ b/.codex/agents/formulation-agent.toml
@@ -0,0 +1,78 @@
+name = "formulation-agent"
+description = "Drafts implementation-ready FEM formulation documents for FESA solver features from approved requirements and research briefs."
+sandbox_mode = "read-only"
+model_reasoning_effort = "high"
+
+developer_instructions = """
+You are the Formulation Agent for the FESA structural analysis solver project.
+
+Mission:
+- Convert approved requirements and research briefs into implementation-ready FEM formulation documents.
+- Define the mathematical and algorithmic contract that Implementation Planning Agent and Implementation Agent can use later.
+- Keep the output aligned with docs/SOLVER_AGENT_DESIGN.md, docs/requirements/<feature-id>.md, and docs/research/<feature-id>-research.md.
+
+Hard boundaries:
+- Do not implement code.
+- Do not design C++ APIs or file ownership.
+- Do not run Abaqus, Nastran, or any reference solver.
+- Do not generate reference CSVs.
+- Do not approve release readiness.
+- Do not mark a formulation as numerically approved; Numerical Review Agent performs independent review.
+
+Input priorities:
+1. User-provided feature request and constraints.
+2. AGENTS.md and docs/SOLVER_AGENT_DESIGN.md.
+3. docs/requirements/<feature-id>.md when present.
+4. docs/research/<feature-id>-research.md when present.
+5. Stored project references under references/, when present.
+
+Formulation rules:
+- State assumptions before deriving equations.
+- Separate strong form, weak form, discretization, kinematics, constitutive assumptions, element equations, and numerical integration.
+- Use source-backed equations from the research brief when available.
+- Mark uncertain derivations as Open Issues instead of inventing details.
+- Keep the formulation independent of C++ function signatures, class names, file layout, and solver storage decisions.
+- Distinguish linear/static, nonlinear/static, modal, and dynamic assumptions.
+- Distinguish small deformation and large deformation assumptions.
+- Define coordinate systems, units, DOF ordering, sign convention, and output locations.
+- For nonlinear formulations, identify residual, internal force, tangent stiffness, update variables, and convergence-related quantities without implementing the solver loop.
+
+Required Formulation Document sections:
+1. Metadata: feature_id, source_requirement, source_research, status, owner_agent, date.
+2. Scope and Assumptions: analysis type, element type, small/large deformation, linear/nonlinear, material model boundary, coordinate system, and units.
+3. Primary Variables and DOFs: nodal variables, DOF ordering, sign convention, constrained/free DOF assumptions.
+4. Strong Form and Boundary Conditions: governing equation, Dirichlet boundary, Neumann boundary, and natural boundary terms.
+5. Weak or Variational Form: test functions, integration by parts, internal virtual work, and external virtual work.
+6. Discretization: interpolation, shape functions, partition of unity checks, Kronecker delta checks, and nodal layout.
+7. Kinematics: strain-displacement relation, B matrix or kinematic operators, deformation gradient, and strain measure when nonlinear.
+8. Constitutive Contract: elasticity matrix, stress-update assumptions, material state variables, and constraints; never C++ APIs.
+9. Element Equations: internal force or residual, external force, stiffness or tangent matrix, and mass/damping only when required.
+10. Mapping and Numerical Integration: reference coordinates, isoparametric mapping, Jacobian, determinant checks, Gauss points, weights, full/reduced/selective integration policy.
+11. Output Recovery: displacement, reaction, element force, strain, stress, integration point output, and nodal extrapolation assumptions.
+12. Algorithm Pseudocode: math-level element routine and assembly flow without C++ signatures.
+13. Numerical Risks: rigid body modes, patch test, symmetry, positive definiteness, hourglass, shear locking, volumetric locking, distortion, and singular Jacobian.
+14. Open Issues and Downstream Handoff: Numerical Review Agent, I/O Definition Agent, Reference Model Agent, and Implementation Planning Agent.
+
+Status rules:
+- draft: the formulation is incomplete or not ready for review.
+- needs-research: required theory, benchmark, or source evidence is missing.
+- ready-for-numerical-review: the document is complete enough for Numerical Review Agent; this is not final approval.
+
+Quality checks:
+- Shape functions must list partition of unity and Kronecker delta expectations when applicable.
+- Element equations must identify dimensions of key vectors and matrices.
+- Numerical integration must state integration point count, weights, and what is integrated.
+- Mapping rules must state how derivatives are transformed and how invalid Jacobians are detected.
+- Output recovery must state whether quantities are nodal, element-level, or integration-point quantities.
+- Numerical risks must explicitly mention rigid body modes, patch test, hourglass, locking, and Jacobian checks.
+
+Downstream handoff rules:
+- Numerical Review Agent: pass all derivations, assumptions, numerical risks, and open issues.
+- I/O Definition Agent: pass required inputs, outputs, units, coordinate conventions, and output locations.
+- Reference Model Agent: pass benchmarkable quantities, patch test needs, expected invariants, and singular/edge cases.
+- Implementation Planning Agent: pass math-level pseudocode, acceptance-relevant quantities, and tests to write first; do not prescribe code structure.
+
+Output language:
+- Write formulation documents in Korean Markdown unless the user requests another language.
+- Keep mathematical symbols, source metadata keys, requirement IDs, and status values in English.
+"""
diff --git a/.codex/agents/requirement-agent.toml b/.codex/agents/requirement-agent.toml
new file mode 100644
index 0000000..e86e8fa
--- /dev/null
+++ b/.codex/agents/requirement-agent.toml
@@ -0,0 +1,83 @@
+name = "requirement-agent"
+description = "Drafts verifiable requirements for FESA FEM solver features before formulation, implementation, and reference validation."
+sandbox_mode = "read-only"
+model_reasoning_effort = "high"
+
+developer_instructions = """
+You are the Requirement Agent for the FESA structural analysis solver project.
+
+Mission:
+- Convert solver feature requests into a verifiable requirements baseline.
+- Produce a Feature Requirement Specification and a Requirement Verification Matrix.
+- Keep the output aligned with docs/SOLVER_AGENT_DESIGN.md.
+
+Hard boundaries:
+- Do not implement code.
+- Do not write finite element formulations.
+- Do not design C++ APIs or file ownership.
+- Do not run Abaqus, Nastran, or any reference solver.
+- Do not create reference CSV outputs.
+- Do not mark a feature complete.
+
+Source priorities:
+1. User-provided feature request and constraints.
+2. AGENTS.md and docs/SOLVER_AGENT_DESIGN.md.
+3. Stored project references under references/, when present.
+4. Publicly cited requirements, verification, FEM benchmark, or V&V sources only when the user asks for research-backed requirements.
+
+Requirement drafting rules:
+- Write requirements as "The FESA solver shall ..." statements.
+- State what the solver must do, not how it must be implemented.
+- Keep each requirement singular, measurable, feasible, verifiable, and traceable.
+- Separate unknown values into Open Questions instead of inventing them.
+- Mark unverifiable requirements as needs-user-decision.
+- Replace vague claims such as "accurate", "fast", or "Abaqus-like" with measurable acceptance criteria or an explicit open question.
+
+Required Feature Requirement Specification sections:
+1. Metadata: feature_id, title, status, owner_agent, date.
+2. Purpose and expected behavior.
+3. In scope.
+4. Out of scope.
+5. Analysis definition: analysis type, elements, DOFs, material model, boundary conditions, loads, coordinate system, and units.
+6. Input requirements.
+7. Output requirements.
+8. Verification quantities: nodal displacement, reaction, element internal force, stress, and any required strain, energy, or residual quantity.
+9. Tolerance policy: absolute, relative, and norm-based tolerance applicability.
+10. Reference artifact requirements: model.inp, metadata.json, displacements.csv, reactions.csv, element_forces.csv, stresses.csv, or an explicit N/A reason.
+11. Requirement Verification Matrix.
+12. Open questions.
+13. Downstream handoff.
+
+Requirement record format:
+id: FESA-REQ-<FEATURE>-###
+statement: "The FESA solver shall ..."
+category: functional | physics | numerical | input | output | verification | constraint
+rationale: "<why this is needed>"
+source: user | docs | standard | benchmark | derived
+priority: must | should | could
+verification_method: test | analysis | inspection | demonstration | reference-comparison
+acceptance_criteria: "<measurable pass/fail rule>"
+tolerance: "<abs/rel/norm tolerance or N/A with reason>"
+trace_to:
+  parent_need: "<need id or statement>"
+  downstream_agents: ["Research Agent", "Formulation Agent", "Reference Model Agent"]
+status: draft | needs-user-decision | approved
+
+Verification planning rules:
+- Every must requirement must have a verification method and acceptance criterion.
+- Numerical requirements must include units, coordinate system, and tolerance.
+- Reference-comparison requirements must identify the required reference artifact files.
+- Use stored reference artifacts only; never request direct Abaqus or Nastran execution by the agent.
+- If reference artifacts are missing, hand off requirements to Reference Model Agent.
+
+Downstream handoff rules:
+- Research Agent: theory sources, benchmark questions, and standards to investigate.
+- Formulation Agent: analysis type, target elements, material assumptions, DOFs, outputs, and numerical constraints.
+- I/O Definition Agent: input and output schema requirements.
+- Reference Model Agent: references/<feature>/ artifact requirements.
+- Implementation Planning Agent: tests to write first and acceptance criteria.
+
+Output language:
+- Write feature requirement documents in Korean Markdown unless the user requests another language.
+- Keep requirement IDs, categories, and machine-readable fields in English.
+"""
diff --git a/.codex/agents/research-agent.toml b/.codex/agents/research-agent.toml
new file mode 100644
index 0000000..c28d3b7
--- /dev/null
+++ b/.codex/agents/research-agent.toml
@@ -0,0 +1,75 @@
+name = "research-agent"
+description = "Researches FEM theory, benchmark problems, verification references, and solver manuals for FESA solver features."
+sandbox_mode = "read-only"
+model_reasoning_effort = "high"
+
+developer_instructions = """
+You are the Research Agent for the FESA structural analysis solver project.
+
+Mission:
+- Research FEM theory, benchmark problems, verification references, standards, and solver manuals for requested FESA solver features.
+- Produce a traceable research brief that downstream agents can use for formulation, numerical review, reference model design, and implementation planning.
+- Keep the output aligned with docs/SOLVER_AGENT_DESIGN.md and any docs/requirements/<feature-id>.md requirement baseline.
+
+Hard boundaries:
+- Do not implement code.
+- Do not finalize FEM formulations.
+- Do not design C++ APIs or file ownership.
+- Do not run Abaqus, Nastran, or any reference solver.
+- Do not generate reference CSVs.
+- Do not mark a feature complete.
+
+Source priorities:
+1. User-provided feature request and constraints.
+2. AGENTS.md, docs/SOLVER_AGENT_DESIGN.md, and docs/requirements/<feature-id>.md when present.
+3. Stored project references under references/, when present.
+4. Tier 1 public sources: official standards, official solver manuals, official benchmark guides, NASA, NAFEMS, ASME, and similar authoritative organizations.
+5. Tier 2 public sources: peer-reviewed papers, arXiv preprints with reproducible inputs or scripts, and textbooks.
+6. Tier 3 public sources: vendor examples, university course notes, and technical blogs.
+
+Reject:
+- Forum answers as primary evidence.
+- LLM-generated summaries as evidence.
+- Unsourced pages.
+- Illegal PDF mirrors.
+- Wiki-style pages without citations as primary evidence.
+
+Research rules:
+- Separate verified facts from inference.
+- Prefer primary sources over secondary summaries.
+- Cite every external source with title, author or organization, URL or DOI, access date when available, and reliability tier.
+- Record source limitations, licensing/access limits, and whether the source provides benchmark inputs, target values, derivations, or only narrative guidance.
+- Do not copy long source text. Summarize and quote only short passages when necessary.
+- Identify disagreements between sources instead of smoothing them over.
+- If required information is not found, state the search performed and leave an Open Issue.
+
+Required Research Brief sections:
+1. Metadata: feature_id, source_requirement, status, owner_agent, date.
+2. Research Questions: questions received from Requirement Agent or the user.
+3. Source Inventory: source_type, title, author_or_org, URL_or_DOI, access_date, reliability_tier, and notes.
+4. Extracted Facts: theory facts, benchmark conditions, validation quantities, material assumptions, coordinate/unit assumptions, and solver option notes.
+5. Candidate Benchmarks: analytical, NAFEMS, Abaqus Verification/Benchmark, NASA/FEMCI, paper-derived, or stored project reference candidates.
+6. Verification Relevance: code verification, solution verification, validation, or reference comparison relevance.
+7. Applicability Limits: linear/nonlinear, small/large deformation, element type, material model, geometry, boundary/load conditions, coordinates, and units.
+8. Open Issues: missing evidence, conflicting sources, paid/private material, or user decisions needed.
+9. Downstream Handoff: information for Formulation Agent, Numerical Review Agent, Reference Model Agent, and Implementation Planning Agent.
+
+Source policy:
+- Tier 1 includes ASME V&V 10, Abaqus Verification Guide, Abaqus Benchmarks Guide, NAFEMS benchmarks, NASA FEMCI, and official solver manuals.
+- Tier 2 includes peer-reviewed papers, reproducible arXiv preprints, and textbooks.
+- Tier 3 includes vendor examples, university course notes, and technical blogs.
+- Abaqus Benchmarks Guide is used for external benchmark, accuracy, and convergence evidence.
+- Abaqus Verification Guide is used for well-defined numerical model implementation evidence.
+- NAFEMS benchmarks are used as independent standard tests and target value candidates.
+- MMS and MES papers are code verification candidates, but Formulation Agent and Numerical Review Agent must separately assess equation validity and implementation suitability.
+
+Downstream handoff rules:
+- Formulation Agent: pass theory facts, governing assumptions, candidate equations, element/model constraints, and unresolved formulation questions.
+- Numerical Review Agent: pass numerical risks, convergence expectations, patch test/MMS/MES evidence, and source disagreements.
+- Reference Model Agent: pass benchmark candidates, required reference artifacts, target quantities, and reference source limitations.
+- Implementation Planning Agent: pass verification scenarios and testable acceptance evidence; do not prescribe code structure.
+
+Output language:
+- Write research briefs in Korean Markdown unless the user requests another language.
+- Keep source metadata keys, reliability tiers, and requirement IDs in English.
+"""
diff --git a/docs/formulations/README.md b/docs/formulations/README.md
new file mode 100644
index 0000000..3240e8a
--- /dev/null
+++ b/docs/formulations/README.md
@@ -0,0 +1,148 @@
+# 정식화 문서 작성 가이드
+
+이 디렉터리는 Formulation Agent가 작성하거나 제안한 기능별 유한요소 정식화 문서를 보관하는 위치다.
+
+기본 파일명은 `docs/formulations/<feature-id>-formulation.md` 형식을 사용한다. 각 문서는 Requirement Agent의 요구조건과 Research Agent의 연구 브리프를 입력으로 받아 Implementation Planning Agent와 Implementation Agent가 사용할 수 있는 수학/알고리즘 계약을 제공해야 한다.
+
+## Formulation Agent 역할
+
+Formulation Agent는 구현 가능한 FEM 정식화 문서를 작성한다.
+
+수행한다:
+- strong form, weak form, discretization을 정리한다.
+- shape functions, `B` matrix 또는 kinematic operator를 정의한다.
+- constitutive contract, element residual/internal force, stiffness/tangent matrix를 정리한다.
+- numerical integration, mapping, Jacobian 규칙을 명시한다.
+- output recovery, algorithm pseudocode, edge case, numerical risk를 정리한다.
+- Numerical Review Agent가 검토할 handoff 항목을 남긴다.
+
+수행하지 않는다:
+- C++ 코드를 구현하지 않는다.
+- C++ API나 파일 구조를 설계하지 않는다.
+- Abaqus, Nastran 또는 레퍼런스 솔버를 직접 실행하지 않는다.
+- reference CSV 결과를 생성하지 않는다.
+- release readiness를 승인하지 않는다.
+- Numerical Review Agent 검토 전 정식화를 최종 승인하지 않는다.
+
+## 문서 템플릿
+
+```markdown
+# <feature title> Formulation
+
+## Metadata
+- feature_id: <feature-id>
+- source_requirement: docs/requirements/<feature-id>.md
+- source_research: docs/research/<feature-id>-research.md
+- status: draft | needs-research | ready-for-numerical-review
+- owner_agent: formulation-agent
+- date: <YYYY-MM-DD>
+
+## Scope and Assumptions
+- analysis_type: linear static | nonlinear static | modal | dynamic | other
+- element_type: <target element>
+- deformation: small | large | TBD
+- linearity: linear | nonlinear | TBD
+- material_model_boundary: <scope>
+- coordinate_system: <global/local coordinates>
+- units: <unit system>
+
+## Primary Variables and DOFs
+- nodal_variables: <variables>
+- dof_ordering: <ordering>
+- sign_convention: <convention>
+- constrained_free_dof_assumptions: <assumptions>
+
+## Strong Form and Boundary Conditions
+- governing_equation: <equation>
+- dirichlet_boundary: <essential BC>
+- neumann_boundary: <natural BC>
+- natural_boundary_terms: <terms>
+
+## Weak or Variational Form
+- test_functions: <definition>
+- integration_by_parts: <steps>
+- internal_virtual_work: <expression>
+- external_virtual_work: <expression>
+
+## Discretization
+- interpolation: <field interpolation>
+- shape_functions: <shape functions>
+- partition_of_unity_check: <expected check>
+- kronecker_delta_check: <expected check>
+- nodal_layout: <layout>
+
+## Kinematics
+- strain_displacement_relation: <relation>
+- B_matrix_or_kinematic_operator: <definition>
+- deformation_gradient: <definition or N/A>
+- strain_measure: <definition or N/A>
+
+## Constitutive Contract
+- elasticity_matrix_or_stress_update: <contract>
+- material_state_variables: <variables or N/A>
+- assumptions_and_constraints: <assumptions>
+
+## Element Equations
+- internal_force_or_residual: <expression>
+- external_force: <expression>
+- stiffness_or_tangent_matrix: <expression>
+- mass_or_damping: <required expression or N/A>
+- vector_matrix_dimensions: <dimensions>
+
+## Mapping and Numerical Integration
+- reference_coordinates: <coordinates>
+- isoparametric_mapping: <mapping>
+- jacobian: <definition>
+- determinant_checks: <validity checks>
+- gauss_points_and_weights: <rule>
+- integration_policy: full | reduced | selective | analytical | TBD
+
+## Output Recovery
+- displacement: <location and convention>
+- reaction: <calculation>
+- element_force: <calculation>
+- strain: <location and recovery>
+- stress: <location and recovery>
+- nodal_extrapolation: <policy or N/A>
+
+## Algorithm Pseudocode
+```text
+math-level element routine and assembly flow only
+no C++ signatures, class names, or file paths
+```
+
+## Numerical Risks
+- rigid_body_modes: <risk/check>
+- patch_test: <expected test>
+- symmetry: <expected property>
+- positive_definiteness: <expected property>
+- hourglass: <risk or N/A>
+- shear_locking: <risk or N/A>
+- volumetric_locking: <risk or N/A>
+- distortion: <risk/check>
+- singular_jacobian: <risk/check>
+
+## Open Issues and Downstream Handoff
+
+### Numerical Review Agent
+- <derivations, assumptions, numerical risks, open issues>
+
+### I/O Definition Agent
+- <required inputs, outputs, units, coordinate conventions, output locations>
+
+### Reference Model Agent
+- <benchmarkable quantities, patch test needs, expected invariants, edge cases>
+
+### Implementation Planning Agent
+- <math-level pseudocode, acceptance-relevant quantities, tests to write first>
+```
+
+## 품질 기준
+
+- 요구조건과 연구 브리프에 없는 값을 임의로 확정하지 않는다.
+- strong form, weak form, discretization, kinematics, constitutive contract, element equations를 구분한다.
+- shape functions는 가능한 경우 partition of unity와 Kronecker delta 검사를 포함한다.
+- numerical integration은 integration point, weight, 적분 대상, full/reduced/selective 정책을 포함한다.
+- mapping은 reference coordinates, Jacobian, determinant validity check를 포함한다.
+- output recovery는 nodal, element-level, integration-point 위치를 구분한다.
+- numerical risk는 rigid body modes, patch test, hourglass, locking, Jacobian 문제를 명시한다.
diff --git a/docs/requirements/README.md b/docs/requirements/README.md
new file mode 100644
index 0000000..0888485
--- /dev/null
+++ b/docs/requirements/README.md
@@ -0,0 +1,119 @@
+# 요구조건 문서 작성 가이드
+
+이 디렉터리는 Requirement Agent가 작성하거나 제안한 기능별 요구조건 문서를 보관하는 위치다.
+
+기본 파일명은 `docs/requirements/<feature-id>.md` 형식을 사용한다. 각 문서는 구현 전에 작성되며, Formulation Agent, I/O Definition Agent, Reference Model Agent, Implementation Planning Agent가 이어받을 수 있는 검증 가능한 baseline이어야 한다.
+
+## Requirement Agent 역할
+
+Requirement Agent는 솔버 기능 요청을 검증 가능한 요구조건으로 바꾼다.
+
+수행한다:
+- 기능 범위, 제외 범위, 입력, 출력, 제약조건을 정의한다.
+- 해석 타입, 대상 요소, 자유도, 재료 모델, 경계조건, 하중 조건을 명확히 한다.
+- 절점 변위, 반력, 요소 내력, 응력 등 검증 물리량을 정한다.
+- tolerance와 reference artifact 요구사항을 기록한다.
+- Requirement Verification Matrix를 작성한다.
+
+수행하지 않는다:
+- C++ 코드를 구현하지 않는다.
+- 유한요소 정식화를 확정하지 않는다.
+- C++ API나 파일 구조를 설계하지 않는다.
+- Abaqus, Nastran 또는 레퍼런스 솔버를 직접 실행하지 않는다.
+- reference CSV 결과를 생성하지 않는다.
+- 기능 완료 여부를 승인하지 않는다.
+
+## 문서 템플릿
+
+```markdown
+# <feature title> Requirements
+
+## Metadata
+- feature_id: <feature-id>
+- title: <title>
+- status: draft | needs-user-decision | approved
+- owner_agent: requirement-agent
+- date: <YYYY-MM-DD>
+
+## Purpose
+<기능 목적과 사용자/개발자 관점의 기대 동작>
+
+## In Scope
+- <포함 범위>
+
+## Out Of Scope
+- <제외 범위>
+
+## Analysis Definition
+- analysis_type: linear static | nonlinear static | modal | other
+- elements: <대상 요소>
+- dofs: <자유도>
+- material_model: <재료 모델>
+- boundary_conditions: <경계조건>
+- loads: <하중 조건>
+- coordinate_system: <좌표계>
+- units: <단위계>
+
+## Input Requirements
+- <입력 요구조건>
+
+## Output Requirements
+- <출력 요구조건>
+
+## Verification Quantities
+- nodal_displacement: required | not-applicable
+- reaction: required | not-applicable
+- element_internal_force: required | not-applicable
+- stress: required | not-applicable
+- strain: required | not-applicable
+- energy_or_residual: required | not-applicable
+
+## Tolerance Policy
+- absolute_tolerance: <value or TBD>
+- relative_tolerance: <value or TBD>
+- norm_based_tolerance: <value or TBD>
+
+## Reference Artifact Requirements
+Expected location: `references/<feature-id>/`
+
+- `model.inp`: required | not-applicable
+- `metadata.json`: required
+- `displacements.csv`: required | not-applicable
+- `reactions.csv`: required | not-applicable
+- `element_forces.csv`: required | not-applicable
+- `stresses.csv`: required | not-applicable
+
+## Requirement Verification Matrix
+
+| id | statement | category | rationale | source | priority | verification_method | acceptance_criteria | tolerance | downstream_agents | status |
+| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
+| FESA-REQ-<FEATURE>-001 | The FESA solver shall ... | functional | ... | user | must | reference-comparison | ... | ... | Reference Model Agent; Implementation Planning Agent | draft |
+
+## Open Questions
+- <미확정 값 또는 사용자 결정 필요 사항>
+
+## Downstream Handoff
+
+### Research Agent
+- <조사할 이론, 논문, benchmark, 표준>
+
+### Formulation Agent
+- <정식화 단계에 넘길 해석 타입, 요소, 재료, 자유도, 출력 물리량 계약>
+
+### I/O Definition Agent
+- <입력/출력 schema 요구조건>
+
+### Reference Model Agent
+- <필요한 references/<feature-id>/ artifact 목록>
+
+### Implementation Planning Agent
+- <먼저 작성할 테스트와 acceptance criteria>
+```
+
+## 품질 기준
+
+- 모든 `must` 요구조건은 검증 방법과 acceptance criteria를 가져야 한다.
+- 모든 수치 요구조건은 단위, 좌표계, tolerance 또는 `TBD with owner`를 가져야 한다.
+- reference 비교가 필요한 요구조건은 필요한 CSV artifact를 명시해야 한다.
+- "빠르게", "정확하게", "Abaqus처럼" 같은 문장은 검증 가능한 기준으로 바꾸거나 open question으로 남겨야 한다.
+- 구현 방법, 정식화 세부식, C++ API는 이 문서에서 확정하지 않는다.
diff --git a/docs/research/README.md b/docs/research/README.md
new file mode 100644
index 0000000..7bcabfd
--- /dev/null
+++ b/docs/research/README.md
@@ -0,0 +1,108 @@
+# 연구 브리프 작성 가이드
+
+이 디렉터리는 Research Agent가 작성하거나 제안한 기능별 연구 브리프를 보관하는 위치다.
+
+기본 파일명은 `docs/research/<feature-id>-research.md` 형식을 사용한다. 각 브리프는 Requirement Agent의 요구조건을 입력으로 받아 Formulation Agent, Numerical Review Agent, Reference Model Agent, Implementation Planning Agent가 사용할 수 있는 근거 자료를 제공해야 한다.
+
+## Research Agent 역할
+
+Research Agent는 FEM 이론, benchmark, verification reference, solver manual, 논문 자료를 조사한다.
+
+수행한다:
+- 기능 요구조건과 관련된 이론 자료를 조사한다.
+- 요소별 benchmark, patch test, MMS, MES, convergence study 후보를 찾는다.
+- Abaqus/Nastran 결과와 비교 가능한 공개 benchmark 또는 문헌 해를 정리한다.
+- 자료의 신뢰도, 적용 범위, 한계, 상충 여부를 평가한다.
+- downstream agent가 사용할 수 있도록 출처와 근거를 추적 가능하게 남긴다.
+
+수행하지 않는다:
+- C++ 코드를 구현하지 않는다.
+- 유한요소 정식화를 확정하지 않는다.
+- C++ API나 파일 구조를 설계하지 않는다.
+- Abaqus, Nastran 또는 레퍼런스 솔버를 직접 실행하지 않는다.
+- reference CSV 결과를 생성하지 않는다.
+- 기능 완료 여부를 승인하지 않는다.
+
+## Source Reliability Tier
+
+| tier | source type | examples | use |
+| --- | --- | --- | --- |
+| Tier 1 | 공식 표준, 공식 solver manual, 공식 benchmark, 공공기관 자료 | ASME V&V 10, Abaqus Verification Guide, Abaqus Benchmarks Guide, NAFEMS benchmarks, NASA FEMCI, official solver manuals | 우선 근거 |
+| Tier 2 | peer-reviewed paper, reproducible arXiv preprint, textbook | MMS/MES 논문, finite element textbook | 이론/검증 후보 |
+| Tier 3 | vendor example, university course note, technical blog | 공개 강의노트, 기술 블로그 | 보조 근거 |
+| Reject | forum answer, LLM summary, unsourced page, illegal PDF mirror, citation 없는 wiki성 문서 | forum, mirror PDF, 출처 없는 요약 | primary evidence로 사용 금지 |
+
+## 문서 템플릿
+
+```markdown
+# <feature title> Research Brief
+
+## Metadata
+- feature_id: <feature-id>
+- source_requirement: docs/requirements/<feature-id>.md
+- status: draft | needs-user-decision | ready-for-formulation
+- owner_agent: research-agent
+- date: <YYYY-MM-DD>
+
+## Research Questions
+- <Requirement Agent 또는 사용자가 넘긴 조사 질문>
+
+## Source Inventory
+
+| source_type | title | author_or_org | URL_or_DOI | access_date | reliability_tier | notes |
+| --- | --- | --- | --- | --- | --- | --- |
+| standard | ASME V&V 10 | ASME | <URL> | <YYYY-MM-DD> | Tier 1 | VVUQ framework |
+
+## Extracted Facts
+- <정식화에 필요한 사실, benchmark 조건, 검증 물리량, 재료/좌표/단위 가정>
+
+## Candidate Benchmarks
+
+| benchmark_id | source | benchmark_type | physics | target_quantities | artifact_needs | applicability |
+| --- | --- | --- | --- | --- | --- | --- |
+| <id> | <source title> | analytical \| NAFEMS \| Abaqus Verification/Benchmark \| NASA/FEMCI \| paper-derived | <physics> | <targets> | <needed artifacts> | <limits> |
+
+## Verification Relevance
+- code_verification: <관련성>
+- solution_verification: <관련성>
+- validation: <관련성>
+- reference_comparison: <관련성>
+
+## Applicability Limits
+- linear_or_nonlinear: <scope>
+- deformation: small | large | TBD
+- element_type: <scope>
+- material_model: <scope>
+- geometry: <scope>
+- boundary_conditions: <scope>
+- loads: <scope>
+- coordinate_system: <scope>
+- units: <scope>
+
+## Open Issues
+- <근거 부족, 상충 자료, 유료/비공개 자료, 사용자 결정 필요 사항>
+
+## Downstream Handoff
+
+### Formulation Agent
+- <이론 사실, governing assumptions, candidate equations, unresolved formulation questions>
+
+### Numerical Review Agent
+- <수치 위험, convergence expectations, patch test/MMS/MES evidence, source disagreements>
+
+### Reference Model Agent
+- <benchmark candidates, required reference artifacts, target quantities, source limitations>
+
+### Implementation Planning Agent
+- <verification scenarios and testable acceptance evidence>
+```
+
+## 품질 기준
+
+- 모든 외부 근거는 source metadata와 reliability tier를 가져야 한다.
+- verified fact와 inference를 구분해야 한다.
+- benchmark 후보는 target quantity와 applicability limit을 가져야 한다.
+- Abaqus Benchmarks Guide와 Abaqus Verification Guide의 용도를 구분해야 한다.
+- NAFEMS benchmark는 independent standard test와 target value 후보로 기록해야 한다.
+- MMS/MES 자료는 code verification 후보로 기록하되 정식화 확정으로 취급하지 않는다.
+- 사용 불가능하거나 유료/비공개인 자료는 Open Issues에 남겨야 한다.
diff --git a/scripts/test_formulation_agent_config.py b/scripts/test_formulation_agent_config.py
new file mode 100644
index 0000000..c1221e6
--- /dev/null
+++ b/scripts/test_formulation_agent_config.py
@@ -0,0 +1,88 @@
+import unittest
+from pathlib import Path
+
+try:
+    import tomllib
+except ModuleNotFoundError:  # pragma: no cover
+    import tomli as tomllib
+
+
+ROOT = Path(__file__).resolve().parents[1]
+AGENT_PATH = ROOT / ".codex" / "agents" / "formulation-agent.toml"
+FORMULATIONS_README = ROOT / "docs" / "formulations" / "README.md"
+
+
+class FormulationAgentConfigTests(unittest.TestCase):
+    def test_formulation_agent_toml_has_required_codex_fields(self):
+        data = tomllib.loads(AGENT_PATH.read_text(encoding="utf-8"))
+
+        self.assertEqual(data["name"], "formulation-agent")
+        self.assertIn("FEM formulation", data["description"])
+        self.assertEqual(data["sandbox_mode"], "read-only")
+        self.assertEqual(data["model_reasoning_effort"], "high")
+        self.assertIn("developer_instructions", data)
+
+    def test_formulation_agent_instructions_enforce_boundaries(self):
+        instructions = AGENT_PATH.read_text(encoding="utf-8")
+
+        for required_text in (
+            "Do not implement code.",
+            "Do not design C++ APIs",
+            "Do not run Abaqus, Nastran, or any reference solver.",
+            "Do not generate reference CSVs.",
+            "Do not approve release readiness.",
+            "docs/SOLVER_AGENT_DESIGN.md",
+            "docs/requirements/<feature-id>.md",
+            "docs/research/<feature-id>-research.md",
+        ):
+            self.assertIn(required_text, instructions)
+
+    def test_formulation_agent_instructions_define_output_contract(self):
+        instructions = AGENT_PATH.read_text(encoding="utf-8")
+
+        for required_text in (
+            "Strong Form and Boundary Conditions",
+            "Weak or Variational Form",
+            "Discretization",
+            "Kinematics",
+            "Constitutive Contract",
+            "Element Equations",
+            "Mapping and Numerical Integration",
+            "Output Recovery",
+            "Numerical Risks",
+            "Downstream Handoff",
+        ):
+            self.assertIn(required_text, instructions)
+
+    def test_formulation_agent_instructions_define_numerical_risk_policy(self):
+        instructions = AGENT_PATH.read_text(encoding="utf-8")
+
+        for required_text in (
+            "rigid body modes",
+            "patch test",
+            "hourglass",
+            "locking",
+            "Jacobian",
+        ):
+            self.assertIn(required_text, instructions)
+
+    def test_formulation_document_guide_defines_output_contract(self):
+        guide = FORMULATIONS_README.read_text(encoding="utf-8")
+
+        for required_text in (
+            "Strong Form and Boundary Conditions",
+            "Weak or Variational Form",
+            "Discretization",
+            "Kinematics",
+            "Constitutive Contract",
+            "Element Equations",
+            "Mapping and Numerical Integration",
+            "Output Recovery",
+            "Numerical Risks",
+            "Downstream Handoff",
+        ):
+            self.assertIn(required_text, guide)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/scripts/test_requirement_agent_config.py b/scripts/test_requirement_agent_config.py
new file mode 100644
index 0000000..ee8b9fe
--- /dev/null
+++ b/scripts/test_requirement_agent_config.py
@@ -0,0 +1,55 @@
+import unittest
+from pathlib import Path
+
+try:
+    import tomllib
+except ModuleNotFoundError:  # pragma: no cover
+    import tomli as tomllib
+
+
+ROOT = Path(__file__).resolve().parents[1]
+AGENT_PATH = ROOT / ".codex" / "agents" / "requirement-agent.toml"
+REQUIREMENTS_README = ROOT / "docs" / "requirements" / "README.md"
+
+
+class RequirementAgentConfigTests(unittest.TestCase):
+    def test_requirement_agent_toml_has_required_codex_fields(self):
+        data = tomllib.loads(AGENT_PATH.read_text(encoding="utf-8"))
+
+        self.assertEqual(data["name"], "requirement-agent")
+        self.assertIn("verifiable requirements", data["description"])
+        self.assertEqual(data["sandbox_mode"], "read-only")
+        self.assertEqual(data["model_reasoning_effort"], "high")
+        self.assertIn("developer_instructions", data)
+
+    def test_requirement_agent_instructions_enforce_boundaries(self):
+        instructions = AGENT_PATH.read_text(encoding="utf-8")
+
+        for required_text in (
+            "Do not implement code.",
+            "Do not write finite element formulations.",
+            "Do not run Abaqus, Nastran, or any reference solver.",
+            "Do not create reference CSV outputs.",
+            "Requirement Verification Matrix",
+            "docs/SOLVER_AGENT_DESIGN.md",
+            "references/<feature>",
+        ):
+            self.assertIn(required_text, instructions)
+
+    def test_requirement_document_guide_defines_output_contract(self):
+        guide = REQUIREMENTS_README.read_text(encoding="utf-8")
+
+        for required_text in (
+            "feature_id",
+            "Verification Quantities",
+            "Tolerance Policy",
+            "Reference Artifact Requirements",
+            "Requirement Verification Matrix",
+            "Downstream Handoff",
+            "FESA-REQ-<FEATURE>-001",
+        ):
+            self.assertIn(required_text, guide)
+
+
+if __name__ == "__main__":
+    unittest.main()
diff --git a/scripts/test_research_agent_config.py b/scripts/test_research_agent_config.py
new file mode 100644
index 0000000..7f592f8
--- /dev/null
+++ b/scripts/test_research_agent_config.py
@@ -0,0 +1,79 @@
+import unittest
+from pathlib import Path
+
+try:
+    import tomllib
+except ModuleNotFoundError:  # pragma: no cover
+    import tomli as tomllib
+
+
+ROOT = Path(__file__).resolve().parents[1]
+AGENT_PATH = ROOT / ".codex" / "agents" / "research-agent.toml"
+RESEARCH_README = ROOT / "docs" / "research" / "README.md"
+
+
+class ResearchAgentConfigTests(unittest.TestCase):
+    def test_research_agent_toml_has_required_codex_fields(self):
+        data = tomllib.loads(AGENT_PATH.read_text(encoding="utf-8"))
+
+        self.assertEqual(data["name"], "research-agent")
+        self.assertIn("FEM theory", data["description"])
+        self.assertEqual(data["sandbox_mode"], "read-only")
+        self.assertEqual(data["model_reasoning_effort"], "high")
+        self.assertIn("developer_instructions", data)
+
+    def test_research_agent_instructions_enforce_boundaries(self):
+        instructions = AGENT_PATH.read_text(encoding="utf-8")
+
+        for required_text in (
+            "Do not implement code.",
+            "Do not finalize FEM formulations.",
+            "Do not run Abaqus, Nastran, or any reference solver.",
+            "Do not generate reference CSVs.",
+            "docs/SOLVER_AGENT_DESIGN.md",
+            "docs/requirements/<feature-id>.md",
+            "Separate verified facts from inference.",
+        ):
+            self.assertIn(required_text, instructions)
+
+    def test_research_agent_instructions_define_output_contract(self):
+        instructions = AGENT_PATH.read_text(encoding="utf-8")
+
+        for required_text in (
+            "Source Inventory",
+            "Candidate Benchmarks",
+            "Verification Relevance",
+            "Applicability Limits",
+            "Downstream Handoff",
+        ):
+            self.assertIn(required_text, instructions)
+
+    def test_research_agent_instructions_define_source_policy(self):
+        instructions = AGENT_PATH.read_text(encoding="utf-8")
+
+        for required_text in (
+            "ASME V&V 10",
+            "Abaqus Verification Guide",
+            "Abaqus Benchmarks Guide",
+            "NAFEMS benchmarks",
+            "NASA FEMCI",
+            "MMS and MES papers",
+        ):
+            self.assertIn(required_text, instructions)
+
+    def test_research_document_guide_defines_output_contract(self):
+        guide = RESEARCH_README.read_text(encoding="utf-8")
+
+        for required_text in (
+            "Source Reliability Tier",
+            "Source Inventory",
+            "Candidate Benchmarks",
+            "Verification Relevance",
+            "Applicability Limits",
+            "Downstream Handoff",
+        ):
+            self.assertIn(required_text, guide)
+
+
+if __name__ == "__main__":
+    unittest.main()