skill-math-research

name	skill-math-research
description	Research mathematical tasks using domain context and codebase exploration. Invoke for math-language research involving algebra, lattice theory, order theory, topology, and category theory.
allowed-tools	Agent, Bash, Edit, Read, Write

Math Research Skill

Thin wrapper that delegates mathematical research to math-research-agent subagent.

IMPORTANT: This skill implements the skill-internal postflight pattern. After the subagent returns, this skill handles all postflight operations (status update, artifact linking, git commit) before returning.

Context References

Reference (do not load eagerly):

• Path: .claude/context/formats/return-metadata-file.md - Metadata file schema

Note: This skill is a thin wrapper with internal postflight. Context is loaded by the delegated agent.

Trigger Conditions

This skill activates when:

• Task type is "math"
• Research involves algebra, lattice theory, order theory, topology, or category theory
• Domain context files are needed for mathematical foundations

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Execution Flow

Stage 1: Input Validation

Validate required inputs:

• task_number - Must be provided and exist in state.json
• focus_prompt - Optional focus for research direction

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Stage 2: Preflight Status Update

Update task status to "researching" BEFORE invoking subagent.

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Stage 3: Create Postflight Marker

Create the marker file to prevent premature termination.

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Stage 4: Prepare Delegation Context

Prepare delegation context for the subagent:

{
  "session_id": "sess_{timestamp}_{random}",
  "delegation_depth": 1,
  "delegation_path": ["orchestrator", "research", "skill-math-research"],
  "timeout": 3600,
  "task_context": {
    "task_number": N,
    "task_name": "{project_name}",
    "description": "{description}",
    "task_type": "math"
  },
  "focus_prompt": "{optional focus}",
  "metadata_file_path": "specs/{NNN}_{SLUG}/.return-meta.json"
}

---

Stage 5: Invoke Subagent

CRITICAL: You MUST use the Agent tool to spawn the subagent.

Required Tool Invocation:

Tool: Agent (NOT Skill, NOT Plan)
Parameters:
  - subagent_type: "math-research-agent"
  - prompt: [Include task_context, delegation_context, focus_prompt, metadata_file_path]
  - description: "Execute math research for task {N}"

DO NOT use Skill(math-research-agent) - this will FAIL.

The subagent will:

• Load domain context files from .claude/context/project/math/
• Search codebase for existing patterns
• Use Mathlib lookup tools
• Execute web research for mathematical literature
• Create research report in specs/{NNN}_{SLUG}/reports/
• Write metadata to specs/{NNN}_{SLUG}/.return-meta.json
• Return a brief text summary (NOT JSON)

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Stage 5b: Self-Execution Fallback

CRITICAL: If you performed the work above WITHOUT using the Agent tool (i.e., you read files, wrote artifacts, or updated metadata directly instead of spawning a subagent), you MUST write a .return-meta.json file now before proceeding to postflight. Use the schema from return-metadata-file.md with status value "researched".

If you DID use the Agent tool, skip this stage -- the subagent already wrote the metadata.

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Postflight (ALWAYS EXECUTE)

The following stages MUST execute after work is complete, whether the work was done by a subagent or inline (Stage 5b). Do NOT skip these stages for any reason.

Stage 6: Parse Subagent Return (Read Metadata File)

Read the metadata file.

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Stage 7: Update Task Status (Postflight)

If status is "researched", update state.json and TODO.md.

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Stage 8: Link Artifacts

Add artifact to state.json with summary. Update TODO.md per @.claude/context/patterns/artifact-linking-todo.md with field_name=**Research**, next_field=**Plan**.

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Stage 9: Git Commit

Commit changes with session ID using targeted staging.

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Stage 10: Cleanup

Remove marker and metadata files.

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Stage 11: Return Brief Summary

Return a brief text summary (NOT JSON). Example:

Research completed for task {N}:
- Found existing patterns in source files
- Loaded domain context for algebra/lattice theory
- Used Mathlib lookup tools to discover relevant theorems
- Created report at specs/{NNN}_{SLUG}/reports/MM_{short-slug}.md
- Status updated to [RESEARCHED]
- Changes committed

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Error Handling

Input Validation Errors

Return immediately with error message if task not found.

Metadata File Missing

If subagent didn't write metadata file, keep status as "researching".

Git Commit Failure

Non-blocking: Log failure but continue with success response.

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Return Format

This skill returns a brief text summary (NOT JSON). The JSON metadata is written to the file and processed internally.