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

---

## 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

---

### Stage 2: Preflight Status Update

Update task status to "researching" BEFORE invoking subagent.

---

### Stage 3: Create Postflight Marker

Create the marker file to prevent premature termination.

---

### Stage 4: Prepare Delegation Context

Prepare delegation context for the subagent:

```json
{
  "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)

---

### 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.

---

## 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.

---

### Stage 7: Update Task Status (Postflight)

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

---

### 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**`.

---

### Stage 9: Git Commit

Commit changes with session ID using targeted staging.

---

### Stage 10: Cleanup

Remove marker and metadata files.

---

### 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
```

---

## 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.

---

## Return Format

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