---
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: Task, 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 language 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}",
"language": "math"
},
"focus_prompt": "{optional focus}",
"metadata_file_path": "specs/{NNN}_{SLUG}/.return-meta.json"
}
```
---
### Stage 5: Invoke Subagent
**CRITICAL**: You MUST use the **Task** tool to spawn the subagent.
**Required Tool Invocation**:
```
Tool: Task (NOT Skill)
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 6: Parse Subagent Return (Read Metadata File)
After subagent returns, 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.
---
### 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.
