Technical Research

Purpose

Conduct thorough, structured research to inform design and implementation decisions. Produce actionable findings with clear sources, not just raw information dumps.

When to Use

• Investigating an algorithm or method before implementing it
• Comparing competing approaches (solvers, formulations, libraries)
• Finding reference implementations or validation data
• Understanding a mathematical formulation from the literature
• Evaluating whether an external package meets requirements

Process

1. Define the Research Question

Clarify with the user:

• What specific question needs answering?
• What decisions will this research inform?
• Are there known starting points (papers, packages, textbooks)?
• What constraints matter (performance, accuracy, AD-compatibility, license)?

2. Search Strategy

Execute multiple search angles:

• Academic/algorithmic: search for papers, textbook references, survey articles
• Implementation: search for existing Julia packages, GitHub repos, reference code
• Community: search Julia Discourse, relevant forums, package documentation
• Comparison: search for benchmarks, trade-off analyses, known limitations

Formulate 3-5 query variations per angle for coverage.

3. Evaluate Sources

For each source found:

• Relevance: Does it directly address the research question?
• Authority: Is it a peer-reviewed paper, official docs, or a blog post?
• Recency: Is the information current? Are there newer approaches?
• Applicability: Does it match our constraints (Julia, AD-compatible, etc.)?

4. Synthesize Findings

Organize results into a structured summary:

## Research: [Topic]

### Question
[The specific question being investigated]

### Key Findings
- Finding 1 (with source)
- Finding 2 (with source)

### Approaches Compared
| Approach | Pros | Cons | Source |
|----------|------|------|--------|
| ...      | ...  | ...  | ...    |

### Recommendation
[Clear recommendation with rationale]

### Open Questions
[Anything unresolved that needs further investigation]

### References
1. [Author, Title, Year, URL/DOI]

5. Verify Key Claims

• Cross-reference important claims across multiple sources
• Flag contradictions or disagreements in the literature
• Note where consensus exists vs. active debate

Output Requirements

• Always provide source URLs or citations for claims
• Use direct quotes for important technical statements
• Clearly distinguish established facts from opinions/recommendations
• Identify gaps where information is missing or uncertain
• End with actionable next steps