tesseract-ripple/research-ideation

Research Ideation

Generate structured research questions, conjectures, and proof strategies from a cryptography or mathematics topic.

Input: $ARGUMENTS — a topic (e.g., "range proofs from lattices"), an open problem (e.g., "transparent setup for Bulletproofs"), or a construction to improve (e.g., "reduce Pedersen commitment opening proof size").

Steps

1. Understand the input. Read $ARGUMENTS and any referenced files in the current directory.

2. Search for context using WebSearch on eprint.iacr.org and arxiv.org to understand the current state of the art.

3. Generate 3-5 research directions ordered by ambition:

   • Incremental: Small improvement to existing construction (e.g., reduce proof size by constant factor)
   • Moderate: New construction or technique within existing paradigm (e.g., new commitment scheme from different assumption)
   • Ambitious: Paradigm shift or resolution of open problem (e.g., achieve X without trusted setup)

4. For each direction, develop:

   • Conjecture/Goal: A precise statement of what you'd want to prove or build
   • Approach: Proof strategy or construction idea
   • Key obstacles: What makes this hard? Where would the proof get stuck?
   • Required assumptions: What hardness assumptions are needed?
   • Potential tools: Existing techniques or lemmas that might help
   • Related work: 2-3 papers using similar approaches
   • Feasibility assessment: How likely is this to work?

5. Save the output to research_ideation_[sanitized_topic].md in the current directory.

Output Format

# Research Ideation: [Topic]

**Date:** [YYYY-MM-DD]
**Input:** [Original input]

## State of the Art
[1-2 paragraphs summarizing current best results]

## Research Directions

### RD1: [Title] (Feasibility: High/Medium/Low)

**Goal:** [Precise statement]
**Approach:** [Proof strategy or construction sketch]
**Key obstacles:**
1. [Obstacle and potential mitigation]
2. [Obstacle and potential mitigation]
**Assumptions:** [Required hardness assumptions]
**Related work:** [Author (Year)], [Author (Year)]

## Ranking
| Direction | Feasibility | Impact | Novelty |
|---|---|---|---|

## Suggested Next Steps
1. [Most promising immediate action]
2. [Paper to read carefully]
3. [Computation to try]

Principles

• Be creative but rigorous. Every suggestion must be mathematically plausible.
• Think like a reviewer. Immediately identify why a proof strategy might fail.
• Do NOT fabricate references.
• Flag connections to known open problems or conjectures.

Adapted from pedrohcgs/claude-code-my-workflow (MIT license).