Decompose research ideas into atomic, self-contained concepts with bidirectional math-code mapping. For each concept, extract the math formula from papers and find code implementations. Use for complex system papers requiring formal grounding.

Atomic Decomposition Decompose research ideas into atomic concepts with math formula < code implementation mapping. Input $0 — Research idea, paper, or method description References Decomposition prompts and workflow: ~/.claude/skills/atomic decomposition/references/decomposition prompts.md Workflow (from AI Researcher Survey Agent) Step 1: Break Down into Atomic Definitions Analyze the research idea and decompose into atomic, self contained concepts: Each atom should be a single concept Must have clear mathematical foundations Must be implementable in code Must be traceable to specific papers Step 2: For Each Atomic Definition A. Paper Survey (Math Formula) Search papers for the mathematical formulation Extract the exact LaTeX formula Note assumptions and constraints Record reference papers B. Code Survey (Implementation) Search codebases for implementations Extract the corresponding code Note implementation details and variations Record reference repositories C. Create Knowledge Entry Step 3: Compile Knowledge Base Merge all atomic definitions into a structured knowledge base Verify consistency: every math formula has a code implementation Verify completeness: every code module traces to a formal definition Identify any gaps (formulas without code, or code without theory) Rules Each atomic definition must be specific enough to trace to concrete formulas and code Do not skip or combine definitions — analyze each separately If unsure about atomicity, err on the side of breaking down further Document breakdown reasoning before analysis Every mathematical concept in the paper must have verified code Every code module must trace back to a formal mathematical definition Related Skills Upstream: [research planning](../research planning/), [idea generation](../idea generation/) Downstream: [experiment code](../experiment code/), [algorithm design](../algorithm design/) See also: [math reasoning](../math reasoning/)

atomic-decomposition