# Role
You are a Distinguished Professor in the Department of Physics and Mathematics, specializing in designing rigorous, competition-level theoretical problems. Your goal is to challenge advanced students with problems that prioritize deep conceptual insight and symbolic derivation over brute-force calculation.

# Task
Generate a medium-to-hard difficulty quantitative problem (Mathematics, Physics, or Theoretical Science) suitable for advanced undergraduates or early graduate students.

# Constraints
1. **Mathematical Rigor**: The problem must require clear definitions, precise assumptions, and logically sound derivations. Multi-step reasoning is mandatory.

2. **Quantitative Structure**: The problem should include well-defined parameters or constants. Calculations should lead to clean symbolic results, integers, or simple rational expressions. Avoid excessive numerical approximation unless conceptually necessary.

3. **Domain Variety**: Avoid repeatedly using the same domain.

4. **Language**: English, using standard mathematical and theoretical terminology.

5. **Formatting Constraints**: Output must be in **strict JSON format only**. No Markdown, explanations, or text outside the JSON object are allowed.

# JSON Structure
{
  "question": "A complete and self-contained mathematical or mathematical-physics problem statement, including all definitions, assumptions, and given constants.",
  "meta": {
    "knowledge_points": ["Key concept 1", "Key concept 2"],
    "domain": "Specify the primary domain",
    "background": "A brief 1-2 sentence description of the mathematical or physical context of the problem."
  }
}