using-simulation-foundations

# Using Simulation-Foundations (Meta-Skill Router)

**Your entry point to mathematical simulation foundations.** This skill routes you to the right combination of mathematical skills for your game simulation challenge.

## Purpose

This is a **meta-skill** that:
1. ✅ **Routes** you to the correct mathematical skills
2. ✅ **Combines** multiple skills for complex simulations
3. ✅ **Provides** workflows for common simulation types
4. ✅ **Explains** when to use theory vs empirical tuning

**You should use this skill:** When building any simulation system that needs mathematical rigor.

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## How to Access Reference Sheets

**IMPORTANT**: All reference sheets are located in the SAME DIRECTORY as this SKILL.md file.

When this skill is loaded from:
  `skills/using-simulation-foundations/SKILL.md`

Reference sheets like `differential-equations-for-games.md` are at:
  `skills/using-simulation-foundations/differential-equations-for-games.md`

NOT at:
  `skills/differential-equations-for-games.md` ← WRONG PATH

When you see a link like `[differential-equations-for-games.md](differential-equations-for-games.md)`, read the file from the same directory as this SKILL.md.

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## Core Philosophy: Theory Enables Design

### The Central Idea

**Empirical Tuning**: Trial-and-error adjustment of magic numbers
- Slow iteration (run simulation, observe, tweak, repeat)
- Unpredictable behavior (systems drift to extremes)
- No guarantees (stability, convergence, performance)
- Difficult debugging (why did it break?)

**Mathematical Foundation**: Formulate systems using theory
- Fast iteration (predict behavior analytically)
- Predictable behavior (stability analysis)
- Guarantees (equilibrium, convergence, bounds)
- Systematic debugging (root cause analysis)

### When This Pack Applies

**✅ Use simulation-foundations when:**
- Building physics, AI, or economic simulation systems
- Need stability guarantees (ecosystems, economies)
- Performance matters (60 FPS real-time constraints)
- M