doc headers

lib/numerics/sqrttrans/Sqrttrans.md

@@ -1,5 +1,22 @@
 # SQRTTRANS: Square Root Transform
 
+| Property         | Value                            |
+| ---------------- | -------------------------------- |
+| **Category**     | Numeric                        |
+| **Inputs**       | Source (close)                          |
+| **Parameters**   | None                      |
+| **Outputs**      | Single series (SQRTTRANS)                       |
+| **Output range** | Varies (see docs)                     |
+| **Warmup**       | `0` bars                          |
+
+### TL;DR
+
+- The Square Root (SQRT) transformer applies $\sqrt{x}$ to each value in a time series.
+- No configurable parameters; computation is stateless per bar.
+- Output range: Varies (see docs).
+- Requires `0` bars of warmup before first valid output (IsHot = true).
+- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
+
 > "The square root is nature's variance-stabilizing trick—halving the exponent space while preserving monotonicity. When price volatility scales with level, sqrt compresses the noise."
 
 The Square Root (SQRT) transformer applies $\sqrt{x}$ to each value in a time series. This variance-stabilizing transformation compresses ranges where volatility scales with magnitude, making it useful for heteroscedastic data where standard deviation increases with price level.
@@ -193,4 +210,4 @@ var recovered = Sqrttrans.Calculate(squared);
 
 - Box, G.E.P., & Cox, D.R. (1964). "An Analysis of Transformations." *Journal of the Royal Statistical Society, Series B*, 26(2), 211-252.
 - Tukey, J.W. (1977). *Exploratory Data Analysis*. Addison-Wesley. (Variance-stabilizing transformations)
-- IEEE 754-2019. *Standard for Floating-Point Arithmetic*. (sqrt specification)
+- IEEE 754-2019. *Standard for Floating-Point Arithmetic*. (sqrt specification)