diff --git a/Tools/Scripts/IslandFalloff.cs b/Tools/Scripts/IslandFalloff.cs
new file mode 100644
index 0000000..710d4c1
--- /dev/null
+++ b/Tools/Scripts/IslandFalloff.cs
@@ -0,0 +1,33 @@
+using Godot;
+
+/// <summary>
+/// The island-falloff shaping functions (terrain-water task 11) — pure numeric
+/// functions of their inputs (D-035; a named future C++ candidate, kept standalone).
+///
+///   SMOOTH CREST — the mountain spine's ridge axis is the line x = centre, and
+///   `1 - |x - cx|` peaks there with a slope discontinuity. Measured on the shipped
+///   terrain, that crease is the single largest slope step anywhere on the map once
+///   the by-design Trench walls are excluded (top 4 of 5999 columns). SmoothAbs
+///   rounds the crest without moving its height.
+/// </summary>
+public static class IslandFalloff
+{
+	// ---- centre-line crest ------------------------------------------------
+	// Rounding radius in normalized spine-width units (1.0 = MapSize/2 * 1.15
+	// ~ 4710 px at 8K). 0.03 ~ 141 px: it cuts the crest's 1-px kink by 99.3%
+	// (-7.64e-04 -> -5.41e-06 raw, against a natural profile curvature of ~1.1e-07)
+	// while filling at most 3.9 m, decaying under 0.5 m by ~1100 px from the axis.
+	public const float CREST_EPSILON = 0.03f;
+
+	/// <summary>
+	/// A C¹ stand-in for |d|: exactly 0 with zero slope at d = 0, and converging to
+	/// |d| within e²/(2|d|) away from it. Replaces the V-shaped crest of the spine
+	/// with a rounded one WITHOUT lowering it — SmoothAbs(0) is 0, so the peak keeps
+	/// its full height.
+	/// </summary>
+	public static float SmoothAbs(float d, float epsilon)
+	{
+		float a = Mathf.Abs(d);
+		return a * a / Mathf.Sqrt(a * a + epsilon * epsilon);
+	}
+}
diff --git a/Tools/Scripts/MapGenerator.cs b/Tools/Scripts/MapGenerator.cs
index 5f1d3ba..b463852 100644
--- a/Tools/Scripts/MapGenerator.cs
+++ b/Tools/Scripts/MapGenerator.cs
@@ -473,12 +473,16 @@ public partial class MapGenerator : TextureRect
 				if (distY > 0.90f) finalFalloff += (distY - 0.90f) * 15.0f;
 
 				// --- 3. THE MOUNTAIN SPINE ---
+				// The ridge axis is the line x = centre. `1 - |x - cx|` peaks there with
+				// a slope discontinuity, which put the single largest slope step on the
+				// whole map at exactly that column (task-11 diagnostic). SmoothAbs rounds
+				// the crest — same peak height, continuous slope through it.
 				float mountainSpine = 0f;
-				if (temperature < 0.65f) 
+				if (temperature < 0.65f)
 				{
 					float distanceToCenterX = Mathf.Abs(x - center.X) / (MapSize / 2.0f * 1.15f);
-					mountainSpine = 1.0f - distanceToCenterX;
-					float southernFade = Mathf.Clamp((0.65f - temperature) * 4.0f, 0.0f, 1.0f); 
+					mountainSpine = 1.0f - IslandFalloff.SmoothAbs(distanceToCenterX, IslandFalloff.CREST_EPSILON);
+					float southernFade = Mathf.Clamp((0.65f - temperature) * 4.0f, 0.0f, 1.0f);
 					mountainSpine = Mathf.Pow(mountainSpine, 3.0f) * southernFade * 0.6f;
 				}