feat(gaussian): add damp_natural helper for EP damping

Computes α·new + (1−α)·self in natural-parameter space. Will be used
by TruncFactor and MarginFactor to support opt-in EP damping via
ConvergenceOptions::alpha.

src/gaussian.rs

@@ -96,6 +96,18 @@ impl Gaussian {
         let var = self.sigma().powi(2) + variance_delta;
         Self::from_ms(self.mu(), var.sqrt())
     }
+
+    /// EP damping in natural-parameter space: `α·new + (1−α)·self`.
+    ///
+    /// Used by within-game inference to stabilise oscillating fixed-point
+    /// loops on hard graphs. `alpha = 1.0` returns `new` exactly;
+    /// `alpha < 1.0` shrinks each per-step update.
+    pub fn damp_natural(self, new: Gaussian, alpha: f64) -> Gaussian {
+        Gaussian::from_natural(
+            alpha * new.pi() + (1.0 - alpha) * self.pi(),
+            alpha * new.tau() + (1.0 - alpha) * self.tau(),
+        )
+    }
 }
 
 impl Default for Gaussian {
@@ -231,4 +243,33 @@ mod tests {
         assert!((r.pi() - expected_pi).abs() < 1e-15);
         assert!((r.tau() - expected_tau).abs() < 1e-15);
     }
+
+    #[test]
+    fn damp_natural_alpha_one_returns_new() {
+        let old = Gaussian::from_ms(1.0, 2.0);
+        let new = Gaussian::from_ms(5.0, 0.5);
+        let damped = old.damp_natural(new, 1.0);
+        assert_eq!(damped.pi(), new.pi());
+        assert_eq!(damped.tau(), new.tau());
+    }
+
+    #[test]
+    fn damp_natural_alpha_zero_returns_self() {
+        let old = Gaussian::from_ms(1.0, 2.0);
+        let new = Gaussian::from_ms(5.0, 0.5);
+        let damped = old.damp_natural(new, 0.0);
+        assert_eq!(damped.pi(), old.pi());
+        assert_eq!(damped.tau(), old.tau());
+    }
+
+    #[test]
+    fn damp_natural_alpha_half_is_midpoint_in_natural_params() {
+        let old = Gaussian::from_ms(1.0, 2.0);
+        let new = Gaussian::from_ms(5.0, 0.5);
+        let damped = old.damp_natural(new, 0.5);
+        let expected_pi = 0.5 * new.pi() + 0.5 * old.pi();
+        let expected_tau = 0.5 * new.tau() + 0.5 * old.tau();
+        assert!((damped.pi() - expected_pi).abs() < 1e-12);
+        assert!((damped.tau() - expected_tau).abs() < 1e-12);
+    }
 }