diff --git a/src/history.rs b/src/history.rs
index c6d1dd5..89f0e16 100644
--- a/src/history.rs
+++ b/src/history.rs
@@ -1812,4 +1812,153 @@ mod tests {
             "α=0.5 should reach the same fixed point as α=1.0; max_diff={max_diff}"
         );
     }
+
+    #[test]
+    fn outcome_scores_default_sigma_uses_history_default() {
+        use crate::Outcome;
+
+        // Path A: explicit sigma=0.5 via override.
+        let mut h_a = crate::History::builder().score_sigma(0.5).build();
+        h_a.add_events([crate::Event {
+            time: 0_i64,
+            teams: smallvec::smallvec![
+                crate::Team::with_members([crate::Member::new("a")]),
+                crate::Team::with_members([crate::Member::new("b")]),
+            ],
+            outcome: Outcome::scores_with_sigma([3.0, 1.0], 0.5),
+        }])
+        .unwrap();
+        h_a.converge().unwrap();
+
+        // Path B: history-wide default 0.5, no per-event override.
+        let mut h_b = crate::History::builder().score_sigma(0.5).build();
+        h_b.add_events([crate::Event {
+            time: 0_i64,
+            teams: smallvec::smallvec![
+                crate::Team::with_members([crate::Member::new("a")]),
+                crate::Team::with_members([crate::Member::new("b")]),
+            ],
+            outcome: Outcome::scores([3.0, 1.0]),
+        }])
+        .unwrap();
+        h_b.converge().unwrap();
+
+        // Inheritance: posteriors must be bit-equal.
+        let curves_a = h_a.learning_curves();
+        let curves_b = h_b.learning_curves();
+        for (key, a_pts) in curves_a.iter() {
+            let b_pts = curves_b.get(key).expect("agent missing in path B");
+            for (a, b) in a_pts.iter().zip(b_pts.iter()) {
+                assert_eq!(a.1.pi(), b.1.pi(), "mismatch at agent {key:?}");
+                assert_eq!(a.1.tau(), b.1.tau(), "mismatch at agent {key:?}");
+            }
+        }
+    }
+
+    #[test]
+    fn outcome_scores_with_sigma_overrides_history_default() {
+        use crate::Outcome;
+
+        // Path A: history-wide default 0.5, per-event override 2.0.
+        let mut h_a = crate::History::builder().score_sigma(0.5).build();
+        h_a.add_events([crate::Event {
+            time: 0_i64,
+            teams: smallvec::smallvec![
+                crate::Team::with_members([crate::Member::new("a")]),
+                crate::Team::with_members([crate::Member::new("b")]),
+            ],
+            outcome: Outcome::scores_with_sigma([3.0, 1.0], 2.0),
+        }])
+        .unwrap();
+        h_a.converge().unwrap();
+
+        // Path B: history-wide default 2.0, no per-event override.
+        let mut h_b = crate::History::builder().score_sigma(2.0).build();
+        h_b.add_events([crate::Event {
+            time: 0_i64,
+            teams: smallvec::smallvec![
+                crate::Team::with_members([crate::Member::new("a")]),
+                crate::Team::with_members([crate::Member::new("b")]),
+            ],
+            outcome: Outcome::scores([3.0, 1.0]),
+        }])
+        .unwrap();
+        h_b.converge().unwrap();
+
+        // Override == default-set-to-the-override-value: bit-equal.
+        let curves_a = h_a.learning_curves();
+        let curves_b = h_b.learning_curves();
+        for (key, a_pts) in curves_a.iter() {
+            let b_pts = curves_b.get(key).expect("agent missing in path B");
+            for (a, b) in a_pts.iter().zip(b_pts.iter()) {
+                assert_eq!(a.1.pi(), b.1.pi(), "mismatch at agent {key:?}");
+                assert_eq!(a.1.tau(), b.1.tau(), "mismatch at agent {key:?}");
+            }
+        }
+
+        // Path C: history-wide default 0.5, no override. Different sigma → different posteriors.
+        let mut h_c = crate::History::builder().score_sigma(0.5).build();
+        h_c.add_events([crate::Event {
+            time: 0_i64,
+            teams: smallvec::smallvec![
+                crate::Team::with_members([crate::Member::new("a")]),
+                crate::Team::with_members([crate::Member::new("b")]),
+            ],
+            outcome: Outcome::scores([3.0, 1.0]),
+        }])
+        .unwrap();
+        h_c.converge().unwrap();
+
+        let curves_c = h_c.learning_curves();
+        let mut max_diff: f64 = 0.0;
+        for (key, a_pts) in curves_a.iter() {
+            let c_pts = curves_c.get(key).expect("agent missing in path C");
+            for (a, c) in a_pts.iter().zip(c_pts.iter()) {
+                max_diff = max_diff.max((a.1.mu() - c.1.mu()).abs());
+                max_diff = max_diff.max((a.1.sigma() - c.1.sigma()).abs());
+            }
+        }
+        assert!(
+            max_diff > 1e-6,
+            "override should produce different posteriors from inherited default; max_diff={max_diff}"
+        );
+    }
+
+    #[test]
+    fn event_builder_scores_with_sigma_threading() {
+        use crate::Outcome;
+
+        // Path A: builder fluent API with sigma override.
+        let mut h_a = crate::History::builder().score_sigma(0.5).build();
+        h_a.event(0_i64)
+            .team(["a"])
+            .team(["b"])
+            .scores_with_sigma([3.0, 1.0], 2.0)
+            .commit()
+            .unwrap();
+        h_a.converge().unwrap();
+
+        // Path B: same outcome via the explicit Outcome constructor.
+        let mut h_b = crate::History::builder().score_sigma(0.5).build();
+        h_b.add_events([crate::Event {
+            time: 0_i64,
+            teams: smallvec::smallvec![
+                crate::Team::with_members([crate::Member::new("a")]),
+                crate::Team::with_members([crate::Member::new("b")]),
+            ],
+            outcome: Outcome::scores_with_sigma([3.0, 1.0], 2.0),
+        }])
+        .unwrap();
+        h_b.converge().unwrap();
+
+        let curves_a = h_a.learning_curves();
+        let curves_b = h_b.learning_curves();
+        for (key, a_pts) in curves_a.iter() {
+            let b_pts = curves_b.get(key).expect("agent missing");
+            for (a, b) in a_pts.iter().zip(b_pts.iter()) {
+                assert_eq!(a.1.pi(), b.1.pi(), "mismatch at agent {key:?}");
+                assert_eq!(a.1.tau(), b.1.tau(), "mismatch at agent {key:?}");
+            }
+        }
+    }
 }