diff --git a/src/history.rs b/src/history.rs
index a2a4c2c..bd86277 100644
--- a/src/history.rs
+++ b/src/history.rs
@@ -1753,6 +1753,29 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
             }
         }
 
+        // A non-finite weight is not a weight. Measured, it behaves exactly as
+        // `0.0` — the member contributes nothing — while `converge` reports
+        // `converged: true` after one iteration with a step of `(0.0, 0.0)`.
+        // So a NaN arriving from a division or a parse is indistinguishable
+        // from a deliberate zero, and looks like a clean fit.
+        //
+        // Zero and negative weights stay accepted: both are expressible
+        // choices about how much a member contributes, and
+        // `tests/degenerate_inputs.rs` pins them deliberately. Only the values
+        // that are not quantities at all are rejected.
+        if let Some(weights) = weights.as_ref() {
+            for team_weights in weights.iter().flatten() {
+                for weight in team_weights {
+                    if !weight.is_finite() {
+                        return Err(InferenceError::InvalidParameter {
+                            name: "weight",
+                            value: *weight,
+                        });
+                    }
+                }
+            }
+        }
+
         // Chokepoint for tie validation: every ingestion route lands here,
         // including `record_draw`, which builds its results directly rather
         // than going through `Outcome`.
diff --git a/tests/ingestion_shape.rs b/tests/ingestion_shape.rs
index 7b1c36e..cd43ab4 100644
--- a/tests/ingestion_shape.rs
+++ b/tests/ingestion_shape.rs
@@ -120,6 +120,49 @@ fn a_non_finite_score_is_rejected_at_ingestion() {
     }
 }
 
+/// A non-finite weight behaved exactly as `0.0` — the member contributed
+/// nothing — while `converge` reported `converged: true` after one iteration
+/// with a step of `(0.0, 0.0)`. So a NaN arriving from a division or a parse
+/// was indistinguishable from a deliberate zero, and looked like a clean fit.
+#[test]
+fn a_non_finite_weight_is_rejected_at_ingestion() {
+    for bad in [f64::NAN, f64::INFINITY, f64::NEG_INFINITY] {
+        let mut h = history();
+        let err = h
+            .event(1)
+            .team(["a"])
+            .weights([bad])
+            .team(["b"])
+            .winner(0)
+            .commit()
+            .unwrap_err();
+        assert!(
+            matches!(err, InferenceError::InvalidParameter { name: "weight", .. }),
+            "{bad}: {err:?}"
+        );
+        assert!(h.current_skill(&"a").is_none(), "{bad} reached the history");
+    }
+}
+
+/// Zero and negative weights are expressible choices about how much a member
+/// contributes, not malformed input, and `tests/degenerate_inputs.rs` pins
+/// their behaviour deliberately. Rejecting non-finite values must not catch
+/// them too.
+#[test]
+fn zero_and_negative_weights_still_ingest() {
+    for w in [0.0, -1.0, 0.5] {
+        let mut h = history();
+        h.event(1)
+            .team(["a"])
+            .weights([w])
+            .team(["b"])
+            .winner(0)
+            .commit()
+            .unwrap_or_else(|e| panic!("weight {w} should ingest: {e:?}"));
+        assert!(h.current_skill(&"a").is_some(), "weight {w}");
+    }
+}
+
 /// The fluent builder routes through the same chokepoint, so it inherits the
 /// checks rather than needing its own.
 #[test]