diff --git a/app-proto/src/diagnostics.rs b/app-proto/src/diagnostics.rs
index 47a9086..a2f090a 100644
--- a/app-proto/src/diagnostics.rs
+++ b/app-proto/src/diagnostics.rs
@@ -119,11 +119,10 @@ fn SpectrumHistory() -> View {
     on_mount(move || {
         create_effect(move || {
             // get the spectrum of the Hessian at each step, split into its
-            // positive and negative parts. exact zero eigenvalues will be
-            // filtered out by `into_log10_time_point` later
+            // positive, negative, and strictly-zero parts
             let (
-                hess_eigvals_pos,
-                hess_eigvals_neg
+                hess_eigvals_zero,
+                hess_eigvals_nonzero
             ): (Vec<_>, Vec<_>) = state.assembly.descent_history.with(
                 |history| history.hess_eigvals
                     .iter()
@@ -134,8 +133,20 @@ fn SpectrumHistory() -> View {
                         )
                     )
                     .flatten()
-                    .partition(|&(_, val)| val > 0.0)
+                    .partition(|&(_, val)| val == 0.0)
             );
+            let zero_level = hess_eigvals_nonzero
+                .iter()
+                .map(|(_, val)| val.abs())
+                .reduce(f64::min)
+                .map(|val| 0.1 * val)
+                .unwrap_or(1.0);
+            let (
+                hess_eigvals_pos,
+                hess_eigvals_neg
+            ): (Vec<_>, Vec<_>) = hess_eigvals_nonzero
+                .into_iter()
+                .partition(|&(_, val)| val > 0.0);
             
             // initialize the chart axes
             let step_axis = Axis::new()
@@ -172,6 +183,20 @@ fn SpectrumHistory() -> View {
                         vec![vec![Some(0.0), None::<f64>]]
                     }
                 );
+            let eigval_series_zero = Scatter::new()
+                .symbol(Symbol::Triangle)
+                .symbol_size(5.0)
+                .data(
+                    if hess_eigvals_zero.len() > 0 {
+                        hess_eigvals_zero
+                            .into_iter()
+                            .map(|(step, _)| (step, zero_level))
+                            .map(into_log10_time_point)
+                            .collect()
+                    } else {
+                        vec![vec![Some(0.0), None::<f64>]]
+                    }
+                );
             let chart = Chart::new()
                 .animation(false)
                 .data_zoom(DataZoom::new().y_axis_index(0).right(40))
@@ -179,7 +204,8 @@ fn SpectrumHistory() -> View {
                 .y_axis(eigval_axis)
                 .grid(Grid::new().top(20).right(80).bottom(30).left(60))
                 .series(eigval_series_pos)
-                .series(eigval_series_neg);
+                .series(eigval_series_neg)
+                .series(eigval_series_zero);
             renderer.render(CONTAINER_ID, &chart).unwrap();
         });
     });