diff --git a/crates/improvise-incremental/tests/oracle.rs b/crates/improvise-incremental/tests/oracle.rs
index e91ce427..380ec6d6 100644
--- a/crates/improvise-incremental/tests/oracle.rs
+++ b/crates/improvise-incremental/tests/oracle.rs
@@ -800,3 +800,145 @@ fn the_harness_checks_a_cell_a_view_draws_that_drops_four_coordinates() {
     assert_eq!(d.step, 0);
     assert_eq!(d.probe, Probe::Value(wide_cell(), Aggregation::Exact));
 }
+
+/// East is hidden and Coastal is collapsed (a group is, by default), so the Coastal row folds West only;
+/// Inland has a cell under A only, so B's column holds just Coastal's.
+fn hidden_workbook() -> improvise_core::workbook::Workbook {
+    let mut wb = improvise_core::workbook::Workbook::new("hidden");
+    for c in ["Region", "Product"] {
+        wb.add_category(c).unwrap();
+    }
+    wb.add_item_in_group("Region", "East", "Coastal").unwrap();
+    wb.add_item_in_group("Region", "West", "Coastal").unwrap();
+    wb.add_item("Region", "Inland").unwrap();
+    wb.add_item("Product", "A").unwrap();
+    wb.add_item("Product", "B").unwrap();
+    wb.add_item("_Measure", "Revenue").unwrap();
+    let cells = [
+        ("East", "A", 10.0),
+        ("West", "A", 5.0),
+        ("East", "B", 20.0),
+        ("West", "B", 1.0),
+        ("Inland", "A", 2.0),
+    ];
+    for (r, p, v) in cells {
+        wb.model.set_cell(key(r, p, "Revenue"), CellValue::Number(v));
+    }
+    let view = wb.active_view_mut();
+    view.set_axis("Region", Axis::Row);
+    view.set_axis("Product", Axis::Column);
+    view.set_axis("_Measure", Axis::None);
+    view.hide_item("Region", "East");
+    wb
+}
+
+/// A backend that reads the view wrongly in exactly one way.
+#[derive(Clone, Copy)]
+enum Blindness {
+    CoversIgnoreHidden,
+    TotalsIgnoreHidden,
+    TotalsDoNotSpan,
+    OccupancyCountsHidden,
+}
+
+struct Blind(Eager, Blindness);
+
+impl Derived for Blind {
+    fn value(&self, k: &CellKey, agg: Aggregation) -> Option<CellValue> {
+        self.0.value(k, agg)
+    }
+    fn raw_fold(&self, p: &CellKey) -> Option<CellValue> {
+        self.0.raw_fold(p)
+    }
+    fn covered(&self, k: &CellKey, r: &Reading) -> Option<CellValue> {
+        match self.1 {
+            Blindness::CoversIgnoreHidden => self.0.covered(k, &Reading::new(r.agg, [])),
+            _ => self.0.covered(k, r),
+        }
+    }
+    fn total(&self, k: &CellKey, over: &[String], r: &Reading) -> Option<CellValue> {
+        match self.1 {
+            Blindness::TotalsIgnoreHidden => self.0.total(k, over, &Reading::new(r.agg, [])),
+            Blindness::TotalsDoNotSpan => self.0.covered(k, r),
+            _ => self.0.total(k, over, r),
+        }
+    }
+    fn occupancy(&self, p: &CellKey, r: &Reading) -> usize {
+        match self.1 {
+            Blindness::OccupancyCountsHidden => self.0.occupancy(p, &Reading::new(r.agg, [])),
+            _ => self.0.occupancy(p, r),
+        }
+    }
+}
+
+impl Maintained for Blind {
+    fn apply(&mut self, edit: &Edit) {
+        self.0.apply(edit);
+    }
+}
+
+fn run_blind(fault: Option<Blindness>) -> Result<improvise_incremental::Report, Divergence> {
+    let wb = hidden_workbook();
+    let none = vec!["_Measure".to_string()];
+    let eager = Eager::new(wb.model.clone(), none.clone());
+    let views: Vec<_> = wb.views.values().cloned().collect();
+    let edit = Edit::SetCell(key("West", "A", "Revenue"), CellValue::Number(6.0));
+    match fault {
+        Some(f) => differential_in(&wb.model, &views, &none, Blind(eager, f), &[edit]),
+        None => differential_in(&wb.model, &views, &none, eager, &[edit]),
+    }
+}
+
+#[test]
+fn the_harness_passes_a_view_reader_that_is_right() {
+    run_blind(None).unwrap();
+}
+
+#[test]
+fn the_harness_catches_a_fold_that_covers_a_hidden_item() {
+    let d = run_blind(Some(Blindness::CoversIgnoreHidden)).unwrap_err();
+    assert!(matches!(d.probe, Probe::Covered(..)), "{d}");
+    assert_eq!((d.eager, d.candidate), (num(5.0), num(15.0)), "Coastal/A");
+}
+
+#[test]
+fn the_harness_catches_a_total_that_counts_a_hidden_item() {
+    let d = run_blind(Some(Blindness::TotalsIgnoreHidden)).unwrap_err();
+    assert!(matches!(d.probe, Probe::Total(..)), "{d}");
+}
+
+#[test]
+fn the_harness_catches_a_total_that_does_not_span_its_rows() {
+    let d = run_blind(Some(Blindness::TotalsDoNotSpan)).unwrap_err();
+    assert!(matches!(d.probe, Probe::Total(..)), "{d}");
+}
+
+#[test]
+fn the_harness_catches_an_occupancy_that_counts_a_hidden_item() {
+    let d = run_blind(Some(Blindness::OccupancyCountsHidden)).unwrap_err();
+    assert!(matches!(d.probe, Probe::Occupancy(..)), "{d}");
+}
+
+#[test]
+fn a_view_is_drawn_as_cells_totals_and_occupancy() {
+    let wb = hidden_workbook();
+    let views: Vec<_> = wb.views.values().cloned().collect();
+    let drawn = drawn_probes(&wb.model, &views);
+    let kinds = [
+        drawn.iter().any(|p| matches!(p, Probe::Covered(..))),
+        drawn.iter().any(|p| matches!(p, Probe::Total(..))),
+        drawn.iter().any(|p| matches!(p, Probe::Occupancy(..))),
+    ];
+    assert_eq!(kinds, [true; 3]);
+}
+
+#[test]
+fn probing_a_key_of_twenty_two_coordinates_is_not_exponential() {
+    let coords = (0..22).map(|i| (format!("C{i:02}"), "a".to_string())).collect();
+    let mut m = Model::new("deep");
+    m.set_cell(CellKey::new(coords), CellValue::Number(1.0));
+    let started = std::time::Instant::now();
+    let n = probes(&m).len();
+    assert!(n > 0);
+    assert!(started.elapsed().as_millis() < 100, "{:?}", started.elapsed());
+}