diff --git a/crates/doc/src/live.rs b/crates/doc/src/live.rs
index fd7886786..8b839c788 100644
--- a/crates/doc/src/live.rs
+++ b/crates/doc/src/live.rs
@@ -587,12 +587,18 @@ fn even_steps(n: u32) -> Vec<f64> {
     (0..=n).map(|i| i as f64 / n as f64).collect()
 }
 
+/// The number of points of a `(rows+1)×(cols+1)` grid, `None` past `usize`: counts come from
+/// files, and u32::MAX rows and columns (65,535 on 32-bit targets) would wrap to an empty grid.
+fn grid_len(rows: u32, cols: u32) -> Option<usize> {
+    (rows as usize).checked_add(1)?.checked_mul((cols as usize).checked_add(1)?)
+}
+
 impl GradientMesh {
     pub fn idx(&self, r: usize, c: usize) -> usize {
         r * (self.cols as usize + 1) + c
     }
     pub fn is_valid(&self) -> bool {
-        self.rows >= 1 && self.cols >= 1 && self.points.len() == (self.rows as usize + 1) * (self.cols as usize + 1)
+        self.rows >= 1 && self.cols >= 1 && grid_len(self.rows, self.cols) == Some(self.points.len())
     }
 
     /// A 1×1 mesh from its four corners (bottom-left, top-left, top-right, bottom-right in u/v
@@ -1158,7 +1164,7 @@ fn surface_of<'a>(kind: &'a EnvelopeKind, src: Rect, frame: Affine) -> Box<dyn F
             {
                 return Box::new(move |u: f64, v: f64| mesh_at(&m, u, v));
             }
-            if *rows == 0 || *cols == 0 || points.len() as u64 != (u64::from(*rows) + 1) * (u64::from(*cols) + 1) {
+            if *rows == 0 || *cols == 0 || grid_len(*rows, *cols) != Some(points.len()) {
                 return Box::new(flat);
             }
             let (rows, cols) = (*rows as usize, *cols as usize);
@@ -1210,8 +1216,7 @@ pub fn smooth_handles(rows: u32, cols: u32, points: &[Point]) -> Vec<[Vec2; 4]>
 /// the smooth ones, see [`smooth_handles`]) as a gradient mesh with black points: what the
 /// canvas draws and the Mesh tool and Direct Selection edit. `None` for a malformed grid.
 pub fn envelope_grid(rows: u32, cols: u32, points: &[Point], handles: &[[Vec2; 4]]) -> Option<GradientMesh> {
-    // (Counts come from files: no overflow on 32-bit targets.)
-    if rows == 0 || cols == 0 || points.len() as u64 != (u64::from(rows) + 1) * (u64::from(cols) + 1) {
+    if rows == 0 || cols == 0 || grid_len(rows, cols) != Some(points.len()) {
         return None;
     }
     let smooth;
@@ -1829,6 +1834,20 @@ mod tests {
         assert!((p.x - 37.0).abs() < 1e-6 && (p.y - 81.0).abs() < 1e-6, "{p:?}");
     }
 
+    /// A file's rows and columns can be anything: a point count too large to compute is no match
+    /// for the points (u32::MAX × u32::MAX wrapped to 0 and passed for a grid without points).
+    #[test]
+    fn a_grid_too_large_to_count_is_malformed() {
+        let m = GradientMesh { rows: u32::MAX, cols: u32::MAX, points: vec![] };
+        assert!(!m.is_valid());
+        assert_eq!((m.lines(), m.outline(), m.quads(8).len()), (PathData::default(), PathData::default(), 0));
+        assert!(envelope_grid(u32::MAX, u32::MAX, &[], &[]).is_none());
+        // A mesh envelope without handles maps through its points: malformed, it leaves art as it is.
+        let kind = EnvelopeKind::Mesh { rows: u32::MAX, cols: u32::MAX, points: vec![], handles: vec![] };
+        let p = Point::new(25.0, 50.0);
+        assert_eq!(envelope_mapper(&kind, Rect::new(0.0, 0.0, 100.0, 100.0))(p), p);
+    }
+
     #[test]
     fn mesh_insert_and_remove_lines() {
         let mut m =