diff --git a/src/lib.rs b/src/lib.rs
index dbdbe3a..b79bea8 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -68,7 +68,9 @@ impl JsonPathStack {
     }
 
     pub fn contains_cycle(&self) -> bool {
-        self.stack.iter().any(|item| item.starts_with(&self.top))
+        self.stack
+            .iter()
+            .any(|item| is_path_ancestor_of(&self.top, item))
     }
 
     pub fn iter(&self) -> impl Iterator<Item = &String> {
@@ -81,3 +83,77 @@ impl Default for JsonPathStack {
         Self::new()
     }
 }
+
+/// Check if `ancestor` is a path-segment-aligned prefix of `path`.
+///
+/// Returns `true` if either of the following conditions are true:
+///
+/// 1. `ancestor` is the same as `path`.
+/// 2. `ancestor` is a prefix of `path`, and the character immediately
+///    following the prefix is `/`.
+///
+/// The second condition prevents false matches where schema names share a
+/// common string prefix (e.g., `Item` matching `ItemPage`).
+fn is_path_ancestor_of(ancestor: &str, path: &str) -> bool {
+    path.starts_with(ancestor)
+        && path
+            .as_bytes()
+            .get(ancestor.len())
+            .is_none_or(|&b| b == b'/')
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_contains_cycle() {
+        // A genuine cycle: pushing back to a schema we've already visited.
+        let stack = JsonPathStack::new()
+            .push("#/components/schemas/Tree")
+            .append("properties")
+            .append("children")
+            .push("#/components/schemas/Tree");
+
+        assert!(stack.contains_cycle());
+
+        // Schemas whose names share a common string prefix must not be treated
+        // as cycles. e.g. the string "Item" is a prefix of "ItemPage", but they
+        // are different schemas.
+        let stack = JsonPathStack::new()
+            .push("#/components/schemas/ItemPage")
+            .append("properties")
+            .append("items")
+            .append("items")
+            .push("#/components/schemas/Item");
+
+        assert!(!stack.contains_cycle());
+    }
+
+    #[test]
+    fn test_is_path_ancestor_of_basics() {
+        // Exact match.
+        assert!(is_path_ancestor_of(
+            "#/components/schemas/Item",
+            "#/components/schemas/Item"
+        ));
+
+        // Proper ancestor.
+        assert!(is_path_ancestor_of(
+            "#/components/schemas/Item",
+            "#/components/schemas/Item/properties/value"
+        ));
+
+        // Shared string prefix but not a path ancestor.
+        assert!(!is_path_ancestor_of(
+            "#/components/schemas/Item",
+            "#/components/schemas/ItemPage"
+        ));
+
+        // Sibling, not ancestor.
+        assert!(!is_path_ancestor_of(
+            "#/components/schemas/Item",
+            "#/components/schemas/Other"
+        ));
+    }
+}
diff --git a/tests/cases/cycle-shared-prefix/base.json b/tests/cases/cycle-shared-prefix/base.json
new file mode 100644
index 0000000..7a409a3
--- /dev/null
+++ b/tests/cases/cycle-shared-prefix/base.json
@@ -0,0 +1,54 @@
+{
+  "openapi": "3.0.0",
+  "info": {
+    "title": "Cycle shared-prefix detection test fixture",
+    "version": "1.0.0",
+    "description": "Item should not be detected as a prefix of ItemPage."
+  },
+  "paths": {
+    "/items": {
+      "get": {
+        "operationId": "list_items",
+        "responses": {
+          "200": {
+            "description": "A page of items",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "$ref": "#/components/schemas/ItemPage"
+                }
+              }
+            }
+          }
+        }
+      }
+    }
+  },
+  "components": {
+    "schemas": {
+      "ItemPage": {
+        "description": "A page of items",
+        "type": "object",
+        "properties": {
+          "items": {
+            "type": "array",
+            "items": {
+              "$ref": "#/components/schemas/Item"
+            }
+          }
+        },
+        "required": ["items"]
+      },
+      "Item": {
+        "description": "An item",
+        "type": "object",
+        "properties": {
+          "value": {
+            "type": "string"
+          }
+        },
+        "required": ["value"]
+      }
+    }
+  }
+}
diff --git a/tests/cases/cycle-shared-prefix/output/change-item-value-type.out b/tests/cases/cycle-shared-prefix/output/change-item-value-type.out
new file mode 100644
index 0000000..b7f0017
--- /dev/null
+++ b/tests/cases/cycle-shared-prefix/output/change-item-value-type.out
@@ -0,0 +1,32 @@
+--- change-item-value-type.json
++++ patched
+@@
+         "description": "An item",
+         "properties": {
+           "value": {
+-            "type": "string"
++            "type": "integer"
+           }
+         },
+         "required": [
+
+
+Result for patch:
+[
+    Change {
+        message: "schema types changed",
+        old_path: [
+            "#/components/schemas/Item/properties/value",
+            "#/components/schemas/ItemPage/properties/items/items/$ref",
+            "#/paths/~1items/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        new_path: [
+            "#/components/schemas/Item/properties/value",
+            "#/components/schemas/ItemPage/properties/items/items/$ref",
+            "#/paths/~1items/get/responses/200/content/application~1json/schema/$ref",
+        ],
+        comparison: Output,
+        class: Incompatible,
+        details: UnknownDifference,
+    },
+]
diff --git a/tests/cases/cycle-shared-prefix/patch/change-item-value-type.json b/tests/cases/cycle-shared-prefix/patch/change-item-value-type.json
new file mode 100644
index 0000000..b4d012b
--- /dev/null
+++ b/tests/cases/cycle-shared-prefix/patch/change-item-value-type.json
@@ -0,0 +1,7 @@
+[
+  {
+    "op": "replace",
+    "path": "/components/schemas/Item/properties/value/type",
+    "value": "integer"
+  }
+]