diff --git a/README.md b/README.md
index c4b05467911..0076d218300 100644
--- a/README.md
+++ b/README.md
@@ -59,6 +59,7 @@ Then send a Pull Request to this repository. GitHub Actions will instantly perfo
 ### After you submit
 
 * **Comments that run something:** `/retest` tests again; `/appstream` explains how to show your own screenshot (via the AppStream metainfo file). A comment that says a fix or a new release is out ("fixed in 1.2.3", "new release", "updated") re-tests a failed pull request automatically; "will be fixed in the next release" does not.
+* **No network:** the test runs the application without network access, on purpose, and that is a requirement: an AppImage must start without network, or at least show a message; one that exits because it cannot reach a server fails with `error-app-exits`.
 * **Labels:** `error-*` names why the test failed (the comment has the hint); `screenshot-ok` means it passed and the screenshot looked fine; `manual-check-needed` means a maintainer must look (e.g. the download location moved to another owner).
 * **Merging:** pull requests will take some time to be reviewed by a maintainer.
 * **Changed your mind?** Comment "please remove my app" (or "opt out") on the pull request: it gets the `opt-out` label and a maintainer closes it. The application is not proposed again.
diff --git a/code/diagnose.sh b/code/diagnose.sh
index 7a3c3e46906..2a1d14b2b11 100755
--- a/code/diagnose.sh
+++ b/code/diagnose.sh
@@ -40,7 +40,7 @@ HINTS=(
 
   "^ERROR: The application exited within [0-9]+ seconds"
   "error-app-exits"
-  "The application quit or crashed right after starting. The error below usually shows why."
+  "The application quit or crashed right after starting; the error below usually shows why. Note that the test runs the application without network access, on purpose, and that this is a requirement for the catalog: an AppImage must start without network (users are offline too). If the application needs a server, a login or an update check to start, please make it show its window (or at least a message) first and connect afterwards, and handle a failed connection instead of exiting."
 
   "^ERROR: Could not find a single window on screen"
   "error-no-window"