Unfortunately it looks like the related count information is not available in a Script for an artifact.
That means it is necessary to use the Resilient API to get that information. This is the API that the UI uses:
/rest/orgs/202/incidents/11033/related_ex?handle_format=objects&want_artifacts=true
So you could use the fn_utilities app (https://exchange.xforce.ibmcloud.com/hub/extension/2b6699ac8a3976b67dfbddee26dbe3a5) and outbound email app (https://exchange.xforce.ibmclouddfdfd.com/hub/extension/caafba4e4f6d130e7db30ed4d5e53504). Use the call rest api function from the fn_utilities app and the send outbound email from the outbound email app.
Something like this:

There is some work to get the function inputs set up correctly and the scripting conditions for the exclusive gateway. But it should be possible.
Ben
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Ben Lurie
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Original Message:
Sent: Tue May 18, 2021 10:25 AM
From: PAUL FORMOSA
Subject: Artifacts
Hi Ben, it would be preferable in a script. Meaning if artifact is created and the related incident count is greater than zero, I would like to notify the owner of the incident of this fact. I am finding that the owners are not checking for the status of the related incident count.
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PAUL FORMOSA
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Original Message:
Sent: Tue May 18, 2021 08:33 AM
From: Ben Lurie
Subject: Artifacts
Are you looking to do this in a workflow or a script? A bit more information about the use case may help.
Ben
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Ben Lurie