The phrase "originating process" refers to the legal documents or paperwork that starts a lawsuit or legal action. It is the initial step taken by a person or organization to officially begin a legal case in court. Full definition
Actions are a type of originating process, and are most commonly commenced by issuing a statement of claim. (mydefence.ca)
I am also aware that some courts have allowed parties to serve originating process as «substitute service» (the traditional service in person having been tried and failed) by electronic means, notably by posting messages to the defendant's Facebook page or by Twitter (a notice of injunction). (slaw.ca)
The whole account of the consequent nature of God, which originated process theism, seems to have been added, possibly to resolve a problem concerning consciousness. (religion-online.org)