Open source is defined by the Open Source Initiative: https://opensource.org/osd

At least it should be. I'm not sure what definition this petition would use.

The petition should use a more restricted definition, because the OSI definition only deals with the way software is developed and distributed, not how software contributes to the common good. That a lot of open source software is foundational to how most other software is written is incidental for the OSI, but important for this recognition.

In fact I see no reason why you can't already get this recognition in the existing legal framework by creating an association with a specific scope.