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In other words, it is a system that was created by forcishaping.
The way the coiner of these terms sees it, "-genic" terms can apply to sidesystems and similar structures if they want it to. However, sometimes it's better to have a sidesystem-specific term for specificity, hence why forcidawn exists as a term.
If you said your system was "shaped" and you meant that that was why it existed in the first place, you would be referring to the experience of being forcigenic. By definition, systems that exist because of programming are forcigenic.