Sure, you can send over the internet if you know your modem's public IP, and set up a proper NAT redirection.
You can do the same with the API.
Keep in mind though, that there is no authentication via OSC or the API, so I'd recommend to set up a VPN instead.
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Yeah without a VPN (makes your WAN a LAN), you're going to probably have to setup a bit of firewall exceptions on whatever network you will be tied into.
I'm more about security, VPN is a lot more pain to set up, than a single port forwarding on your router.
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