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Note that there is no lag. This error comes from the local end of the
VPN tunnel. I checked everything, from route tables to firewall
configuration. I can only assume that tinc gives these errors, probably
because it doesn't know about these subnets.

I think this should just work. The route to 192.168.4.0/24 is configured
with the other vpn router as gateway, so as far as tinc is concerned, it
should just forward the traffic to that host (which by itself is
reachable) and let the other side care about routing the traffic
further. With ospf this is always configured correctly on both sides, so
it should always work.

Is there any way to have tinc allow this traffic?

Kind regards,

Erik.