monstertruck
First, thanks!
By internal contradictions, do you mean conflicting evidence in the relationship between topics or metrics? That will (and does) come up regularly - peer-reviewed studies investigating the same topics have differently measured (or contradictory) results. We have tools for assessing the statistical quality of submitted relationships (through things like statistical reproducibility, algorithm type, statistical controls, etc.), so unreproducible or statistically unlikely relationships will be clearly seen as such. Building tools to programmatically test reproducibility of evidence is definitely something we've thought about (if that's the "formal verification" you are talking about).
Ultimately the goal will be to (statistically) approximate the sum total of all evidence between pairs of topics, and also to provide users with the tools and sources to assess (and apply!) that evidence.
First, thanks! If you'd like to reach out and learn more or talk about your learnings from building something like this we'd be very interested (we have a Slack community and a direct contact form on the site).
As for your questions - we have tools for assessing the reproducibility (in the statistical sense) of models and relationships added to System, as well as tools for users (and built in to the platform itself) to assess the relative statistical strength between any two relationships that you find on the site.
And, yes, we're early on in the process of writing (peer-reviewed) evidence on various topics, and as you note, the value of seeing these systems will grow with how detailed the topics are covered and the overall number of the world's topics shown to be related. I hope you'll stay engaged to see!