What is the best medium for presenting more technical details? In my talk I attempted to use stories (which is a very laymen approach) to explain algorithms - this may have been too high level. So instead, what is easiest for you to digest and verify? Actual code and working samples/demos that prove the behavior? Mathematics? Case studies by large customers?

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I dislike consensus protocols because they are difficult to scale. Deterministic algorithms however are not. Why? Consensus requires communication, and communication takes time. As you add more peers, you then have to do more communication in order to maintain consensus. But as more communication occurs, things bottleneck and get even slower. However some problems require consensus (like finances, traditionally) and therefore GUN would not be a good choice.

Deterministic algorithms only need the same inputs and they then spit out the same output as any other machine (running that algorithm) anywhere in the universe. This is why "immutable data structures" are all the rage lately. This is incredibly scalable because as long as the inputs are received (which might have been sent slowly over the network) then all the databases will converge to the same result (for the same inputs) regardless of whatever current state those databases might be in. And because a database maintains state, this type of guarantee is really important for databases.

WARNING NOTE: Missing input causes the databases to be temporarily out of sync because their inputs are different, however when the inputs are finally received (via retries or what not) the databases will sync up regardless of the ordering. Making sure the inputs can be sent in any order or retried is the idea of idempotency and is explored more with CRDTs and commutativity. This means GUN is "Eventually Consistent" and not Strongly Consistent, so don't use GUN in those scenarios.