> n ∈ N (p), where N (g) is the set of gnomes who can hear g, including himself. Note that h ∈ N (g) ⇐⇒ g ∈ N (h).
> Each gnome g tracks the spread of the proposal in the following way: once all his neighbors n ∈ N (g) say their k-neighborhood (or bigger) is aware of the proposal
If I understand this correctly, a single node crashing would stall it's entire neighbourhood. @gritzko, can you confirm?
Nope. Missed a heartbeat means gone. We discuss churn later in the article.
Its effects are complicated, but as long as d holds, everything else holds.
I will stop looking into this now, I have to get back to my work. The colorful language doesn't make it easy for someone who follows the literature to review your idea.
I still have doubts that you can handle a dropped message or how much control a faulty node has over decisions, but I'll leave that to you to work out.
> Each gnome g tracks the spread of the proposal in the following way: once all his neighbors n ∈ N (g) say their k-neighborhood (or bigger) is aware of the proposal
If I understand this correctly, a single node crashing would stall it's entire neighbourhood. @gritzko, can you confirm?