[davidrusu]

> 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?

[gritzko]

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.

[davidrusu]

Ok, the red flag to me is the reliance on all neighbours responding to a proposal.

Suppose we have a faulty node heart-beating correctly but not responding to proposals, or selectively responding to proposals.

This would seem to imply that dishonest nodes have full control over which decisions are made.

[gritzko]

see later in the article, Ctrl+F "mushrooms"

[davidrusu]

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.