> 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?