Why it is a question
THEORY-321 now states Golub and Jackson’s characterization (LIT-999) as a theorem about repeated DeGroot averaging in a strongly connected society: the consensus converges to the truth as the society grows if and only if the largest influence weight vanishes. The mathematics is proved and was re-derived. What is open is whether real communities update closely enough to DeGroot for the condition to decide their beliefs. The model’s members are naïve: they do not discount repeated information, signals are independent, and weights are fixed (NOTE-840).
A second, narrower matter is held here too. NOTE-840 records Proposition 2 for any convergent weight matrix, with several closed groups allowed. The audit’s sketch suggests a vanishing largest weight may not then suffice: many small closed groups, each of growing size, can each settle on its own average, and the chance that some of them misses the truth need not vanish. Whether the paper’s definitions exclude this was not checked against the source.
What would answer it
A laboratory network experiment or field data in which the updating rule is held fixed, the influence structure is changed, and the group’s settled estimate moves away from the truth as the largest influence weight grows would answer it yes. Such an experiment in which accuracy does not track maximal influence would answer it no. Further simulations of the DeGroot model do not settle it: they only restate the theorem. For the narrower matter, reading Golub and Jackson’s Proposition 2 and Theorem 3 with their definitions of influence and wisdom for several closed groups settles it.