Motivated by the ongoing discussion of spectrum scarcity, this paper considers the K-user cognitive interference channel with K − 1 primary/licensed users and one cognitive/secondary user who has non-causal knowledge of the messages of all primary users. This message sharing mechanism is referred to as cognitive-only message sharing. For certain parameter regimes, the sum-capacity of the symmetric Gaussian noise channel is characterized to within an additive constant gap from an outer bound originally derived for a channel model with cumulative message sharing, which consists of one primary user and K−1 cognitive users where cognitive transmitter i ∈ [2 : K] has non-causal knowledge of the messages of the users with index less than i. The approximately optimal achievability scheme is a combination of simultaneous interference neutralization at the primary receivers, dirty-paper coding to remove the effect of interference at the cognitive receiver, and rate-splitting, where the power splits are chosen such that the signals treated as noise are received below the noise floor of the receiver. This shows that “distributed cognition” may not be necessary in the considered network model since (approximately) the same sum-capacity can be achieved by having only one “globally cognitive” user whose role is to manage all the interference in the network.