I am finishing writing a joint paper with a collaborator and we are both extremely excited about the results. However, we cannot agree on when to announce the results.
In my opinion the paper is essentially ready and we should announce the results very soon. The field in which we are working in is booming right now, there are several brilliant, quick people we are competing with. We have a breakthrough result and in my field it is not unusual to see people arrive at the same results simultaneously and independently. Seeing a lot of activity and knowing more or less what people are working on I feel that we need to secure priority essentially immediately. This would mean e.g. circulating the current version of the preprint among colleagues or, ideally, posting it on a preprint server.
My co-author on the other hand would like to explore other potential applications of our results. The main result of the paper is complete, and the only question is how many applications we can have. We currently have 5 very nice applications but my co-author would like to look for more. If they are found they would be certainly good, but at this point it is more of a fishing expedition. However, because of this my co-author demands that we announce our results three months from now and is insisting on a gag order until then. (In our field it is not uncommon to lose results to dishonest researchers who learn about your result early and can try to publish/attach their name to it before you).
Basically, I feel like we are sitting at a roulette table with a million dollars but instead of cashing in we are waiting to see if we can win another 100k. I would really appreciate some advice on how to reasonably resolve this situation.