Isn't this what Sunrise is doing?
Oh, I've answered this question in part on Medium. I think this link gets you there: https://medium.com/@psilfver/no-one-is-more-happy-than-i-am-that-you-raised-this-question-we-did-put-a-lot-of-thinking-into-it-1c7a9368d918
Not sure about the "gentle nudge" concept. That could get incredibly distracting. If you have a calendar of "moments", you'll be getting nudged every other minute. If a friend posts on Facebook, you get nudged. If an interesting article is favorited, you get a nudged. And so on. After awhile, I'll just stop all the nudging and take a nap.
Oh, sorry if that was in any way unclear — but the whole point was not to get disturbed by things happening all over the place that you probably have no interest in (mentions in social media.). This would be fully curated and up to you, just as you decide how aggressive Calendar reminders are today. More on the "The game starts in 10 minutes" end of the scale rather than "Someone mentioned you on Facebook".