Defining a 'core' can be a bit ambiguous. I personally only selected players that are very difficult to acquire through trade, the UFA market or drafting. So for me, it was Monahan, Bennett, Brodie, Giordano, Gaudreau and I included Hudler in there (even though I am well aware we acquired him as a FA
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I found it difficult not to expand further. If we are discussing the core that includes important pieces - but pieces that aren't so rare/expensive to acquire - but pieces that every team needs to have in order to win - I would add in Russell, Backlund, Bouma and Colborne (even though his play of late hasn't been the best). They are not easily replaceable, but they are easier-type players to acquire. Some listed may very well end up becoming a core piece regardless of definition.
I didn't include prospects outside of Bennett. 2 years ago, I would have included Baertschi as part of the core. Until I see prospects entering the NHL and becoming regulars, I can't consider them the core really - just very important assets you hope become solid additions to the core, rather than just complimentary players. It is not to say that I don't think Baertschi, or Poirier, or 'x' doesn't have a chance at becoming a part of the core, just that until they show that they are, I haven't included them. Bennett is just a special case due to pedigree and position. I think it is very likely that a few prospects currently in the system become core pieces.