A commitment to deliver (a service, funding, an item) that is subsequently set aside. The broken promise is then explained with the glib expression "oh, but that promise was non-core".

Now generalised to non-political situations, too.

Origin: Australian federal elections at the turn of the 20th/21st centuries. The conservative party (known as the Liberal/National coalition) made a number of election promises which were broken soon after the election. The prime minister, John Howard, attempted to explain this behaviour by claiming that some promises are "core" and some are "non-core" and thus, don't count.

An election promise that you have gone back on after the election is over. It is important not to define what promises are core and what are non-core before the election itself.

There really is no specific anthem for emo kids because they all have slightly different choices in their x.core music. However, most emo anthems would usually have lyrics about suicide, how their life sucks, how the world sucks, how their girlfriend/boyfriend dumped them...it really depends on the occasion of the listener.