I just got done doing a series of presentations on Martin Fowler'sRobert Martin's SOLID principles for my co-workers. I don't know how well these principles translate to G2, but since you're looking for 5-7 core fundamentals, these seem like a well-established set to start out with. If you want to round it up to 7, you could start with DRY and throw in Fail-Fast.
corrected the name, based on http://en.wikipedia.org/wiki/SOLID_(object-oriented_design)
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