How do you define a NAP?

[Agema]

I would suggest a breach of NAP as anything that causes you loss of units, income, territory, gems, and domination (except by border expansion). Although as someone said above, I'd consider building temples and preaching along the border that pushed back your Dom grounds to complain.

Someone sneaking their way through your lands would therefore be basically legit unless specifically demanded. A sneaking unit that was accidentally discovered and was stompy enough to defeat the PD or otherwise harm should merit an apology and compensation for lost income and gems, or be considered a breach of NAP.

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One thing that happened in one of our n00b games was that someone signed a 3-turn NAP and thought it meant no attacks for three turns, the other no attacking without a 3-turn warning. That caused a bit of a fuss. Since then, I've generally specified which I mean.