How we cite our quotes: (Sentence)
Quote #1
Each of the Parties to this Treaty undertakes to prohibit, to prevent, and not to carry out any nuclear weapon test explosion, or any other nuclear explosion, at any place under its jurisdiction or control: in the atmosphere; beyond its limits, including outer space; or under water, including territorial waters or high seas [...]. (6-7)
In terms of warfare, perhaps the most important point here—aside from the prohibition on nuclear weapons testing in the air, space, etc.—is the mention of territorial waters and high seas. These aquatic areas are not easy to define, which means boundaries are easily crossed, and countries tend not to take kindly to having their borders violated. More often than not, it's considered a declaration of war. So lower the pirate flag, original parties, because the watery depths are super off-limits.
Quote #2
It is understood in this connection that the provisions of this subparagraph are without prejudice to the conclusion of a Treaty resulting in the permanent banning of all nuclear test explosions, including all such explosions underground, the conclusion of which, as the Parties have stated in the Preamble to this Treaty, they seek to achieve. (9)
One of the most admirable intentions of the PTBT is the prevention of future nuclear conflict. Here, it's trying to make room for any diplomatic improvements regarding the issue that might someday appear. Thanks for your willingness to step aside for the greater good, PTBT. It's very chivalrous of you.