The book does actually say that.
Then by all means cite it; page, column, paragraph.
The only way ambiguity becomes introduced is when you decide that surprise is not synonymous with its effects.
It cannot logically be synonymous with two or more different things.
The reason the thread hasn't ended is due to posters wedded to versions that add words and commit the ludic fallacy of finishing the narrative without rolling the dice.
You mean, like adding the words 'you are no longer surprised when you can take reactions?
That ignores the words "In addition" before the second ability. If you win initiative Assassinate gives advantage, and in addition if your target is surprised you auto-crit. The contrary view causes the words in addition to have no meaning. Which commits the legal fallacy of failing to concede meaning to words in rules.
Really? The Assassinate ability gives you *this* ability.
In addition, it gives you *this* ability. No need for it to be one ability in two parts. Those words have a perfectly valid meaning that keeps them as two separate sub-abilities gained at the same time.
But even if they were independent effects, that wouldn't constitute a reason for surprise to extend beyond end of a combatant's first-turn. Because that would commit the logical fallacy of begging the question since it would include its conclusion directly in its premises.
You keep saying that, but conveniently forget that your case is as unwritten as mine, and begs the same question in the same way.
We are both forced to postulate both cases, and choose which makes the most sense.
Bottom line, the version of surprise you prefer adds words to RAW (about ending on noticing a threat).
So does yours.
You have argued that adding those words is logical, and logically the burden of proof falls on the person making a claim to prove it.
This also applies to you.
However, no proof has been offered beyond repeating a preconceived narrative demanding that surprise be not only caused but also maintained by not-noticing threats. Nothing in RAW points to that.
Actually, it has supporting evidence in the RAW; since the cause of surprise is 'not noticing a threat' by RAW, taking away the reason for surprise should take away the surprise.
While not proof, it is evidence. As opposed to the case you favour which has no such supporting evidence.
In fact, RAW expressly calls out that checking the noticing or otherwise of threats occurs outside of turns and rounds.
And now your saying that because you check to see if a threat has been noticed at the start of combat, that it is impossible to notice threats while actually in combat? That is absurd.