Does an accidentally true belief that I am nearby constitute "awareness?"

Question

From the Core Rulebook:

If you are unnoticed by a creature, that creature has no idea you are present at all. When you’re unnoticed, you’re also undetected by the creature. This condition matters for abilities that can be used only against targets totally unaware of your presence.

Am I unnoticed if an enemy genuinely and correctly believes that I am lurking about, but the reasons for which they believe it are incorrect?

In the scenario, a castle guard on patrol enters a room for the first time that day, finding the door broken open and the room itself a mess. Upon seeing this, they believe some intruder must be nearby. I am an intruder and do happen to be close by avoiding notice, but the room is in its state because another guard, drunk on duty, came through a short time earlier and wrecked the place.

My GM says the guard is aware of my presence, thus making me noticed. I think that would only be the case had it been me who forced my way in and made the mess.

Answer 1

You are undetected

From the Core Rulebook (emphasis mine):

If a creature is undetected, that doesn’t necessarily mean you’re unaware of its presence—you might suspect an undetected creature is in the room with you, even though you’re unable to find its space. The unnoticed condition covers creatures you’re entirely unaware of.

You aren't unnoticed, since the guard is suspecting a hostile presence. The rulebook doesn't have any caveats around whether they suspect it for the right reasons; they might not even know that it is you. The guard simply suspects some hostile presence. You still have a number of advantages, notably:

If a creature is undetected, you don’t know what space it occupies, you’re flat-footed to it, and you can’t easily target it.

This allows you to still get off Sneak Attack, for example. It also would probably allow you to roll Stealth for initiative, although that's always up to the GM.

More on targeting undetected creatures:

Targeting an undetected creature is difficult. If you suspect there’s a creature around, you can pick a square and attempt an attack. This works like targeting a hidden creature, but the flat check and attack roll are both rolled in secret by the GM. The GM won’t tell you why you missed—whether it was due to failing the flat check, rolling an insufficient attack roll, or choosing the wrong square. The GM might allow you to try targeting an undetected creature with some spells or other abilities in a similar fashion. Undetected creatures are subject to area effects normally.

Answer 2

You are noticed but undetected

The guard found out that mess, and expect to find someone nearby. The fact that you or any other person caused the mess is not taken into account, for example he'll probably accuse you if he finds you.

Noticed here means that he thinks that someone is nearby and he's actually on his guards.

Unnoticed would rather correspond to a situation where your guard does not even expect to find someone here.

You were just unlucky in this situation, i'd agree with your DM.