an attack includes any spell targeting a foe or whose area or effect includes a foe (Cloudkill does neither when cast in empty space. Strike 1).
On casting in an empty square it doesn't affect any foes, but the invisibility test is on the spell itself, not an immediate result of casting the spell. When it affects a foe 3 rounds after casting, the condition is satisfied, the spell has included a foe in its effect. Yes, cloudkill can affect a foe even when cast on an empty space.
Actions directed at unattended objects do not break the spell. (Like casting cloudkill in an empty square? Strike 2.)
An empty square is not an unattended object. A reasonable person knows the spell is directed at the foe especially, as well as everything else in its path, regardless of where it originates, and its funny how you're willing to mince words about directing an action, considering what follows. This rule you quoted is pretty obviously just saying that you can smash inanimate objects without losing invisibility.
Causing harm indirectly is not an attack.(We can mince words all day about causing harm directly or indirectly, but as that's entirely subjective and CANNOT be actually defined in the certain terms you are looking for, I'm staying out of it.)
That's the crux of the matter on your side of the argument, and utterly irrelevant to me, doesn't look like you're "staying out of it" though since you're already rationalizing about other clauses about directing the spell as justification for your pov. I read the rules and understand spells are attacks if they affect a foe. You read the rules and understand that an indirect attack is not an attack, so the delay in the spell affecting the target becomes relevant to you. Without interpreting the indirect attack clause, you have no argument that makes sense, because it's the only thing that conflicts with the direct statement that spells that include foes are attacks.
Thus, an invisible being can open doors, talk, eat, climb stairs, summon monsters and have them attack This is a big one. Both spells create a dangerous spell effect, directed in part by the caster. If directing a summoned monster to rip someone's face off doesn't end invisibility, then the argument of "intent of the caster" doesn't hold up.
The summon spell isn't the attacker, the summoned monster is. If you cast a burning hands spell at an oil slick 50 yards wide and it catches fire, you aren't casting burning hands on the people at the opposite end of the oil slick, even though they are harmed. Likewise if you buff or transport an ally, you don't inherit their actions.
In fact, cloudkill isn't directed beyond the initial target location.),
Incorrect, though that is probably rai. The cloud moves away from you (the caster), not the casting location or any other fixed location. If you move, the cloudkill still moves away from you, by the raw. Directed if the caster cares to pay attention and move.
cut the ropes holding a rope bridge while enemies are on the bridge (While not a spell, this is a far more direct example of expressing intent to kill.), remotely trigger traps, open a portcullis to release attack dogs, and so forth.
Spells (and only spells) have a separate test specifically calling out perceptions about the target. Perception/intent to kill a foe is only relevant for spells. For everything else it's attack a creature directly y/n?
Cloudkill fits none of the criteria for removing invisibility, except a completely ambiguous (and frankly unresolvable with this crowd) statement about direct vs indirect damage. As the rest of the spell gives examples to the contrary though, our group ruled that delayed effects are not attacks. This means pushing a boulder off a cliff on someone. This also means casting a cloudkill with no targets inside and letting it roll across the street.
It does fit the criteria of being a spell that includes a foe in its effect at some point during its existence, else its a pretty useless spell.