Knowledge (any one) means pick one knowledge skill.

If a creature was meant to have such broad knowledge that they had the same bonus to all knowledge skills, the entry would probably read Knowledge (all), though I don't believe there any creatures written this way. Knowledge (any) would be a bit more ambiguous, but Knowledge (any one) would be commonly understood to mean that of any of the available choices, you get only one.

I'm struggling to find somewhere this is explicitly stated, but taking for example the Lyrakien Azata in your example, it is consistent with the skill ranks that are available to the creature if you reverse-engineer its entry.

As an outsider, the Lyrakien has 6+2 (for 14 Int) skill ranks per hit die, and the entry shows it has invested max skill ranks in 8 skills, matching its available skill points (though it has a very high Fly skill modifier listed, that's based entirely on its size, dexterity, and perfect flight speed manoeuvrability, it has no actual skill ranks in Fly).

That means it has ranks invested in exactly one knowledge skill and one perform skill. It has no ranks left over to invest in any other specific knowledge or perform (or profession, etc.) skills. The question of exactly which knowledge or perform skills those are are left to the DM to decide, as best serves the game they're running.

Knowledge (any one) means pick one knowledge skill.

If a creature was meant to have such broad knowledge that they had the same bonus to all knowledge skills, the entry would probably read Knowledge (all), though I don't believe there any creatures written this way (though this wording is sometimes seen in lists of class skills, where it means that all Knowledge skills are class skills for the class or creature type). Knowledge (any) would be a bit more ambiguous, but Knowledge (any one) would be commonly understood to mean that of any of the available choices, you get only one.

I'm struggling to find somewhere this is explicitly stated, but taking for example the Lyrakien Azata in your example, it is consistent with the skill ranks that are available to the creature if you reverse-engineer its entry.

As an outsider, the Lyrakien has 6+2 (for 14 Int) skill ranks per hit die, and the entry shows it has invested max skill ranks in 8 skills, matching its available skill points (though it has a very high Fly skill modifier listed, that's based entirely on its size, dexterity, and perfect flight speed manoeuvrability, it has no actual skill ranks in Fly).

That means it has ranks invested in exactly one knowledge skill and one perform skill. It has no ranks left over to invest in any other specific knowledge or perform (or profession, etc.) skills. The question of exactly which knowledge or perform skills those are are left to the DM to decide, as best serves the game they're running.

Knowledge (any one) means pick one knowledge skill.

If a creature was meant to have such broad knowledge that they had the same bonus to all knowledge skills, the entry would probably read Knowledge (all), though I don't believe there any creatures written this way. Knowledge (any) would be a bit more ambiguous, but Knowledge (any one) would be commonly understood to mean that of any of the available choices, you get only one.

I'm struggling to find somewhere this is explicitly stated, but taking for example the Lyrakien Azata in your example, it is consistent with the skill ranks that are available to the creature if you reverse-engineer its entry.

As an outsider, the Lyrakien has 6+2 (for 14 Int) skill ranks per hit die, and the entry shows it has invested max skill ranks in 8 skills, matching its available skill points (though it has a very high Fly skill modifier listed, that's based entirely on its size, dexterity, and perfect flight speed manoeuvrability, it has no actual skill ranks in Fly).

That means it has ranks invested in exactly one knowledge skill and one perform skill. It has no ranks left over to invest in any other specific knowledge or perform (or profession, etc.) skills. The question of exactly which knowledge or perform skills those are are left to the DM to decide, as best serves the game they're running.

Knowledge (any one) means pick one knowledge skill.

If a creature was meant to have such broad knowledge that they had the same bonus to all knowledge skills, the entry would probably read Knowledge (all), though I don't believe there any creatures written this way. Knowledge (any) would be a bit more ambiguous, but Knowledge (any one) would be commonly understood to mean that of any of the available choices, you get only one.

I'm struggling to find somewhere this is explicitly stated, but taking for example the Lyrakien Azata in your example, it is consistent with the skill ranks that are available to the creature if you reverse-engineer its entry.

As an outsider, the Lyrakien has 6+2 (for 14 Int) skill ranks per hit die, and the entry shows it has invested max skill ranks in 8 skills, matching its available skill points (though it has a very high Fly skill modifier listed, that's based entirely on its size, dexterity, and perfect flight speed manoeuvrability, it has no actual skill ranks in Fly).

That means it has ranks invested in exactly one knowledge skill and one perform skill. It has no ranks left over to invest in any other specific knowledge or perform (or profession, etc.) skills. The question of exactly which knowledge or perform skills those are are left to the DM to decide, as best serves the game they're running.