Three Arcanist Abilities?
The arcanists in Scrivener's Hall have three abilities: Seeking Runescrawl, Circle of Knowledge, and Tentacular Flail.
Disclaimer: These abilities may not be what actually may be player Arcanist class abilities and are based on the ESOLogs obtained by ESOU Professor Nilandia on top of the 2023 Global Reveal's hinting that there are clues for the aesthetics and functionalities of the new Arcanist class found on NPCs.
Seeking Runescrawl
The arcanist briefly summons a book and fires at least one green projectile at the target. Since it is a projectile, the hit may not be instantaneous as it travels to the target. It can be blocked, dodged, and shielded.
Seeking Runescrawl appears to be a crux ability, though I didn't see the green triangles around the caster that we assumed were visual indicators of crux. Perhaps that’s only visual to the caster. I'm not entirely sure on how it works, but it looks like they cast two offensive spells to build the crux. The offensive spells can be Seeking Runescrawl or their other offensive spell, Tentacular Flail.
Once the crux is generated, the next cast of Seeking Runescrawl will instead fire 5 projectiles, all hitting within about 0.3 seconds. The 5 ticks each do the same damage, but they are each about 60% of the damage of a regular cast. To use numbers from a log, a regular cast might do 2188 damage. A boosted cast will have 5 ticks, each doing 1312 damage. So a total of 6560 damage.
It appears that the casting is what generates the crux, not dealing damage. I had dodged or shielded some unboosted casts, taking no damage, but the boosted cast still fired as if all of the casts hit me normally. I’m not sure if it matters if a second target is a companion or another player, but it may not matter if the full sequence is cast on the same target. Bastian took a few casts of Seeking Runescrawl, which built up the crux. When taunt wore off, I got hit by a boosted Seeking Runescrawl right off the bat. So overall it seems the crux generation is based on the caster's actions, not the results.
Once the crux is generated, it is held until released. Casting a different ability won't remove the crux unless that ability also uses crux. So, for example, if the arcanist has already generated enough crux for a boosted Seeking Runescrawl, they can cast Tentacular Flail instead and still cast the boosted Seeking Runescrawl right after.
I did notice that the unboosted casts fire a single projectile, while boosted casts will fire multiple.
For enemies, the ability has a cast time of 0.266 seconds and a range of 32 meters. The unboosted casts appear to have a 2 second cooldown, while the boosted cast has a cooldown of 5 seconds. Seems like it might just be to keep the boosted version from firing too often. I doubt it would matter for players.
Circle of Knowledge
Circle of Knowledge - The arcanist conjures a ring of green energy on the floor centered on their position with a 15 meter radius. The energy ring generates a 50k HP damage shield that is shared by all allies within it. That's 50k shared, not per person. The energy ring remains stationary if the caster is pulled out of it, but the caster retains the benefits of the shield even when outside of it. Anyone leaving the area appears to lose the shield, however. The shield remains for 10 seconds, unless the caster is killed or the targets take sufficient damage to break the shield.
For enemies, this ability appears to have a 0.5 second cast time and a 30 second cooldown.
Tentacular Flail
Tentacular Flail - The arcanist thrusts their hand forward and fires a cluster of tentacles in front of them. Anyone hit by this takes damage and is immobilized for 2 seconds. Multiple targets can get hit in a single cast. This can be blocked or shielded, but I couldn’t dodge it to save my life. It's possible it can't even be dodged. I've had the roll dodge buff on me and still gotten hit. Even people blocking and shielding are immobilized. Someone immobilized can still otherwise cast skills or do attacks, though. It appears to be a narrow cone that reaches up to 15 meters from the caster.
For enemies, this ability appears to have a 0.5 second cast time and an 8 second cooldown.
ESOLogs
(Note by Nilandia: There are multiple logs due to the need to retest different times).