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https://pathfinderkingmaker.fandom.com/wiki/Sorcerer#Spells_Known_per_Level
And the same number of daily casts progression as wizards have slots:
https://pathfinderkingmaker.fandom.com/wiki/Wizard#Progression_Table
Only the latter are affected by their casting modifier and by abundant casting.
It's a weird class with spells per day and spell slots for memorized spells being tracked separately.
The idea is that it's a wizard in the sense of having lots of ability to learn spells, but it's a sorcerer in the sense of the flexibility of casting spells.
https://pathfinderwrathoftherighteous.wiki.fextralife.com/Arcanist
Not sure that that one answers your question...
Ah, checked the pathfinder forum.
"You get additional spell slots for casting if you have high Intelligence, but spells prepared per day does not get modified by ability scores."
Maybe the progression is slower though, not sure about that.
Stats are irrelevant. Nothing in the game can increase the number of Arcanist's slots, only the number of daily casts.
That is wrong.
You don't get slots. Nothing affects Arcanist's slots.
You only get more casts per day.
Where does it say so?
https://steamcommunity.com/sharedfiles/filedetails/?id=2838930026
I do have 4 slots for level 1-2 spells, but I only have 3 for level 3-5, 2 for level 6, and 1 for level 7-8.
At any rate, you've chosen an archetype that gets more casts per day, but can prepare fewer spells.
The stat line in your screenshot, comparing against pfsrd, that's the number of casts per day a level 16 arcanist gets. As for number of prepped spells, you should have 5-5-4-4-4-3-2-1 base.
That's the table for bonus spells.
https://www.d20pfsrd.com/classes/hybrid-classes/arcanist/
And the arcanist's page (which has both spell/day and preps/day tables) for reference. From which your archetype should be giving you an extra cast at each spell level, but one fewer spell prepped for each.