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Actually I am pretty sure you have that part backwards. The section that discusses spellbooks and prepared spells explicitly points the reader to the wizard spell preparation section of the core rulebook.

"Spellbooks: An arcanist must study her spellbook each
day to prepare her spells. She can't prepare any spell not
recorded in her spellbook, except for read manic (which all
arcanists can prepare from memory). ... (see Chapter 9 of the Core Rulebook)"

So it is clear that the rules are the same for an arcanist and a wizard that lose access to their spellbooks: they're stuck with whatever spells they had last until they get another spellbook.


So the Arcanist opens up an interesting possibility. Consider an 11th level arcanist with the Greater Metamagic Knowledge exploit. Memorize a spell one day with a metamagic feat (say, a widened fireball). The next day, swap out widen spell for empower spell using greater metamagic knowledge. Since the arcanist memorizes like a wizard, only memorize a new 5th level spell. Then memorize an empowered lightning bolt.

The question is: If the arcanist no longer has the widen spell feat, does the arcanist lose the ability to use the previously memorized spell and lose the ability to cast the widened fireball? Or is the act of memorizing the spell the action that requires the metamagic feat (since memorizing the spell is 'almost-casting' the spell per the core rulebook) and casting the spell just releases the energy?

This opens up the possibility of an arcanist building up a tailored repertoire of memorized spells each with different metamagic feats over a period of several weeks.