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Arcane Thesis

Source Core Rulebook pg. 205 1.1
During your studies to become a full-fledged wizard, you produced a thesis of unique magical research on one of a variety of topics. You gain a special benefit depending on the topic of your thesis research. The arcane thesis topics presented in this book are below; your specific thesis probably has a much longer and more technical title like “On the Methods of Spell Interpolation and the Genesis of a New Understanding of the Building Blocks of Magic.”

PFS StandardImproved Familiar Attunement

Source Core Rulebook pg. 205 1.1
You’ve long held that fine-tuning the magic that bonds wizard and familiar can improve the mystic connection, compared to the safe yet generic bond most wizards currently use. You’ve formed such a pact with your familiar, gaining more advantages from it than most wizards. You gain the Familiar wizard feat as a bonus feat. Your familiar gains an extra ability, and it gains an additional extra ability when you reach 6th, 12th, and 18th levels. Your connection with your familiar alters your arcane bond class feature so that you store your magical energy in your familiar, rather than an item you own; you also gain the Drain Familiar free action instead of Drain Bonded Item. Drain Familiar can be used any time an ability would allow you to use Drain Bonded Item and functions identically, except that you draw magic from your familiar instead of an item.

PFS StandardMetamagical Experimentation

Source Core Rulebook pg. 205 1.1
You’ve realized that the practice known as metamagic is a holdover from a time long ago, when wizards had to work out their own spells and variations rather than rely on spells recorded by others and passed down over the years. This allows you efficient access to various metamagic effects. You gain a 1st-level metamagic wizard feat as a bonus feat. Starting at 4th level, during your daily preparations, you can gain a metamagic wizard feat of your choice that has a level requirement of no more than half your level, which you can use until your next daily preparations.

PFS StandardSpell Blending

Source Core Rulebook pg. 206 1.1
You theorize that spell slots are a shorthand for an underlying energy that powers all spellcasting, and you’ve found a way to tinker with the hierarchy of spell slots, combining them to fuel more powerful spells. When you make your daily preparations, you can trade two spell slots of the same level for a bonus spell slot of up to 2 levels higher than the traded spell slots. You can exchange as many spell slots as you have available. Bonus spell slots must be of a level you can normally cast, and each bonus spell slot must be of a different spell level. You can also trade any spell slot for two additional cantrips, though you cannot trade more than one spell slot at a time for additional cantrips in this way.

PFS StandardSpell Substitution

Source Core Rulebook pg. 206 1.1
You don’t accept the fact that once spells are prepared, they can’t be changed until your next daily preparation, and you have uncovered a shortcut allowing you to substitute new spells for those you originally prepared. You can spend 10 minutes to empty one of your prepared spell slots and prepare a different spell from your spellbook in its place. If you are interrupted during such a swap, the original spell remains prepared and can still be cast. You can try again to swap out the spell later, but you must start the process over again.

PFS StandardStaff Nexus

Source Advanced Player's Guide pg. 142
Your thesis maintains that early and intense adoption of staves from the first days of study can create a symbiotic bond between spellcaster and staff, allowing them to create remarkable magic together. You've formed such a connection with a makeshift staff you built, and you are ready to infuse any staff you encounter with greater power.

You begin play with a makeshift staff of your own invention. It contains one cantrip and one 1st-level spell, both from your spellbook, but it gains no charges normally during your preparations; you must expend a spell slot to grant it charges in the same way you would add additional charges to a normal staff. You can Craft your makeshift staff into any other type of staff for the new staff's usual cost, adding the two spells you originally chose to the staff you Craft.

At 8th level, you can expend two spells instead of one when preparing your staff, adding additional charges equal to the combined levels of the expended spells. At 16th level, you can expend up to a total of three spells to add charges to the staff, adding additional charges equal to the combined levels of all three spells.