I'm curious as to whether getting a permanent enhancement bonus to Intelligence (e.g., by wearing a headband of vast intelligence +2 for more than 24 hours) increases the number of 1st-level spells/formulae known (for, e.g., an alchemist). I'd like to assume it does not, as these spells are determined at character creation, and presumably use your (unmodified) starting Intelligence; but I'm curious whether anyone has a reference that might clarify this.
For example, the alchemist's Alchemy supernatural ability states: "An alchemist begins play with two 1st-level formulae of his choice, plus a number of additional formulae equal to his Intelligence modifier." To me, this sounds like my alchemist should gain a number of bonus 1st-level formulae/spells known equal to whatever his presumably unmodified Intelligence bonus was at 1st level. However, I know Pathfinder mechanics favor retroactively gaining, e.g., skill ranks, when your Intelligence increases, as stated here and here. James Jacobs doesn't explicitly mention spells, but maybe they're included in "… all of them." Is it the case then that, having acquired the headband (at 9th-level), my alchemist also gains an additional 1st-level spell/formula?
Thanks in advance for any input!