Actually it is written into the constitution article IX section 15. 

Essentially 50% mineral royalties go to the general fund for government funding, the remaining 50% goes to the pfd with a calculation 5 year average of interest earnings to be equally distributed to Alaska residents. 

Sure govoner walker can line item veto the payout, but that money stays in the pfd unless the constitution is changed. The first year the funds he vetoed can't be used, but this year with the legislature backing it, it can because the legislature effectively temporarily amended the constitution capping the payout and redistribute to the genral fund. While not covered in the media real well, this was effectively the AK Supreme Court ruling. Ie last years excess interest goes back into the pfd, this years transfers to the gf. 

http://www.apfc.org/home/Content/aboutAPFC/constAndLaw.cfm