alright u have had the first great point of the build im a changing it now!
i hadnt considerd the AD vs AP

what i'm saying with Trinity Force vs Lich Bane is that Trinity Force does the exact same thing, except off sivir's base ad of 101, whereas Lich Bane only does it off ap, which with this build is your ap is only 80, so the trinity force proc OCCURS JUST AS OFTEN, BUT IS MORE POWERFUL. the rest is pure preference, but aside from the bonus crc, as, and ad from Trinity Force over Lich Bane, is that the proc occurs just as often but is more powerful. so if you want the boost, the trinity force will get you much more

Uhh masts reason i use havoc is the dmg helps with carries trinty i prefer lich bane over TF because the boost on dmg occult for a good cary its a no brainer

drop Havoc and Sorcery. a Trinity Force will do much more for you than a Lich Bane. Sword of the Occult is too unrealiable to count on for a build. your glyhs, seals, and quints are all bad. quints might be fine iff (if and only if) you have 80% crc or more. you should go defensive seals and mp5 glyphs.