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Did the download really complete (100%)? Because it sounds like corrupted download to me. If it still doesn't work, maybe try downloading with different browser.
Also did you make sure you've enough storage space before updating? You can backup saves, uninstall 0.3, install 0.4 and then placing saves back as a last resort if other methods doesn't work.
Remove the old version of the game from your phone and do a clean install with the new version (you will lose all your savefiles though, unless you back them up). I have this wellknown issue with almost all apk builds of renpy games, update app does not work. A clean install will most of the time resolve it, unless you have no more storage space.