Nothing: There is no such authority. I am one of serveral who adhere to that philosophical system. sometimes we are in agreement sometimes not. we all purport to be in keeping with the precepts set forth by Miss Rand. It is up to you to decide if that is the case and if you like it.
the question is how do you do that? I have stated the reading material that you need to be familiar with for minimum competence here. Does what I say match that in methodology (reason and logic) if not in content? Now, if you challenge me and have not read the material, and I can tell if you have, then you have no standing and I will obliterate your ideas. If you have done the work, then we have an even match. If I am right, you will learn: If you are right, I will be able to figure it out and will learn. in either case, if we are both honest then it is a win-win for each of us and I might want to take you on as a writer or blogger.
But there is no "authority", just reason and logic applied to ideas. Beyond all of that, nobody can claim to speak with the authority of Ayn Rand; two reasons:
Well the next, and real, question is "How do I know I'm getting the Real Thing?" Now that's what it's really all about. The phiosophical system that Miss Rand founded, whether you call it Objicitivism, Randism, or even if you misname it andd call it Jahaboudiism, has an identity. Now this identity is stated in terms that were commonly understood by the persons of the time. Terms like Metaphysics, a priori existence, knowetic unity and others. It is a fact that for the system to spread and become widely used and adnered to and, ultimately, the dominant system, it has to be put in layman's terms and a layman has to be willing to upgrade his understanding. Somewhere between the mundane and arcane the two must meet. Since Randite philosophy was designed to be "...a philosphy for living on earth [in the world of normal persons]..." then it ought tend toward the mundane level of understandability. A bricklayer or factory worker needs to be able to access it as readily as Ph D. Unfortunately, Miss Rand's disciples came from the college ranks, However she did do some writing. This writing was in journals, The three of which were The Objectivist Newletter, The Objectivist and The Ayn Rand Letter. By 1973 certain of these essays were put in book form. It is these books that constitute "Randism 101", There volumes are the Virtue of Selfishness, Capitalism: the Unknown Ideal, The Romantic Manifesto and The New Left: The Anti-Industrial Revolution (reissued as The Return of the Primitive. I strongly recommend Introduction to Objectisit Epistemology, however, that goes heavily into the arcane. After that, you're golden. There are others and those ought be considered "Randism 301".
But, you ask, what has this to do with whether you are giving us the Real Thing? Is what I write in line with what is there in terms of how I come to my ideas? For instance, I can disagree with certain things that have gone before, such as the status of a draft and it's constitutionality (at the time that the article appeared in the Objectivist the "age of majority" was 21, and I certainly oppose a military draft since military work is risky and nobody has a right to compel another person into danger). However what I cannot do without tossing the thing under the bus, is deviate in how I cmoe to the idea that a non-military draft is OK and that the age of majority ought be put back to 21. (for the latter, a 19 year old is not equipped experientially nor in terms of physiological psych, to sustain an adult mentality and the government, in cooperation with the parents, or if the parents are negligent or criminal, against their wishes, has the right to circumscribe the actions of a minor. For the first, it eases the kid out of the house; i.e. cuts the apron strings, puts the adolescent partially on his own but with supervision, gives insight into the way the world works without dumping the whole thing into the late adolescent's lap in a confusing heap, sets him or her up with a small "grub stake", teaches coping skills, helps the kid get out of the ego-centered world and develop a world-centered ego, keeps them off the streets and out of the clutches of Marxist professors until they can command and use the mental faculty and gets the kids into the opportunity stream). I came to this rather heretical notion by looking at the facts around me, thinking about what was needed to create a strong citzen of a free country (using "free" as a functional adult, not a half-developed adolescent) and applying logic. That is the Randite way. The test of wheter what I say is the Real Thing is how does my method click with how the articles in the 4 volumes I use as the yardstick "click"?