The fourth-moment tail bound is the concentration bound this carrier can state; Hoeffding is blocked on the joint law, not on the exponential

Recorded description

Let X be a rational-valued random variable on a finite index range [0, n) with a distribution p, and let a be a positive rational. Then a^4 times the expectation of the indicator of the event {(X - E X)^4 >= a^4} is at most E[(X - E X)^4] -- i.e. P(|X - E X| >= a) <= E[(X - E X)^4]/a^4, multiplied through so that no Rat.inv appears. It is Rat.markov_constructed at threshold a^4 against the summand ((X - E X)^2)^2, whose nonnegativity is Rat.sq_nonneg applied to (X - E X)^2 rather than to X - E X, and whose threshold positivity is Rat.mul_pos twice. No hypothesis beyond Markov's own. This is the tail bound reached INSTEAD of Hoeffding, and the two obstructions to Hoeffding are structural rather than effort. First, Hoeffding needs E[prod_j f(X_j)] = prod_j E[f(X_j)], a statement about a joint law over a product space, and a shape_search over 4,260 declarations including every constructed carrier finds no product or joint distribution of any spelling. Second, Hoeffding's lemma needs exp on the carrier the moments live on: CReal.expFn DOES exist, but the functional equation e^(x+y) = e^x * e^y -- without which the product step is not even statable -- does not, in the same index.