Research proof index

Lemma 4.4, [AHIV22] (mutual-exclusion corollary). Either all points on the affine line are e-close to the Reed–Solomon code, or at most ‖RS‖₀ points are. The assumptions v ≠ 0 and ‖RS‖₀ < |F| are necessary for mutual exclusion: if v = 0, the affine line degenerates to a singleton and the two branches can hold simultaneously.

If A and B are coprime and agree on sufficiently many lines, then A is constant.

Main existence: if B/A agrees with low-degree quotients on enough lines, then A ∣ B.

Existence of P with B = P * A when both A and B are nonzero.

A bivariate polynomial of degree zero in both variables divides every polynomial.

After cancellation in X, a large subset of evaluation points witnesses P = quot_y.