Total-Collapse Primes of Polynomial Maps over GF(p): Eighteen Families and Two Related Sequences

Companion mathematical preprint (Markdown and PDF), 20 OEIS sequence cards, and self-contained exact Julia and C verification suite for 18 families of total-collapse primes of polynomial maps over GF(p) — including the odd cubic ladder K_n(u) = (u^3 - (n^2 + n + 1)u)/(n(n + 1)), squares of monic Chebyshev-Dickson polynomials V_m(x)^2, Hilbert class field maps for D = -59, -83, -251, and the diagonal SL_3 trace square x^2(x - 2)^2 — together with two related integer sequences: the least collapsing prime along K_n (with the Pell-Pythagorean obstruction) and sums of n-bit primes having a single circular run of 1s and at most one internal block of 0s.