Public unrefereed combined theorem candidate. Relative to named primitive-polynomial-monodromy, block-kernel, finite-projective-group, and Ritt inputs, it gives the all-degree fixed-seed coefficient atlas at cyclic rank at most three and classifies all rank-preserving polynomial extensions. It further treats arbitrary polynomial amplitudes, exact vanishing on specified zero-cycles, persistent endpoint moments for Atlas phases, and an exact Laurent local-channel criterion. No finite all-Laurent atlas, external reproduction, complete formalisation, peer review, or priority certification is claimed.