Two classes of explicitly solvable sextic equations

The paper establishes two solvable classes of monic sextics via composition (Class I: Q∘C; Class II: C∘Q) and provides coefficient maps, root reconstructions, parameter recovery, and coefficient constraints. The model reproduces the same construction and formulas for Class I exactly (equations (3), (6), (7) in the paper) and for Class II matches the coefficient maps (8) and constraints (11) and derives the parameter recovery with an explicit correction to a typographical error in a1 (paper’s (10c) has an extraneous factor 2). Aside from this typo and a couple of minor slips in wording/symbols, the logic and results coincide and are obtained by the same composition-and-expansion argument (see Propositions 2-1, 2-2, 3-1, 3-2) . The constraints 27 c3 − 18 c4 c5 + 5 c5^3 = 0 and c1 = [27 c2 − 3 c4 c5^2 + c5^4] c5 / 81 exactly match the model’s derivation for Class II as well (paper (11a),(11b)) . The only substantive discrepancy is the printed factor “2” in (10c); expanding c2 = a1 + a2(2b0 + b1^2) + 3b0(b0 + b1^2) with b1 = c5/3 and a2 = c4 − 3b0 − c5^2/3 shows the correct expression has coefficient 1, and the difference from the paper’s printed version equals a2(18 b0 + c5^2)/9, generically nonzero—as the model notes.