A Lean 4 formalization of the core results in "Section Operators on Rational Functions and Colored Eulerian Factorizations for G(m,1,n)." The formalization works at the coefficient-sequence level, defining the section operator Phi_{b,c} as the reindexing f(k) -> f(bk+c) and proving the key arithmetic identity m(bk+c)+1 = b(mk+1) when b = 1 (mod m) and c = (b-1)/m. This identity makes the sequences k -> (mk+1)^r into eigenfunctions of Phi with eigenvalue b^r, and a Vandermonde argument on the nodes 1, m+1, 2m+1, ..., mn+1 establishes their linear independence.

Building on these foundations, the formalization proves the semigroup composition law Phi_{b,c} . Phi_{b',c'} = Phi_{bb',c''} with c'' = (bb'-1)/m, the congruence closure m|(b-1) and m|(b'-1) => m|(bb'-1), and the spectral expansion showing that Phi acts diagonally on any linear combination of the eigenbasis. All 12 theorems are fully proved with zero sorry statements, verified against only the standard Lean 4 axioms (propext, Quot.sound, Classical.choice).