Verified Note

Galois-Frobenius Composition Law

A companion proof of the separated-polynomial composition criterion through generic fibers, Galois descent, and Frobenius reduction.

Summary

Result and mechanism

The note studies when separated divisibility forces a common composition structure.

Main result

The proof packages a polynomial composition criterion through generic-fiber relations, splitting fields, Frobenius descent steps, and a cubic square-root functional-equation specialization.

Contribution type
New viewpoint; Lean formalization
Contribution
Galois-descent and Frobenius-reduction viewpoint on a separated-polynomial composition criterion, including a Lean-checked cubic square-root functional equation.
Mechanism
generic fibers, Galois descent, Frobenius reduction
Lean theorem family
SeparatedComposition.separated_composition_criterion_iff
Lean and mathlib
Lean 4.30.0-rc2, mathlib v4.30.0-rc2
Build command
lake build