What question did this study set out to answer?

The aim is to provide a new proof of the equivalence between the inverse Galois problem and its finite-quotient formulation.

June 29, 2026Open Access

The Inverse Galois Problem Through Migration Groupoids: A New Proof of the Finite-Quotient Equivalence and the Irrelevance of External Symmetry

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Randomized trial shows relevance of finite-quotient in inverse Galois problem, highlighting implications of external symmetry.

The aim is to provide a new proof of the equivalence between the inverse Galois problem and its finite-quotient formulation.
Developed a new formalism using migration groupoids within Vieta coefficient-rearrangement framework.
Constructed a Vieta completion bridge to show equivalence between rational and real coefficient migration groupoids.
Applied a forgetful functor to focus on profinite Galois quotient data by removing external symmetry records.
Established that the finite-quotient formulation is equivalent to the classical inverse Galois problem.
Proved external symmetry does not contribute additional Galois realizations or arithmetic content.
Demonstrated the groupoid framework clarifies the irrelevance of external symmetry.

Jianming Wang (2026) studied this question.

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