Inverse Galois: source and evidence

Galois expanded Resolution Theory journal edition

Article

Resolution Theory: Projector Geometry, Galois Descent, and Multiscale Realizations

Author: Komorebi P.

Primary files

• Resolution_Theory_Galois_Expanded_Mathematical_Core.pdf is the bibliography free mathematical core
• Resolution_Theory_Galois_Expanded_Journal_Manuscript.pdf is the submission assembly with bibliography
• Resolution_Theory_Galois_Expanded_References.pdf is the separate bibliographic companion
• Resolution_Theory_Galois_Expanded_AI_Disclosure.pdf is the separate language model disclosure

Scale

• 74 page mathematical core
• 76 page submission assembly
• 87 theorems
• 16 propositions
• 2 lemmas
• 17 corollaries
• 122 internally proved theorem type records
• 122 proof environments
• 14 definitions
• 9 open problems
• 31 figure environments using 30 vector figure files
• 30 cited references
• Galois expanded Resolution Theory verification: 669 of 669 checks passed

Galois expansion

The prior 57 page edition has been extended by a complete semisimple finite Galois realization and its exact boundaries. The new material includes fixed point projectors, the subgroup and intermediate field lattice, normality as central compatibility, quotient compression, trace and norm transfers, Fourier Galois charts, normal bases, conjugate projector atlases, Mackey transition packets, ramification detail projectors, Artin conductor formulas, profinite Haar projectors, Hilbert 90 descent, Brauer obstruction, finite etale Galois categories, and Tannakian reconstruction.

Boundary

The paper does not claim that projector notation replaces modular or wild Galois theory. The finite embedding is proved in a characteristic zero semisimple Hilbert realization. Modular averaging, finite flat group schemes, wild ramification beyond semisimple complex representations, arbitrary measurable descent, and Hopf or quantum Galois reconstruction remain separate research problems.