What question did this study set out to answer?

This research aims to resolve the Inverse Galois Problem by using geometric folding techniques to construct Galois extensions for finite groups.

June 19, 2026Open Access

Orbit Sum Origami: A Machine-Certified Universal Folding Approach to the Inverse Galois Problem

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Authors

JRJonathan ƒ(n) Reed

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Implication

Randomized trial demonstrates a universal folding approach to algebraic structures in finite groups, suggesting new solutions to the Inverse Galois Problem.

Key Points

This research aims to resolve the Inverse Galois Problem by using geometric folding techniques to construct Galois extensions for finite groups.
Conceptualizing the rational function field as a flat sheet of paper.
Applying the Reynolds operator as a universal folding mechanism.
Formal verification of the construction using Lean 4.
Established the Universal Folding Identity as a consequence of the Fundamental Theorem of Symmetric Polynomials.
Demonstrated that the realization of any finite group is algebraically necessary based on the orbit sum.
Showed that internal symmetry relations of finite groups can be mapped to the rational field without deformation.

Cite This Study

Jonathan ƒ(n) Reed (2026) studied this question.

synapsesocial.com/papers/6a34dfcd65a5b0777af2ed81 https://doi.org/10.5281/zenodo.20724086

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Implication

Randomized trial demonstrates a universal folding approach to algebraic structures in finite groups, suggesting new solutions to the Inverse Galois Problem.

Orbit Sum Origami: A Machine-Certified Universal Folding Approach to the Inverse Galois Problem

Discussion

Member takes

Implication

Key Points

Cite This Study

Orbit Sum Origami: A Machine-Certified Universal Folding Approach to the Inverse Galois Problem

Discussion

Member takes

Implication

Key Points

Cite This Study

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