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This work aims to establish a rigorous theoretical foundation for exterior integral equations and their connections across various mathematical domains.

March 3, 2026Open Access

Generalizations of the Fundamental Theorem of Algebra and Vieta's Theorem in Exterior Integral Equations: A Unified Categorical Foundation for Mathematics

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SLshifa liuPeking University

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Develops a comprehensive theory of exterior integral equations, linking mathematics with several advanced theories.

Key Points

This work aims to establish a rigorous theoretical foundation for exterior integral equations and their connections across various mathematical domains.
Developed fundamental theory for linear exterior integral equations with degenerate kernels.
Proved an exterior analogue of the Fundamental Theorem of Integral Equations.
Introduced exterior Fredholm determinants and established their properties with rigorous proofs.
Connected the solution space to Sato's Grassmannian and KP hierarchy through differential algebra frameworks.
Explored stochastic and noncommutative exterior integral equations with detailed examples.
Demonstrated rigorous connections between exterior Fredholm determinants and integrable systems.
Established the compatibility of differential Vieta theorem with Picard-Vessiot theory.
Proved that the index can be expressed as a contour integral, extending it to noncommutative scenarios.
Constructed an $ ext{ExtInt}_ ext{infty}$ framework that serves as the ultimate foundation of mathematics.
Showed how cosmological constants relate to exterior Fredholm determinants with quantum corrections.

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shifa liu (2025) studied this question.

synapsesocial.com/papers/69a67f1ff353c071a6f0b1b6 https://doi.org/10.5281/zenodo.18827903

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Generalizations of the Fundamental Theorem of Algebra and Vieta's Theorem in Exterior Integral Equations: A Unified Categorical Foundation for Mathematics

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Implication

Key Points

Cite This Study

Generalizations of the Fundamental Theorem of Algebra and Vieta's Theorem in Exterior Integral Equations: A Unified Categorical Foundation for Mathematics

Discussion

Member takes

Implication

Key Points

Cite This Study

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