Tootfinder

interesting discussion about algebraic types … all the examples of type subtraction are in a context that has subtyping
https://lobste.rs/s/jxprbr/algebraic_types_are_not_scary_actually#c_271guc

State Algebra for Propositional Logic
Dmitry Lesnik, Tobias Sch\"afer
https://arxiv.org/abs/2509.10326 https://arxiv.org/pdf/2509.10326

State Algebra for Propositional Logic
This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row Decomposition. These representations anchor the system in well-known semantics while facilitating the computation using a powerful algebraic engine. A key aspect of State Algebra is its flexibility in representation. We show that although the default reduction of a stat…

Gr\"obner Bases Native to Term-ordered Commutative Algebras, with Application to the Hodge Algebra of Minors
Joshua A. Grochow, Abhiram Natarajan
https://arxiv.org/abs/2510.11212

Gröbner Bases Native to Term-ordered Commutative Algebras, with Application to the Hodge Algebra of Minors
Motivated by better understanding the bideterminant (=product of minors) basis on the polynomial ring in $n \times m$ variables, we develop theory \& algorithms for Gröbner bases in not only algebras with straightening law (ASLs or Hodge algebras), but in any commutative algebra over a field that comes equipped with a notion of "monomial" (generalizing the standard monomials of ASLs) and a suitable term order. Rather than treating such an algebra $A$ as a quotient of a polynomial ring and then…

Finite generation of higher rank quasi-monomial valuations via the extended Rees algebra
Zhiyuan Chen
https://arxiv.org/abs/2510.10737 https://arxiv.org/pd…

Finite generation of higher rank quasi-monomial valuations via the extended Rees algebra
In the algebraic theory of K-stability, one of the most challenging problems is to show the graded algebra associated with certain higher rank quasi-monomial valuations are finitely generated. In the global case of Fano varieties and local case of klt singularities, the finite generation has been proved for quasi-monomial valuations on models of qdlt Fano type. In this paper, we generalize these results using a different argument, by studying the extended Rees algebra via a more algebraic appro…

The Levi-Civita products of Leibniz algebras with nondegenerate skew-symmetric 2-cocycles
Quan Zhao, Guilai Liu
https://arxiv.org/abs/2510.10949 https://ar…

The Levi-Civita products of Leibniz algebras with nondegenerate skew-symmetric 2-cocycles
This paper studies the associated Levi-Civita products of a Leibniz algebra with a nondegenerate skew-symmetric $2$-cocycle. Such products form into the notion of an anti-pre-Leibniz algebra, which is characterized as a Leibniz-admissible algebra which renders a representation of the sub-adjacent Leibniz algebra through the negative multiplication operators. Such a characterization serves as the converse side of the role that pre-Liebniz algebras play in the splitting theory of Leibniz algebras…

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Initial Algebras of Domains via Quotient Inductive-Inductive Types
Simcha van Collem, Niels van der Weide, Herman Geuvers
https://arxiv.org/abs/2509.10187 https://

Initial Algebras of Domains via Quotient Inductive-Inductive Types
Domain theory has been developed as a mathematical theory of computation and to give a denotational semantics to programming languages. It helps us to fix the meaning of language concepts, to understand how programs behave and to reason about programs. At the same time it serves as a great theory to model various algebraic effects such as non-determinism, partial functions, side effects and numerous other forms of computation. In the present paper, we present a general framework to construct …

Classical Algebraic Geometry and Discrete Integrable Systems
Gessica Alecci, Michele Graffeo, Alexander Stokes
https://arxiv.org/abs/2510.12647 https://arx…

Classical Algebraic Geometry and Discrete Integrable Systems
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry side, which is applied to differential and discrete Painlevé equations on the integrable systems side. Along the way we also discuss the theory of resolution of indeterminacies, which is applied to the cohomological computation of algebraic entropy of biration…

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras
Chengming Bai, Li Guo, Guilai Liu, Quan Zhao
https://arxiv.org/abs/2509.09884

Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras
It is well-known that an averaging operator on a commutative associative algebra gives rise to a perm algebra. This paper lifts this process to the level of bialgebras. For this purpose, we first give an infinitesimal bialgebra structure for averaging commutative associative algebras and characterize it by double constructions of averaging Frobenius commutative algebras. To find the bialgebra counterpart of perm algebras that is induced by such averaging bialgebras, we need a new two-part split…

O-Forge: An LLM Computer Algebra Framework for Asymptotic Analysis
Ayush Khaitan, Vijay Ganesh
https://arxiv.org/abs/2510.12350 https://arxiv.org/pdf/251…

O-Forge: An LLM + Computer Algebra Framework for Asymptotic Analysis
Large language models have recently demonstrated advanced capabilities in solving IMO and Putnam problems; yet their role in research mathematics has remained fairly limited. The key difficulty is verification: suggested proofs may look plausible, but cannot be trusted without rigorous checking. We present a framework, called LLM+CAS, and an associated tool, O-Forge, that couples frontier LLMs with a computer algebra systems (CAS) in an In-Context Symbolic Feedback loop to produce proofs that a…