Related papers: The Consistency Correctness in CoPPar Tree

We prove that rooted divergence-preserving branching bisimilarity is a congruence for the process specification language consisting of nil, action prefix, choice, and the recursion construct.

Trees are partial orders in which every element has a linearly ordered set of predecessors. Here we initiate the exploration of the structural theory of trees with the study of different notions of \emph{branching in trees} and of…

In this paper we provide a general tool to prove the consistency of $I1(\lambda)$ with various combinatorial properties at $\lambda$ typical at settings with $2^\lambda>\lambda^+$, that does not need a profound knowledge of the forcing…

In this note, we prove a conjecture of Puder on an extension of the co-growth formula to any non-negative function defined on a bi-regular tree. A key component of our proof is the establishment of a resolvent identity, which serves as an…

In recent work of Bringmann, Guerzhoy, and the first author, p-adic modular forms were constructed from mock modular forms. This paper proves explicit congruences for these p-adic modular forms.

In this paper, we study tree--like tableaux, combinatorial objects which exhibit a natural tree structure and are connected to the partially asymmetric simple exclusion process (PASEP). There was a conjecture made on the total number of…

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

In the article "Construction of the discrete hull for the combinatorics of a regular pentagonal tiling of the plane" we gave the construction of a discrete hull for a combinatorial pentagonal tiling of the plane. In this paper, we give the…

This is a survey on coarse geometry with an emphasis on coarse homology theories.

In this paper, we introduce the notion of Cartesian Forest, which generalizes Cartesian Trees, in order to deal with partially ordered sequences. We show that algorithms that solve both exact and approximate Cartesian Tree Matching can be…

We prove a new "Toeplitz exactness" theorem for strong convergence. This is a machine to upgrade strong convergence in the general setting of $C^\ast$-correspondences, and has several applications.

The `Congruence Conjecture' was developed by the second author in a previous paper. It provides a conjectural explicit reciprocity law for a certain element associated to an abelian extension of a totally real number field whose existence…

In case the stability relation is a congruence, a necessary and also a sufficient condition for its equality with the center congruence is given.

Advancements in computer science and AI lead to the development of larger, more complex knowledge bases. These are susceptible to contradictions, particularly when multiple experts are involved. To ensure integrity during changes,…

This paper is the concise addition to the foregoing work "Inconsistency of Inaccessibility", containing the presentation of main theorem proof (in ZF) about inaccessible cardinals nonexistence. Here some refinement of this presentation is…

Recently Taylor and Socolar introduced an aperiodic mono-tile. The associated tiling can be viewed as a substitution tiling. We use the substitution rule for this tiling and apply the algorithm of \cite{AL} to check overlap coincidence. It…

A congruence of the weak order is simple if its quotientope is a simple polytope. We provide an alternative elementary proof of the characterization of the simple congruences in terms of forbidden up and down arcs. For this, we provide a…

We define the bounded coarse structure attached to a family of pseudometrics and give some counterexamples to conjectures that arise naturally.

In this work, we translate at the level of decorated trees some of the crucial arguments which have been used in arXiv:2112.10739 for proposing a diagram-free approach for the convergence of the model in Regularity Structures. This allows…

In this note we compare two kinds of systems that verify the correctness of mathematical developments: roof checking and proof construction by tactics and we propose to merge them in a single system.