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A Graphical Calculus for Stable Curvature Invariants
Gregor Weingart
https://arxiv.org/abs/2404.16355 https://arxiv.org/pdf/2404.1635…

A Graphical Calculus for Stable Curvature Invariants
In this article we develop a graphical calculus for stable invariants of Riemannian manifolds akin to the graphical calculus for Rozansky-Witten invariants for hyperkähler manifolds; based on interpreting trivalent graphs with colored edges as stably invariant polynomials on the space of algebraic curvature tensors. In this graphical calculus we describe explicitly the Pfaffian polynomials central to the Theorem of Chern-Gauß-Bonnet and the normalized moment polynomials calculating the moment…

The Flower Calculus
Pablo DonatoPARTOUT
https://arxiv.org/abs/2402.15174 https://arxiv.org/pdf/2402.15174

The Flower Calculus
We introduce the flower calculus, a deep inference proof system for intuitionistic first-order logic inspired by Peirce's existential graphs. It works as a rewriting system over inductive objects called "flowers", that enjoy both a graphical interpretation as topological diagrams, and a textual presentation as nested sequents akin to coherent formulas. Importantly, the calculus dispenses completely with the traditional notion of symbolic connective, operating solely on nested flowers containing…

This https://arxiv.org/abs/2101.05754 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Strong Bisimulation for a Classical Term Calculus
When translating a term calculus into a graphical formalism many inessential details are abstracted away. In the case of $λ$-calculus translated to proof-nets, these inessential details are captured by a notion of equivalence on $λ$-terms known as $\simeq_σ$-equivalence, in both the intuitionistic (due to Regnier) and classical (due to Laurent) cases. The purpose of this paper is to uncover a strong bisimulation behind $\simeq_σ$-equivalence, as formulated by Laurent for Parigot's $λμ$-ca…

This https://arxiv.org/abs/2309.13014 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Completeness of qufinite ZXW calculus, a graphical language for finite-dimensional quantum theory
Finite-dimensional quantum theory serves as the theoretical foundation for quantum information and computation. Mathematically, it is formalized in the category FHilb, comprising all finite-dimensional Hilbert spaces and linear maps between them. However, there has not been a graphical language for FHilb which is both universal and complete and thus incorporates a set of rules rich enough to derive any equality of the underlying formalism solely by rewriting. In this paper, we introduce the quf…

Minimality in Finite-Dimensional ZW-Calculi
Marc de Visme, Renaud Vilmart
https://arXiv.org/abs/2401.16225 https://arXiv.org/pdf/2401…

Minimality in Finite-Dimensional ZW-Calculi
The ZW-calculus is a graphical language capable of representing 2-dimensional quantum systems (qubit) through its diagrams, and manipulating them through its equational theory. We extend the formalism to accommodate finite dimensional Hilbert spaces beyond qubit systems. First we define a qudit version of the language, where all systems have the same arbitrary finite dimension d, and show that the provided equational theory is both complete -- i.e. semantical equivalence is entirely captured by…