Institute Output
An Invitation to Higher Arity Science
Carlos Zapata-Carratalá, Xerxes D. Arsiwalla
Exploration of a wide range of higher-order phenomena across multiple disciplines and the preliminary application of hypergraph and hypermatrix methods.
General Relativistic Hydrodynamics in Discrete Spacetime: Perfect Fluid Accretion onto Static and Spinning Black Holes
Jonathan Gorard
This study investigates the effect of spacetime discretization on accretion dynamics of a relativistic fluid onto a spinning black hole, specifically noting that accretion rates decrease with increased discretization scale and that drag force sensitivity and instabilities intensify at critical discretization values.
Computational General Relativity in the Wolfram Language using Gravitas II: ADM Formalism and Numerical Relativity
Jonathan Gorard
This paper introduces the Gravitas computational general relativity framework's numerical subsystem, emphasizing its ability to perform 3 + 1 spacetime decompositions via the ADM formalism, handle complex simulations of gravitational phenomena like binary black hole mergers, and leverage adaptive refinement algorithms based on hypergraph rewriting within the Wolfram Language.
Ruliology: Linking Computation, Observers and Physical Law
Dean Rickles, Hatem Elshatlawy, Xerxes D. Arsiwalla
Computational General Relativity in the Wolfram Language using Gravitas I: Symbolic and Analytic Computation
Jonathan Gorard
Gravitas introduces a robust computational framework for general relativity in the Wolfram Language, featuring seamless integration of symbolic and numerical tools to handle complex spacetime geometries and solve the Einstein field equations.
Biunit pairs in semiheaps and associated semigroups
Bernard Rybołowicz, Carlos Zapata-Carratalá
This research introduces biunit pairs in semiheaps, and establishes a direct correspondence between monoids with specific switches and semiheaps, leading to the novel concept of diheaps.
Hypermatrix Algebra and Irreducible Arity in Higher-Order Systems: Concepts and Perspectives
Carlos Zapata-Carratalá, Maximilian Schich, Taliesin Beynon, Xerxes D. Arsiwalla
Hypergraph and hypermatrix methods are applied to detect irreducible interactions in higher-order systems.
Non-Vacuum Solutions, Gravitational Collapse and Discrete Singularity Theorems in Wolfram Model Systems
Jonathan Gorard
This study extends the Raychaudhuri equation to discrete spacetimes, exploring conditions under which they might exhibit geodesic incompleteness, and applies numerical simulations to predict black hole formations.
Axiomatic Quantum Field Theory in Discrete Spacetime via Multiway Causal Structure: The Case of Entanglement Entropies
Jonathan Gorard, Julia Dannemann-Freitag
This research examines a covariant approach to entanglement entropy in discrete quantum gravity, comparing causal set and Wolfram model frameworks to reveal a monotonic relationship.
Heaps of Fish: arrays, generalized associativity and heapoids
Carlos Zapata-Carratalá, Xerxes D. Arsiwalla, Taliesin Beynon
Homotopies in Multiway (Non-Deterministic) Rewriting Systems as n-Fold Categories
Xerxes D. Arsiwalla, Jonathan Gorard, Hatem Elshatlawy
Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types
Xerxes D. Arsiwalla, Jonathan Gorard
The study explores how spatial structures in physics can emerge from pregeometric combinatorial models governed by computational rules, using higher category theory and homotopy types.
Some Relativistic and Gravitational Properties of the Wolfram Model
Jonathan Gorard
The article shows that causal invariance in the Wolfram Model leads to discrete general and Lorentz covariance, introducing curvature concepts for hypergraphs related to the Ricci tensor and Einstein field equations
Algorithmic Causal Sets and the Wolfram Model
Jonathan Gorard
This study links causal set theory and the Wolfram model, showing hypergraph rewriting facilitates causal set evolution, infers conformal invariance, and derives the Benincasa-Dowker action from discrete Einstein-Hilbert action.
Hypergraph Discretization of the Cauchy Problem in General Relativity via Wolfram Model Evolution
Jonathan Gorard
This article introduces a numerical general relativity code using the Z4 formulation with hypergraph-based Cauchy data and adaptive mesh refinement, validating results against standard spacetimes and comparing with Wolfram model evolution.
Fast Automated Reasoning over String Diagrams using Multiway Causal Structure
Jonathan Gorard, Manojna Namuduri, Xerxes D. Arsiwalla
ZX-Calculus and Extended Wolfram Model Systems II: Fast Diagrammatic Reasoning with an Application to Quantum Circuit Simplification
Jonathan Gorard, Manojna Namuduri, Xerxes D. Arsiwalla
ZX-Calculus and Extended Hypergraph Rewriting Systems I: A Multiway Approach to Categorical Quantum Information Theory
Jonathan Gorard, Manojna Namuduri, Xerxes D. Arsiwalla
