Technical Documents
& Related Material
Launch Documents
![](https://content.wolfram.com/sites/33/2020/06/intro.png)
Stephen Wolfram, “A Class of Models with the Potential to Represent Fundamental Physics”
(448 pages)
![](https://content.wolfram.com/sites/33/2020/06/props.png)
Jonathan Gorard, “Some Relativistic and Gravitational Properties of the Wolfram Model”
(59 pages)
![](https://content.wolfram.com/sites/33/2020/06/quantum.png)
Jonathan Gorard, “Some Quantum Mechanical Properties of the Wolfram Model”
(65 pages)
Wolfram Physics Project Bulletins & Recent Research
- Stephen Wolfram, “Expression Evaluation and Fundamental Physics (2023)”
- Stephen Wolfram, “Computational Foundations for the Second Law of Thermodynamics (2023)”
- Stephen Wolfram, “How Did We Get Here? The Tangled History of the Second Law of Thermodynamics (2023)”
- Stephen Wolfram, “A 50-Year Quest: My Personal Journey with the Second Law of Thermodynamics (2023)”
- Jonathan Gorard, “Computational General Relativity in the Wolfram Language using Gravitas I: Symbolic and Analytic Computation (2023)”
- Jonathan Gorard, “Non-Vacuum Solutions, Gravitational Collapse and Discrete Singularity Theorems in Wolfram Model Systems (2023)”
- J. Gorard and J. Dannemann-Freitag, “Axiomatic Quantum Field Theory in Discrete Spacetime via Multiway Causal Structure: The Case of Entanglement Entropies (2023)”
- D. Rickles, H. Elshatlawy and X. D. Arsiwalla, “Ruliology: Linking Computation, Observers and Physical Law (2023)”
- Jonathan Gorard, “A Functorial Perspective on (Multi)computational Irreducibility (2022)”
- Stephen Wolfram, “Games and Puzzles as Multicomputational Systems”
- James Boyd, “Multicomputational Irreducibility”
- Stephen Wolfram, “Twenty Years Later: The Surprising Greater Implications of A New Kind of Science”
- Stephen Wolfram, “On the Concept of Motion”
- Stephen Wolfram, “The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics”
- Stephen Wolfram, “The Concept of the Ruliad”
- Xerxes D. Arsiwalla, Jonathan Gorard, “Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types”
- Stephen Wolfram, “Multicomputation with Numbers: The Case of Simple Multiway Systems”
- Stephen Wolfram, “Even beyond Physics: Introducing Multicomputation as a Fourth General Paradigm for Theoretical Science”
- Stephen Wolfram, “How Inevitable Is the Concept of Numbers?”
- Xerxes D. Arsiwalla, Jonathan Gorard, Hatem Elshatlawy, “Homotopies in Multiway (Non-Deterministic) Rewriting Systems as n-Fold Categories”
- Stephen Wolfram, “The Problem of Distributed Consensus”
- Jonathan Gorard, Manojna Namuduri, Xerxes D. Arsiwalla, “Fast Automated Reasoning over String Diagrams using Multiway Causal Structure”
- Stephen Wolfram, “Why Does the Universe Exist? Some Perspectives from Our Physics Project”
- Stephen Wolfram, “The Wolfram Physics Project: A One-Year Update”
- 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”
- Stephen Wolfram, “What Is Consciousness? Some New Perspectives from Our Physics Project”
- Stephen Wolfram, “After 100 Years, Can We Finally Crack Post’s Problem of Tag? A Story of Computational Irreducibility, and More”
- Jonathan Gorard, “Hypergraph Discretization of the Cauchy Problem in General Relativity via Wolfram Model Evolution”
- Stephen Wolfram, “Combinators and the Story of Computation”
- Yorick Zeschke, “Growth Functions, Rates and Classes of String-Based Multiway Systems”
- Stephen Wolfram, “Multiway Turing Machines”
- Jonathan Gorard, “Algorithmic Causal Sets and the Wolfram Model”
- Stephen Wolfram, “Combinators: A Centennial View”
- Jonathan Gorard, “Algorithmic Causal Sets and the Wolfram Model”
- Max Piskunov, “Confluence and Causal Invariance”
- Max Piskunov, “Local Multiway Systems: A New Approach to Wolfram Model Evolution”
- Jonathan Gorard, Manojna Namuduri, & Xerxes D. Arsiwalla, “ZX-Calculus and Extended Hypergraph Rewriting Systems I: A Multiway Approach to Categorical Quantum Information Theory”
- Stephen Wolfram, “Faster than Light in Our Model of Physics: Some Preliminary Thoughts”
- Stephen Wolfram, “The Empirical Metamathematics of Euclid and Beyond”
- Jonathan Gorard, “A Short Note on the Double-Slit Experiment and Other Quantum Interference Effects in the Wolfram Model”
- Jonathan Gorard, “A Candidate Geometrical Formalism for the Foundations of Mathematics and Physics”
- Stephen Wolfram, “A Burst of Physics Progress at the 2020 Wolfram Summer School”
- Stephen Wolfram, “Exploring Rulial Space: The Case of Turing Machines”
- Stephen Wolfram, “Event Horizons, Singularities and Other Exotic Spacetime Phenomena”
- Stephen Wolfram, “The Wolfram Physics Project: The First Two Weeks”
Other Bulletins & Research
- Carlos Zapata-Carratalá, Xerxes D. Arsiwalla & Taliesin Beynon “Heaps of Fish: Arrays, Generalized Associativity and Heapoids”
- Carlos Zapata-Carratalá & Xerxes D. Arsiwalla, “An Invitation to Higher Arity Science”
- Utkarsh Bajaj, “Visual Appearance of Extended objects in Special Relativity”
- Tobías Canavesi & Truman Tapia, “Observational Evidence of Fractality in the Large-scale Distribution of Galaxies”
Community Research Posts
- William Munizzi, “Establishing Maximal Entanglement Speed via Branchial Lightcones,” Wolfram Summer School 2022
- Abishek Joshi, “Fluid Dynamics on Graphs,” Wolfram Summer School 2022
- Sinuhe Perea, “Topological Invariants in Discrete Lattice Geom via Graph Rewriting,” Wolfram Summer School 2022
- Kurt Swanson, “Evolver-Wolfram intersection,” Wolfram Summer School 2022
- Mark Merner, “QuantumToMultiwaySystem to Explore Quantum Entanglement,” Wolfram Summer School 2022
- Dugan Hammock, “Temporally Coherent Animations of the Evolution of Wolfram Models,” Wolfram Summer School 2022
- Simon Fischer, “Photon Propagation Through Variable-Dimensional Space,” Wolfram Summer School 2022
- Gianmarco Morbelli, “Computational Implications of the Third Law of Thermodynamics,” Wolfram Summer School 2022
- Utkarsh Patel, “Study of Regge Theory Using 2-body Motion in Fractional Spacetime,” Wolfram Summer School 2022
- Aisha Kermiche, “Branchial Graph Density Diffusion in Dynamic Multiway Systems,” Wolfram Summer School 2022
- Nikola Bukowiecka, “Investigating the Weak Censorship Hypothesis in the Wolfram Model,” Wolfram Summer School 2022
- Sanjib Katuwal, “Generalizing Electromagnetism to Fractional Dimensions,” Wolfram Summer School 2022
- Hans Christiansen, “Gravitational Lensing in the Wolfram Model,” Wolfram Summer School 2022
- Felipe Amorim, “Multiway Mobile Automata,” Wolfram Summer School 2022
- Morgan Gillis, “Implementing Adinkras in the Wolfram Physics Project,” Wolfram Summer School 2022
- Utkarsh Bajaj, “Compiling Different Models of Computation into Hypergraph Rewriting,” Wolfram Summer School 2022
- Paul Borrill, “Quantum Ethernet,” Wolfram Summer School 2022
- Aritra Sarkar, “RuliadTrotter: Meta-modeling Metamathematical Observers,” Wolfram Summer School 2022
- Dean Gladish, “Multi-way Tag Systems in Coordinatized Rulial Space,” Wolfram Summer School 2022
- Richard Charette, “A Study In Proof Space Topology,” Wolfram Summer School 2022
- Lukasz Majsiak, “Some Structural and Categorical Aspects of Metamathematical space,” Wolfram Summer School 2022
- Richard Assar, “Characterisation of Infinitary Rewrite Systems,” Wolfram Winter School 2022
- Renzo Takagui Pérez, “Explore and Classify Horizons in Causal Graphs,” Wolfram Winter School 2022
- Rose Knight, “Identification of the Quantum Zeno Effect in the Wolfram Model,” Wolfram Winter School 2022
- John Joseph Marchetta, “Black Hole Entropy of 2D Spin Networks,” Wolfram Winter School 2022
- Delaram Mirfendereski, “Modeling Spin Network Interactions via Branchial Graphs,” Wolfram Winter School 2022
- Suvadeep Roy, “Translating Holographic Entanglement Entropy to Rewriting Model,” Wolfram Winter School 2022
- Dmytro Melnichenko, “Algebra of Graph Operators,” Wolfram Winter School 2022
- Regen Petu-Stiles, “Identifying Homogeneity in Hypergraphs via Approximate Isomorphism,” Wolfram Winter School 2022
- Hannah Green, “Emergent Geometry in String Rewrite Systems,” Wolfram Winter School 2022
- Enrico Caprioglio, “An Investigation on Possible Notions of Physical Distance in the WM,” Wolfram Winter School 2022
- Kartik Tiwari, “A Novel Multiway Isomorphism Model of Consistency and Completeness,” Wolfram Winter School 2022
- Juan Pablo Varela, “Growth Rates of Non-linear and Non-exponential Scaling Wolfram Models,” Wolfram Winter School 2022
- Miles Mountney, “Deducing Commutativity Relations from String Multiway Systems,” Wolfram Winter School 2022
- James Boyd, “Computational Complexity Classes, Homotopy Classes, and n-Machines,” Wolfram Summer School 2021
- Joana Teixeira, “Exploring the Effects of Causal Graph Dimension Variations in Null Geodesics,” Wolfram Summer School 2021
- Jan Chojnacki, “Dimension Decay in the Early Universe,” Wolfram Summer School 2021
- Salvatore Vultaggio, “Recovering Scalar Fields Effects in the Wolfram Model,” Wolfram Summer School 2021
- Rafael Turner, “A Topological Introduction to Causal Set Theory & Wolfram Physics,” Wolfram Summer School 2021
- Ariadna Uxue Palomino Ylla, “Kretschmann Scalar for Hypergraphs,” Wolfram Summer School 2021
- Antonia Seifert, “Lie Algebras and Curvature in Discrete Geometry,” Wolfram Summer School 2021
- Carlos Zapata Carratala, “Into the Ternary World,” Wolfram Summer School 2021
- Matthew Maddock, “Gauge Field Theories on Discrete Principal Fibre Bundles,” Wolfram Summer School 2021
- Julia Dannemann-Freitag, “Comparing Wolfram Model and Causal Set Entanglement Entropies,” Wolfram Summer School 2021
- Vladyslav Kuchkin, “Non-trivial Homotopies of Arbitrary Hypergraphs and Their Solitons,” Wolfram Summer School 2021
- Andrés Felipe Bermúdez Mendoza, “Distributed Consensus in Multiway Graph Cellular Automata,” Wolfram Summer School 2021
- Michael Reed, “Foundations of Differential Geometric Algebra in Wolfram Language,” Wolfram Summer School 2021
- Alessandro Pisana, “Quantum Gravity in (2+1) Dimensions and Multiway System,” Wolfram Summer School 2021
- Ray Aschheim, “Color Spin Networks,” Wolfram Summer School 2021
- Indira Ocampo, “Studying Cosmology in the Case of Dimension Change,” Wolfram Summer School 2021
- Jessica Yuan, “Coarse-Graining State Networks with Approximate Graph Isomorphism,” Wolfram Summer School 2021
- Silas Grossberndt, “Towards Causal Invariance Proofs in the Wolfram Physics Project,” Wolfram Summer School 2021
- Alisson Silva, “Functorial QFT and Its Connections with the Wolfram Model,” Wolfram Summer School 2021
- Farhan Tanvir Chowdhury, “Multi-way Tiling Systems,” Wolfram Summer School 2021
- Ryan Lau, “The 3-Colored Distributed Consensus Problem,” Wolfram Summer School 2021
- Georgios Smyridis, “Bloch Sphere and Gate Complexity,” Wolfram Summer School 2021
- Archana Radhakrishnan, “Exploring 1+1D Euclidean Dynamical Triangulations,” Wolfram Summer School 2021
- Marcelo Amaral, “On Charge-Spin Networks from Multiway Systems Branchial Graphs,” Wolfram Summer School 2021
- Tiecheng Guo, “Multiway Quantum Many-Body System,” Wolfram Summer School 2021
- Fang Fang, “Cellular Automata in Nested Quasicrystals,” Wolfram Summer School 2021
- Mark Merner, “Bell's Equation in the Wolfram Model Multiway Formalism,” Wolfram Summer School 2021
- Dugan Hammock, “Plotting the Evolution of a Wolfram Model in 3-Dimensions,” Wolfram Summer School 2021
- Daksh Aggarwal, “Multiway Systems as Cayley Graphs,” Wolfram Winter School 2021
- Roberto Caiozzo, “Checking the Preservation of the Schwarzschild Metric in a Graph Evolution,” Wolfram Winter School 2021
- Simone Caletti, “Towards a Spin-Statistics Theorem for Wolfram Model Multiway Systems,” Wolfram Winter School 2021
- Gene Chen, “Causal Graph Geodesics to Continuous Geodesics,” Wolfram Winter School 2021
- Jean du Plessis, “Geometric Constructions in Discrete Non-integer Dimensional Spaces,” Wolfram Winter School 2021
- Paul Fischer, “Searching for Rules That Generate Elementary Particle Behavior in the Wolfram Model,” Wolfram Winter School 2021
- Santiago Giner, “Analyzing Effects of Dimensional Perturbations in Wolfram Models,” Wolfram Winter School 2021
- Tom Lee, “Relativistic Mass Transformations for Topological Obstructions in Hypergraphs/Causal Graphs,” Wolfram Winter School 2021
- Henry Liu, “Application of Machine Learning in Complex System Simplification,” Wolfram Winter School 2021
- Yousof Mardoukhi, “Alexander–Orbach Relation and Random Walks on Hypergraphs,” Wolfram Winter School 2021
- Omar Medina, “Discretization of a Non-Abelian SU(2) Gauge Theory,” Wolfram Winter School 2021
- Geeth Ongole, “Relationship between Causal Multiway Systems and Spin Foams in Loop,” Wolfram Winter School 2021
- Keith Patarroyo, “Defect Movement in Lattice Rewriting Systems,” Wolfram Winter School 2021
- Sourav Raha, “Hypergraphs as Chains of String Bits,” Wolfram Winter School 2021
- Sam Whittington, “The Multiway Systems of Dynkin Diagrams,” Wolfram Winter School 2021
- Chang Wu, “Exploring the Gauge Symmetries in Wolfram Model,” Wolfram Winter School 2021
- Jack Xing, “Investigate Dimension Estimation Algorithm and Dimension Tensor in Wolfram Physics Model,” Wolfram Winter School 2021
- Asir Abrar, “Interpreting the Distributions of Dimensions in the Wolfram Models,” Wolfram Summer School 2020
- Andoni Royo Abrego, “Particles and Fields from Topological Defects in Spacetime Mesh,” Wolfram Summer School 2020
- Carlos Rafael Garduno Acolt, “Hunting for Black Holes,” Wolfram Summer School 2020
- Xerxes Arsiwalla, “Homotopic Foundations of Wolfram Models,” Wolfram Summer School 2020
- Cameron Beetar, “A Path to Higher Order Corrections for Einstein's Equations,” Wolfram Summer School 2020
- Joseph Blazer, “EPR Interactions in Generational Multiway Systems,” Wolfram Summer School 2020
- Tobias Canavesi, “Local Dimension Measure and Rotation Groups in Wolfram Models,” Wolfram Summer School 2020
- Joseph Crowley, “Multiway Circular-String Rewrite Systems,” Wolfram Summer School 2020
- Darya Dyachkova, “Exploring the Dimensionality of Wolfram Models,” Wolfram Summer School 2020
- Hatem Elshatlawy, “Investigating Quantum Interference Effects in Wolfram Models,” Wolfram Summer School 2020
- Mohamed Gaber, “Studying State Transition Diagrams in Finite Wolfram Models,” Wolfram Summer School 2020
- Chandra Gangavarapu, “Cyclic String Substitution and Multiway Systems,” Wolfram Summer Camp 2020
- Xiyuan Gao, “Exploring CPT Invariance in Wolfram Models,” Wolfram Summer School 2020
- Patrick Geraghty, “The Quantum Harmonic Oscillator in the Wolfram Physics Model,” Wolfram Summer School 2020
- Simon I. Golombek, “Random Walks in Branchial Turing Machine Space & Quest for Simplest Universal NDTM,” Wolfram Summer School 2020
- Antony Halim, “Finding Conservation Laws in (Hyper)graph Rewritings,” Wolfram Summer School 2020
- Antonia Kaestner, “Graph Representation of Biological Evolution,” Wolfram Summer School 2020
- Matthew Kafker, “Exploring Networks in Hard Sphere Models,” Wolfram Summer School 2020
- Jatin Kansal, “Classify Growth Rates for Wolfram Models,” Wolfram Summer School 2020
- Jon Lederman, “Weyl’s Law and the Wolfram Model of Physics,” Wolfram Summer School 2020
- Macy Maurer Levin, “Visualisations of a Multiway Graph,” Wolfram Summer Camp 2020
- Chenshuo Ma, “Terminations and Completions in String Multiway Systems,” Wolfram Summer School 2020
- Yanal Marji, “Wolfram Models as Discretization Methods for Numerical PDE Solver,” Wolfram Summer School 2020
- Ivan Martinez, “Quantum Effects in Fluid Flow Cellular Automata,” Wolfram Summer School 2020
- Quinn McIntyre, “Explorations of the Hypergraph wm44586,” Wolfram Summer Camp 2020
- Maurizio Moreschi, “Evolution of (Hyper)Graph Invariants under (Hyper)Graph Rewritings,” Wolfram Summer School 2020
- Taufiq Murtadho, “Quantum Teleportation in String Substitution System,” Wolfram Summer School 2020
- Manojna Namuduri, “Comparing Expansion in Physical and Branchial Space,” Wolfram Summer School 2020
- Luke Neville, “Exploring Statistical Mechanics in String Substitution Systems,” Wolfram Summer School 2020
- Christian Pratt, “Particle-Like Excitation's Causal Influence in Wolfram Models,” Wolfram Summer School 2020
- Yoav Rabinovich, “Shor’s Algorithm in Multiway Systems,” Wolfram Summer School 2020
- Marc Sperzel, “An Exploration of the AdS/CFT Correspondence within Wolfram Models,” Wolfram Summer School 2020
- Graham Van Goffrier, “Full Discretization of Local Gauge Invariance,” Wolfram Summer School 2020
- Sam Wilson, “Multiple Transformation Rules That Give Slow Growth,” Wolfram Summer School 2020
- William Yam, “Finding Gravitational Waves in Wolfram Models,” Wolfram Summer School 2020
- Jin Yan, “Wolfram Models: State Transition Networks of Non-growing Hypergraph Evolutions,” Wolfram Summer School 2020
- Yorick Zeschke, “Looking for Multiway Systems of Intermediate Growth,” Wolfram Summer Camp 2020
Notable Expositions & Commentary
- Rudy Rucker, “The Wolfram Physics Project”
- Alex Lamb, “Should You Take Wolfram's Physics Seriously?”
- Date un Vlog, “WOLFRAM: ‘Una Nueva Teoría Fundamental de la Física... y es Bella’ | REACCIÓN”
- Tom Siegfried, “Stephen Wolfram’s Hypergraph Project Aims for a Fundamental Theory of Physics”
- Jose Manuel Rodriguez Caballero, “Brainstorming about the Geometric Structures in the Wolfram Model of Fundamental Physics”
- Nicholas Teague, “A New Kind of Physics: The Unifying Theory of the Wolfram Model”
Earlier Material
- Stephen Wolfram, “Network Substitution Systems”
- Stephen Wolfram, “String Substitution Systems”
- Stephen Wolfram, “A New Kind of Science: A 15-Year View”
- Stephen Wolfram, “What Is Spacetime, Really?”
- Oyvind Tafjord, “NKS and the Nature of Space and Time”
- Isabella Retter [Thiesen], “Networks as Manifolds”
- Max Piskunov, “Confluent Set Substitution Systems,” Wolfram Summer School 2019
- Max Piskunov, “Deterministic Planar Network Systems”
- Max Piskunov, “Planar Network Systems”