# Technical Documents

& Related Material

## Launch Documents

Stephen Wolfram, “

*A Class of Models with the Potential to Represent Fundamental Physics*”*(448 pages)*

Jonathan Gorard, “

*Some Relativistic and Gravitational Properties of the Wolfram Model*”*(59 pages)*

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*”