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Observer Theory and the Ruliad: An Extension to the Wolfram Model
Community Essay Sam Senchal Community Essay Sam Senchal

Observer Theory and the Ruliad: An Extension to the Wolfram Model

Sam A. Senchal

This paper introduces a rigorous category-theoretic extension to Observer Theory within Wolfram's Ruliad framework, demonstrating how observers and observes like us sample and integrate information across hierarchical domains, addressing consciousness, causation, and the transition from discrete computational processes to continuous perceived reality.

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Hypergraph rewriting and Causal structure of $\lambda$-calculus
Research Paper Utkarsh Bajaj Research Paper Utkarsh Bajaj

Hypergraph rewriting and Causal structure of $\lambda$-calculus

Utkarsh Bajaj

Hypergraph rewriting is studied through categorical frameworks to establish foundational concepts of events and causality in graph rewriting systems. Novel concepts are introduced within double-pushout rewriting in adhesive categories. An algorithm is constructed to determine causal relations between events during λ-calculus evaluation, with extensions developed for arbitrary λ-expressions.

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Quantum Potato Chips
Research Paper Nikolay Murzin Research Paper Nikolay Murzin

Quantum Potato Chips

Nikolay Murzin, Bruno Tenorio, Sebastian Rodriguez, John McNally, Mohammad Bahrami

This study maps qubit states under symmetric informationally-complete measurements to a tetrahedron in 3D space, identifying a "quantum potato chip" region where quantum states reduce to classical binary variables. States in this special region can be fully reconstructed using only two projective measurements, unlike states elsewhere in the quantum state space.

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General Relativistic Hydrodynamics in Discrete Spacetime: Perfect Fluid Accretion onto Static and Spinning Black Holes
Research Paper Jonathan Gorard Research Paper Jonathan Gorard

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.

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Computational General Relativity in the Wolfram Language using Gravitas II: ADM Formalism and Numerical Relativity
Research Paper Jonathan Gorard Research Paper Jonathan Gorard

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.

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Ruliology: Linking Computation, Observers and Physical Law
Research Paper Xerxes D. Arsiwalla Research Paper Xerxes D. Arsiwalla

Ruliology: Linking Computation, Observers and Physical Law

Dean Rickles, Hatem Elshatlawy, Xerxes D. Arsiwalla

Physical laws arise from the sampling of the Ruliad by observers (including us). This naturally leads to several conceptual issues, such as what kind of object is the Ruliad? What is the nature of the observers carrying out the sampling, and how do they relate to the Ruliad itself? What is the precise nature of the sampling? This paper provides a philosophical examination of these questions, and other related foundational issues, including the identification of a limitation that must face any attempt to describe or model reality in such a way that the modeller-observers are included.

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