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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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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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The Concept of the Ruliad
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

The Concept of the Ruliad

Stephen Wolfram

I call it the ruliad. Think of it as the entangled limit of everything that is computationally possible: the result of following all possible computational rules in all possible ways. It’s yet another surprising construct that’s arisen from our Physics Project. And it’s one that I think has extremely deep implications—both in science and beyond.

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The Problem of Distributed Consensus
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

The Problem of Distributed Consensus

Stephen Wolfram

In any decentralized system with computers, people, databases, measuring devices or anything else one can end up with different values or results at different “nodes”. But for all sorts of reasons one often wants to agree on a single “consensus” value, that one can for example use to “make a decision and go on to the next step”.

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