Institute Output

SetReplace
Open-Source Software Max Piskunov Open-Source Software Max Piskunov

SetReplace

Max Piskunov

SetReplace is an open‑source Wolfram Language package that executes set‑substitution systems. It evolves user‑defined rules from an initial state and returns structured objects that expose events, causal dependencies, and branching dynamics for analysis and visualization.

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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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The Wolfram Physics Project: A One-Year Update
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

The Wolfram Physics Project: A One-Year Update

Stephen Wolfram

When we launched the Wolfram Physics Project a year ago today, I was fairly certain that—to my great surprise—we’d finally found a path to a truly fundamental theory of physics, and it was beautiful. A year later it’s looking even better. We’ve been steadily understanding more and more about the structure and implications of our models—and they continue to fit beautifully with what we already know about physics, particularly connecting with some of the most elegant existing approaches, strengthening and extending them, and involving the communities that have developed them.

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Exploring Rulial Space: The Case of Turing Machines
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

Exploring Rulial Space: The Case of Turing Machines

Stephen Wolfram

Let’s say we find a rule that reproduces physics. A big question would then be: “Why this rule, and not another?” I think there’s a very elegant potential answer to this question, that uses what we’re calling rule space relativity—and that essentially says that there isn’t just one rule: actually all possible rules are being used, but we’re basically picking a reference frame that makes us attribute what we see to some particular rule. In other words, our description of the universe is a sense of our making, and there can be many other—potentially utterly incoherent—descriptions, etc.

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Event Horizons, Singularities and Other Exotic Spacetime Phenomena
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

Event Horizons, Singularities and Other Exotic Spacetime Phenomena

Stephen Wolfram

In our models, space emerges as the large-scale limit of our spatial hypergraph, while spacetime effectively emerges as the large-scale limit of the causal graph that represents causal relationships between updating events in the spatial hypergraph. An important result is that (subject to various assumptions) there is a continuum limit in which the emergent spacetime follows Einstein’s equations from general relativity.

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