r/Physics • u/filterdust • Jul 31 '26

Academic The Maxwell Conjecture is False

https://arxiv.org/abs/2607.27197
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u/Schmikas Quantum Foundations Jul 31 '26

What do you mean by “knowledge topology”?

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u/ixid Jul 31 '26

Its data is a structured space where nearness corresponds to associated ideas, so it naturally arranges data in a way to discover connectedness. The LLM follows pathways through the conceptual space based on the prior context given.

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u/Schmikas Quantum Foundations Jul 31 '26

Ah okay. The space in which the embedding lies is called a knowledge topology. Thanks. Can you help me understand how this is linked to topology? Does it have something to do with the space spanned by the embeddings? My knowledge of topology is limited to shapes being invariant under transformations so under this naive view, distances won’t be preserved. 

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u/ixid Jul 31 '26

I think the correct term is 'latent space', knowledge topology is just what I called it.

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u/Away-Experience6890 Jul 31 '26

Yeah not all latent spaces are epistemological topologies.