analysis / Operator algebras

Word-length spectral triples as compact quantum metric spaces

The first explicit counterexample rather than a first suspicion: the abstract is clear that the failure was widely expected and that what was missing was a witness. It gives an infinite family, one for each d >= 2, all Lamplighter groups over free groups.

20Significance / 100
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analysisAug 12, 2026Significance 20/100Registry: unreviewed

Word-length spectral triples as compact quantum metric spaces

Prior state unknown→disproved

The first explicit counterexample rather than a first suspicion: the abstract is clear that the failure was widely expected and that what was missing was a witness. It gives an infinite family, one for each d >= 2, all Lamplighter groups over free groups.

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The first explicit counterexample rather than a first suspicion: the abstract is clear that the failure was widely expected and that what was missing was a witness. It gives an infinite family, one for each d >= 2, all Lamplighter groups over free groups.

The first explicit counterexample rather than a first suspicion: the abstract is clear that the failure was widely expected and that what was missing was a witness. It gives an infinite family, one for each d >= 2, all Lamplighter groups over free groups.

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Connected research record

Word-length spectral triples as compact quantum metric spaces — Mathematical Frontier Network