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Hyperbolic distance matrix completion — arXiv:2609.10403

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.10403
License (as archived): CC0-1.0
Archived: 2026-10-16T10:19:06.963Z
SHA-256 of the archived text: 3348d313bbc7a30d3d237fb16cb2367a0de86e9c4736f897105c644aecfb807d
Stable URL of this page: https://metraipolis.com/documento/dc_36d752c855bf

How to cite

Hyperbolic distance matrix completion — arXiv:2609.10403 — arXiv (en), https://arxiv.org/abs/2609.10403 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_36d752c855bf (Metraipolis archive dc_36d752c855bf, sha256 3348d313bbc7a30d3d237fb16cb2367a0de86e9c4736f897105c644aecfb807d)

BibTeX

@misc{dc36d752c855bf,
  title = {Hyperbolic distance matrix completion — arXiv:2609.10403},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.10403},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_36d752c855bf; sha256 3348d313bbc7a30d3d237fb16cb2367a0de86e9c4736f897105c644aecfb807d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.10403. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A completion theory for hyperbolic distance data is developed at the interface of matrix analysis, graph theory, and hyperbolic geometry. Krein's characterization of the metric space embeddability in Lobachevsky space leads to a natural anchoring procedure that transforms the indefinite data into a positive semidefinite kernel. In analogy with positive semidefinite and Euclidean distance matrix completion, chordality of the specification graph is shown to be the necessary and sufficient condition for local Lorentz-Gram data to admit global completion. Existence is complemented by explicit constructions. For trees, we obtain geodesic-rectification and product-distance completions; for chordal graphs, the latter extends to matrix-valued transfers along clique-trees. The resulting canonical completion is characterized by sparsity of its inverse and by a maximum-absolute-determinant principle. Its metric distortion exhibits a sharp dichotomy governed by clique separator size. Applications to exact recovery from sparse hyperbolic measurements and to hierarchical and phylogenetic data are developed.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-10 in math.CO).
Categorie arXiv: Metric Geometry (math.MG) ; Combinatorics (math.CO); Rings and Algebras (math.RA).
Pagina del lavoro: https://arxiv.org/abs/2609.10403 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T08:47:06.330Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-10?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).