Paper Citation Record · LEDGER

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family

As of 21 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2508.14369.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2508.14369 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T18:53:22.637862Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

36 of 36 outbound references displayed

verified exact3
verified fuzzy32
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4a8282a8-5835-4063-b036-f83b1d2dce15 · outbound

This paper cites On approximating the Riemannian 1-center.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family On approximating the Riemannian 1-center

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:32.996428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 27b480ad-7e64-4f53-bbd8-8c94e8a3d62b · outbound

This paper cites Log-Euclidean metrics for fast and simple calculus on diffusion tensors.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Log-Euclidean metrics for fast and simple calculus on diffusion tensors

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:32.625941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ccd19046-49f4-4c0f-a073-1714e585c57b · outbound

This paper cites Smaller core-sets for balls.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Smaller core-sets for balls

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:32.409230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation df8b4613-b08f-40f2-b7ce-82698625b47c · outbound

This paper cites On The Heine-Borel Property and Minimum Enclosing Balls.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family On The Heine-Borel Property and Minimum Enclosing Balls

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:53:23.563678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1fae6370-fe9b-4119-a98c-4c18b53521e4 · outbound

This paper cites an unresolved cited work.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:53:32.165878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 79284f31-b336-4085-9dc9-4591800a9da7 · outbound

This paper cites Extensions of Jentzsch’s theorem.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Extensions of Jentzsch’s theorem

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:31.856751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fb419cd6-25b8-4042-9c21-85f5bccff1bd · outbound

This paper cites A distance between elliptical distributions based in an embed- ding into the Siegel group.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family A distance between elliptical distributions based in an embed- ding into the Siegel group

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:31.550373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation cccb8d8e-807f-4c7b-b4db-c02c1b9d6d42 · outbound

This paper cites Stochastic control liaisons: Richard Sinkhorn meets Gaspard Monge on a Schr¨ odinger bridge.Siam Review, 63(2):249–313, 2021.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Stochastic control liaisons: Richard Sinkhorn meets Gaspard Monge on a Schr¨ odinger bridge.Siam Review, 63(2):249–313, 2021

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:31.321123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f7042279-0979-422e-aa2d-1bc1a82d0929 · outbound

This paper cites On Hilbert’s Metric for Simplices.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family On Hilbert’s Metric for Simplices

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:31.119673Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation af2d1a49-9b10-4978-8754-b83ee2161ff9 · outbound

This paper cites On representing the positive semidefinite cone using the second-order cone.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family On representing the positive semidefinite cone using the second-order cone

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:30.873734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6220ad29-a274-4ed7-969b-c12a31771f3f · outbound

This paper cites Delaunay Triangulations in the Hilbert Metric.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Delaunay Triangulations in the Hilbert Metric

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:30.528646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ec9fda68-64d9-480e-add4-f71654790ded · outbound

This paper cites Gezalyan and David M.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Gezalyan and David M

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:30.221947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 37c8b06b-73d8-490c-a11d-23403b6b1154 · outbound

This paper cites Geometric structures on manifolds, volume 227.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Geometric structures on manifolds, volume 227

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:29.934621Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 553465b1-11ff-474f-be69-33f090fe59ca · outbound

This paper cites Seetharama Gowda, Roman Sznajder, and Jiyuan Tao.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Seetharama Gowda, Roman Sznajder, and Jiyuan Tao

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:29.564782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 648f983d-2069-4223-8041-29bdadf72e14 · outbound

This paper cites ¨Uber die gerade linie als k¨ urzeste verbindung zweier punkte: Aus einem an herrn f.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family ¨Uber die gerade linie als k¨ urzeste verbindung zweier punkte: Aus einem an herrn f

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:29.285716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b6f2c5dc-07e2-45b2-a4a9-c750c786fc6b · outbound

This paper cites The variance information manifold and the functions on it.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family The variance information manifold and the functions on it

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:28.949327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8546f7ba-3bc0-43d9-964c-25d072d9e9d1 · outbound

This paper cites Birkhoff’s version of Hilbert’s metric and its applications in analysis.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Birkhoff’s version of Hilbert’s metric and its applications in analysis

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:28.650482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation dc8521d2-dd2c-43d6-97aa-6899654c6c97 · outbound

This paper cites Nussbaum.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Nussbaum

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:28.341302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8e5807c3-5882-4709-a5bb-17bc53d88ac9 · outbound

This paper cites Isometries of polyhedral Hilbert geometries.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Isometries of polyhedral Hilbert geometries

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:53:23.311844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4ce4ba43-c5f3-4db1-b02c-4345fb4a27bb · outbound

This paper cites Differ- ential geometry with extreme eigenvalues in the positive semidefinite cone.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Differ- ential geometry with extreme eigenvalues in the positive semidefinite cone

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:28.080703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d44efc3a-3aef-4ddf-bd17-f92cfb02f58c · outbound

This paper cites The Siegel–Klein disk: Hilbert geometry of the Siegel disk domain.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family The Siegel–Klein disk: Hilbert geometry of the Siegel disk domain

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:27.724827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b2795b41-eb13-4604-be2c-a7c32d4823ea · outbound

This paper cites On balls in a Hilbert polygonal geometry.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family On balls in a Hilbert polygonal geometry

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:27.444369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 06d99916-2fb6-4ca0-9109-15327376f7c4 · outbound

This paper cites Clustering in Hilbert’s projective geometry: The case studies of the probability simplex and the elliptope of correlation matrices.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Clustering in Hilbert’s projective geometry: The case studies of the probability simplex and the elliptope of correlation matrices

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:27.234735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 28f3f104-432b-48eb-b3ad-b9c72261173b · outbound

This paper cites Non-linear embeddings in Hilbert simplex geometry.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Non-linear embeddings in Hilbert simplex geometry

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:26.947412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 96ec0dea-4ab3-48f8-8270-2d5a2f113823 · outbound

This paper cites Hilbert’s projective metric and iterated nonlinear maps , volume 1.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Hilbert’s projective metric and iterated nonlinear maps , volume 1

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:26.650639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d4ebda69-fa9d-4867-bac8-0245843083fa · outbound

This paper cites Doubly autoparallel structure on positive definite matrices and its applica- tions.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Doubly autoparallel structure on positive definite matrices and its applica- tions

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:26.356536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation debe7175-b82d-4187-b0c6-53636ddd389a · outbound

This paper cites Dualistic differential geometry of positive definite matrices and its applications to related problems.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Dualistic differential geometry of positive definite matrices and its applications to related problems

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:26.059222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2a87b0d1-2948-4a91-bdb0-fcfac357ebb3 · outbound

This paper cites A Riemannian framework for tensor computing.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family A Riemannian framework for tensor computing

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:25.831542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fc8c081d-33b1-4989-b03e-6b00cb373863 · outbound

This paper cites Synthetic projective geometry and Poincar´ e’s theorem on automorphisms of the ball.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Synthetic projective geometry and Poincar´ e’s theorem on automorphisms of the ball

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:25.518639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f8257b95-7cae-4f37-a11d-650c5b89aacc · outbound

This paper cites A Category for Unifying Gaussian Probability and Non- determinism.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family A Category for Unifying Gaussian Probability and Non- determinism

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:25.269585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 926787d8-f286-41bc-8f80-9910519b4684 · outbound

This paper cites Loewner order in terms of eigenvalues.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Loewner order in terms of eigenvalues

Reference 31

Resolution: verified exact; raw_fallback, observed 2026-08-05T18:53:23.013447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation cb1cb235-3328-4ad1-9dc8-697f0b465a7f · outbound

This paper cites O(n)-invariant Riemannian metrics on SPD matrices.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family O(n)-invariant Riemannian metrics on SPD matrices

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:24.907509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6f844722-74ee-40fa-b3ed-eae9f79570cd · outbound

This paper cites Simplicial faces of the set of correlation matrices.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Simplicial faces of the set of correlation matrices

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:24.570818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4861e039-cd0e-4d49-84c1-ef3c361956ff · outbound

This paper cites Support Vector Machines in the Hilbert Geometry.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Support Vector Machines in the Hilbert Geometry

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:24.294598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 04b00ded-6724-468a-8a1e-605721be3d47 · outbound

This paper cites Gauge-reversing maps on cones, and Hilbert and Thompson isometries.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Gauge-reversing maps on cones, and Hilbert and Thompson isometries

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:24.030693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 41cd5518-1eb5-42f9-b960-82c2d883c8c9 · outbound

This paper cites Open stochastic systems.

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family Open stochastic systems

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:53:23.758927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.