Paper Citation Record · LEDGER

Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions

As of 9 August 2026, this Paper Citation Record lists 9 of 9 outbound references and 0 inbound Pith citation observations for arXiv:2607.27605.

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

pith.paper-citation-record.v1
2607.27605 v1

Coverage vector

measured 9 of 9 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T04:59:52.564227Z

measured 9 of 9 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

9 of 9 outbound references displayed

verified exact0
verified fuzzy0
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 07f3a72a-625f-4796-97e5-a54e7309c841 · outbound

This paper cites Gromov.Metric structures for Riemannian and non-Riemannian spaces.

Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions Gromov.Metric structures for Riemannian and non-Riemannian spaces

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T04:59:51.930869Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 398a94aa-fc6b-4863-9167-b4e0fcb3cd85 · outbound

This paper cites A Wrapped Normal Distribution on Hyperbolic Space for Gradient-Based Learning.

Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions A Wrapped Normal Distribution on Hyperbolic Space for Gradient-Based Learning

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T04:59:52.004665Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba80991f-5dca-4091-94f0-d176623f6dab · outbound

This paper cites Box distance and observable distance via optimal transport.

Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions Box distance and observable distance via optimal transport

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T04:59:52.100174Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c97f96cf-0e31-43ac-bc36-a0be11cb314b · outbound

This paper cites Ozawa and T.

Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions Ozawa and T

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T04:59:52.193440Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0fd063cc-52f0-401e-9e6e-76401db36521 · outbound

This paper cites Shioya.Metric measure geometry, volume 25 ofIRMA Lectures in Mathematics and The- oretical Physics.

Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions Shioya.Metric measure geometry, volume 25 ofIRMA Lectures in Mathematics and The- oretical Physics

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T04:59:52.278861Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 577d4182-d375-4b63-8475-a3f8d2d03271 · outbound

This paper cites an unresolved cited work.

Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T04:59:52.361409Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e67c18bd-e0a9-4c31-9532-a9f6bbe47d47 · outbound

This paper cites A Complete Proof of the Limit Formula for Observable Diameter.

Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions A Complete Proof of the Limit Formula for Observable Diameter

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T04:59:52.443281Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a5b1a91b-4690-4fb2-8347-c840b17a955a · outbound

This paper cites Finite Mixture Modeling with Riemannian Gaussian Distributions on Hyperbolic Space.

Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions Finite Mixture Modeling with Riemannian Gaussian Distributions on Hyperbolic Space

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T04:59:52.551453Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ec9bc36-aec3-4536-992f-a37d9f2fa0f4 · outbound

This paper cites Profile Likelihood Inference for Anisotropic Hyperbolic Wrapped Normal Models on Hyperbolic Space.

Radial Hyperbolic Measures: Shell Geometry, Pyramid Limits, and Gaussian Phase Transitions Profile Likelihood Inference for Anisotropic Hyperbolic Wrapped Normal Models on Hyperbolic Space

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T04:59:52.564227Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.