Pith. sign in

Paper Citation Record · LEDGER

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity

As of 13 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2412.20560.

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

pith.paper-citation-record.v1
2412.20560 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:30:25.159428Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

26 of 26 outbound references displayed

  • verified exact1
  • verified fuzzy23
  • unresolved2
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 59f4499d-efc3-4fbe-97ec-1a1b21cbe609 · outbound

This paper cites Conformal invariants, inequalities, and quasiconformal maps.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Conformal invariants, inequalities, and quasiconformal maps

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.519488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.061611Z digest=sha256:bd0b65be9e5ef1bca005e1a832bae0547773b8c0ae5052d48c161ef575eceb2a

Observation f1706f90-09c5-4bd8-ab1c-2aab888c82ce · outbound

This paper cites F.; Minda D.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity F.; Minda D

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.504827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.066320Z digest=sha256:94441081eef640718efdda10a9ce65fff4b1f87459cb56c8500d98b9154e9019

Observation da0635ab-cc4b-41ea-b1e7-10d11d109351 · outbound

This paper cites Uniformizing Gromov hyperbolic spaces.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Uniformizing Gromov hyperbolic spaces

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.490982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.070134Z digest=sha256:ee4b4c99b9d8b680c75b6d337a472fa2cfc85f04a029a3676238a0965a043762

Observation c3687a1d-b44e-4e15-968c-7ed3c1393bb5 · outbound

This paper cites A course in metric geometry , Graduate Studies in Mathe- matics, vol.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity A course in metric geometry , Graduate Studies in Mathe- matics, vol

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.478251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.074358Z digest=sha256:15f5a3f6c8ee7688046fcaf7a790f41a7fd66b7eb6b7c6c38c3fb4c902c27302

Observation bf37f2ae-1a4b-4453-a2a0-227aed604798 · outbound

This paper cites an unresolved cited work.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:30:25.464140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.078286Z digest=sha256:f4c6f85c8929bd36c19bfe3b52e9bff36211e97398e39eea48278412e8334198

Observation f4ae1b4b-5b68-45f1-9537-a15701c8f1dd · outbound

This paper cites Comparison theorems for hyperbolic type metrics.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Comparison theorems for hyperbolic type metrics

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.450842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.082638Z digest=sha256:c5273b9437ba13240598e04d43beef27fd7381415d908c385ff5757a7175bf15

Observation c59f4e66-e950-48a7-87ca-d5c2df1b593f · outbound

This paper cites On distortion of quasiregular mappings of the upper half plane.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity On distortion of quasiregular mappings of the upper half plane

Reference 7

Resolution
verified exact
local_arxiv, observed 2026-08-10T23:30:25.200822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.086575Z digest=sha256:ffdbdf96f4023fb4499aa14b2e79c162930a8ef63e03d4637d945c604a84ebc4

Observation 58911bc9-8999-48ed-b8aa-c1cf4e098166 · outbound

This paper cites Uniform domains and the quasi-hyperb olic metric.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Uniform domains and the quasi-hyperb olic metric

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.437471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.090922Z digest=sha256:de494e2667ff36d1610b46a39f377f74de5fc924afaeb06f17ea3215c1f55663

Observation b5fd19ea-8d07-4f3f-8bd3-95da577b2b01 · outbound

This paper cites Hyperbolic Groups, in Essays in Group Theory (edited by S.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Hyperbolic Groups, in Essays in Group Theory (edited by S

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.423317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.094690Z digest=sha256:d9583b2d6404055010bedfb0d221fb5ab12250810739df89d91f5a92525c0eb0

Observation 9f64b9b3-d186-4d7a-941d-bef57045452b · outbound

This paper cites Conformally Invariant Metrics and Quasiconformal Map- pings.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Conformally Invariant Metrics and Quasiconformal Map- pings

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.410923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.098228Z digest=sha256:aeb1c59ce122e27939f96b5a8e738920ada8156af69f5bbe777c8ccee2ab3534

Observation ae98cfff-470e-412d-89c8-e35fe2e9578f · outbound

This paper cites Gromov hyperbolicity of thejG and~jG metrics.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Gromov hyperbolicity of thejG and~jG metrics

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.399829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.102038Z digest=sha256:852f18295229ddc4faca38c0eca9b2a094b90b7c75a5e5fb26df9b3aacbfc425

Observation 71f11e41-4b5a-45aa-8f93-5da173706824 · outbound

This paper cites A new weighted metric: the relative metric I.,J.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity A new weighted metric: the relative metric I.,J

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.388335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.105674Z digest=sha256:558ce4115b0982761996fd07412300dfb47edf112ba02e04680b14555f680d4c

Observation d03357c1-3955-419e-818c-a6cfeb445d84 · outbound

This paper cites Isometries of the half-Apollonian metric.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Isometries of the half-Apollonian metric

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.376343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.109524Z digest=sha256:53294a39ae42134eb1e86fb880f878477e4f67f9926864a29016abafe11f949b

Observation f7fac29d-832b-4105-8750-bee6dfcec983 · outbound

This paper cites Quasiconformal maps in metric spaces with controlled geometry, Acta Math., 1998, 1811, 1-61.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Quasiconformal maps in metric spaces with controlled geometry, Acta Math., 1998, 1811, 1-61

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.364430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.114531Z digest=sha256:70d88c76e8e8bb77df0e6064bf996c45d4b406f8a11032d052438aa73088ab69

Observation f6015b62-0310-413b-8331-2e05f2cdb420 · outbound

This paper cites Hyperbolizing metric spaces.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Hyperbolizing metric spaces

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.351544Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.118243Z digest=sha256:c34bf6ddd36989b505366fa3148827fac59b658e9821ca591a6c3f5b387d31a8

Observation def5db56-41d5-4365-8060-4c50ec48c1f5 · outbound

This paper cites The Cassinian metric of a domain in Rn.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity The Cassinian metric of a domain in Rn

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.339662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.121930Z digest=sha256:f2d293f64c17800564755007de2bbd4b1d0b660855a4f807e0569123bfaed013

Observation d513848b-c8f0-42a8-9f2e-a718ff12f3b9 · outbound

This paper cites The visual angle me tric and M¨ obius transfor- mations.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity The visual angle me tric and M¨ obius transfor- mations

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.326102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.125501Z digest=sha256:fa7b717a39d65bc981b430ed6e3b052fe62290516b4148642d0e1431cd5e099d

Observation 36fd3114-a743-418c-b01d-ba4310c3d521 · outbound

This paper cites an unresolved cited work.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:30:25.313758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.129457Z digest=sha256:689d7c426df155df7d614ffeb7f77c17f5dbe93481a87f83e3b11ccb361eed56

Observation ccf187ba-f697-409e-8b23-48ed715385eb · outbound

This paper cites Hyperbolic-type metrics.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Hyperbolic-type metrics

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.301730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.133083Z digest=sha256:9f3580465867a7a25afcfe21a5308d5105e547a314c243ec16c40f53acaad79d

Observation 4ef5dbfc-7411-4e90-acdd-790a2cf3ad63 · outbound

This paper cites : The Nikolov–Andreev Metr ic and Gromov Hyper- bolicity.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity : The Nikolov–Andreev Metr ic and Gromov Hyper- bolicity

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.290451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.136867Z digest=sha256:36b873510e93cb6960b4459f14237ee7388b53d2d8095ce34142b1c43045e1ef

Observation 6dca8855-711b-400a-9e3f-6840cffd8248 · outbound

This paper cites Estimates of the Kobayashi and quasi- hyperbolic distances.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Estimates of the Kobayashi and quasi- hyperbolic distances

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.278012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.140687Z digest=sha256:0edf6b48b773b8029806117a3124091ad7e0e68be9c1e8356e3173e11a192a03

Observation 4a5501fd-353f-4da2-9c0e-0321d7aa673b · outbound

This paper cites Gromov hyperbolic spaces,Expo.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Gromov hyperbolic spaces,Expo

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.264274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.144257Z digest=sha256:64a9f16f7ac76b78add8f707bb45ded24f9fc2fe1f75f3e84e866ca17ff5f91b

Observation 0a1bdf84-b406-426d-9010-9258acaf5819 · outbound

This paper cites Conformal invariants and quasiregular mappings, J.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Conformal invariants and quasiregular mappings, J

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.249982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.147806Z digest=sha256:6e373d70dc6dd66c826dd1c0d9478a63ab657314982d97a44305c1073e2f19b4

Observation 4fb37e71-42a1-4b6c-aa27-daa3536ff5a9 · outbound

This paper cites Conformal geometry and quasiregular mappings.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Conformal geometry and quasiregular mappings

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.237080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.151380Z digest=sha256:76b72eb03956c13caf205cb27123ea137047955618213a9345ddf61b6c2261d5

Observation 134fcccf-d422-4f02-9fc7-59c1e1d54dac · outbound

This paper cites Strongly hyperbolic metrics on Ptolemy spaces , J.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Strongly hyperbolic metrics on Ptolemy spaces , J

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.224961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.155051Z digest=sha256:a283a75f068a1feacf9f694dcb7ff71b8c600b380d282b14725c4cc44b7eb7e8

Observation 82ecf5ee-6596-491c-9328-0a814787c69b · outbound

This paper cites Dovgoshey–Hariri– Vuorinen’s metric and Gro- mov hyperbolicity.

Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity Dovgoshey–Hariri– Vuorinen’s metric and Gro- mov hyperbolicity

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:30:25.213381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-10T23:30:25.159428Z digest=sha256:249d760c7253df72cf23e1a41658c6f24d5cd711c2b11f94906b21f54f6444ef

Pith citing papers

No inbound Pith citation observations are available.