{"as_of":"2026-08-13T05:18:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d1a19f266296e56b4112d6cc9d15a15e104daac0f5f6ec404d49c642799396dc","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T23:30:25.159428Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2412.20560/citation-record","integrity":"/paper/2412.20560/integrity","json":"/paper/2412.20560/citation-record.json","paper":"/paper/2412.20560"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.513953Z","title":"Conformal invariants, inequalities, and quasiconformal maps","venue":null,"work_id":"32397dc6-732d-42cc-af3a-b97be893ad77","year":1997},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.061611Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:bd0b65be9e5ef1bca005e1a832bae0547773b8c0ae5052d48c161ef575eceb2a","observation_id":"59f4499d-efc3-4fbe-97ec-1a1b21cbe609","resolution":{"observed_at":"2026-08-10T23:30:25.519488Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.499962Z","title":"F.; Minda D","venue":null,"work_id":"2f67210e-1171-4954-9594-830705c8af04","year":2007},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.066320Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:94441081eef640718efdda10a9ce65fff4b1f87459cb56c8500d98b9154e9019","observation_id":"f1706f90-09c5-4bd8-ab1c-2aab888c82ce","resolution":{"observed_at":"2026-08-10T23:30:25.504827Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.486223Z","title":"Uniformizing Gromov hyperbolic spaces","venue":null,"work_id":"cd05a3b2-3ab1-4a3b-909e-f06ecd533615","year":2001},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.070134Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:ee4b4c99b9d8b680c75b6d337a472fa2cfc85f04a029a3676238a0965a043762","observation_id":"da0635ab-cc4b-41ea-b1e7-10d11d109351","resolution":{"observed_at":"2026-08-10T23:30:25.490982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.473320Z","title":"A course in metric geometry , Graduate Studies in Mathe- matics, vol","venue":null,"work_id":"1feb1818-f459-4e41-a797-1b3e44b58b86","year":2001},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.074358Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:15f5a3f6c8ee7688046fcaf7a790f41a7fd66b7eb6b7c6c38c3fb4c902c27302","observation_id":"c3687a1d-b44e-4e15-968c-7ed3c1393bb5","resolution":{"observed_at":"2026-08-10T23:30:25.478251Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.459244Z","title":null,"venue":null,"work_id":"d58e953d-f105-4e39-99f2-d1e0d1c09934","year":2009},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.078286Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:f4c6f85c8929bd36c19bfe3b52e9bff36211e97398e39eea48278412e8334198","observation_id":"bf37f2ae-1a4b-4453-a2a0-227aed604798","resolution":{"observed_at":"2026-08-10T23:30:25.464140Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.446244Z","title":"Comparison theorems for hyperbolic type metrics","venue":null,"work_id":"c42af89b-3927-4beb-bac6-f6628a51e93f","year":2016},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.082638Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:c5273b9437ba13240598e04d43beef27fd7381415d908c385ff5757a7175bf15","observation_id":"f4ae1b4b-5b68-45f1-9537-a15701c8f1dd","resolution":{"observed_at":"2026-08-10T23:30:25.450842Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.16966","last_updated":"2025-03-13T01:02:26Z","snapshot_observed_at":"2026-08-12T12:39:09.434180Z","submitted_at":"2024-11-25T22:16:27Z","title":"On distortion of quasiregular mappings of the upper half plane","version":2},"cited_work":{"arxiv_id":"2411.16966","doi":"10.48550/arxiv.2411.16966","metadata_source":"pith","pith_arxiv_id":"2411.16966","snapshot_observed_at":"2026-08-11T00:16:15.729268Z","title":"On distortion of quasiregular mappings of the upper half plane","venue":"math.CV","work_id":"02ec8ef7-1f05-4c3c-8736-a0a8ef6b7f80","year":2024},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.086575Z"},"links":{"cited_paper":"/paper/2411.16966","citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:ffdbdf96f4023fb4499aa14b2e79c162930a8ef63e03d4637d945c604a84ebc4","observation_id":"c59f4e66-e950-48a7-87ca-d5c2df1b593f","resolution":{"observed_at":"2026-08-10T23:30:25.200822Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.432379Z","title":"Uniform domains and the quasi-hyperb olic metric","venue":null,"work_id":"85b39e91-fb72-47af-9245-8d03fb8ea31b","year":1979},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.090922Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:de494e2667ff36d1610b46a39f377f74de5fc924afaeb06f17ea3215c1f55663","observation_id":"58911bc9-8999-48ed-b8aa-c1cf4e098166","resolution":{"observed_at":"2026-08-10T23:30:25.437471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.418845Z","title":"Hyperbolic Groups, in Essays in Group Theory (edited by S","venue":null,"work_id":"fcddfaeb-2570-4bc3-bcb3-b9ed6f63fc3b","year":1987},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.094690Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:d9583b2d6404055010bedfb0d221fb5ab12250810739df89d91f5a92525c0eb0","observation_id":"b5fd19ea-8d07-4f3f-8bd3-95da577b2b01","resolution":{"observed_at":"2026-08-10T23:30:25.423317Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.407076Z","title":"Conformally Invariant Metrics and Quasiconformal Map- pings","venue":null,"work_id":"72618444-d7df-4ba3-8b99-1ad5d7dc4cfd","year":2020},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.098228Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:aeb1c59ce122e27939f96b5a8e738920ada8156af69f5bbe777c8ccee2ab3534","observation_id":"9f64b9b3-d186-4d7a-941d-bef57045452b","resolution":{"observed_at":"2026-08-10T23:30:25.410923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.396327Z","title":"Gromov hyperbolicity of thejG and~jG metrics","venue":null,"work_id":"8a77fb39-9be8-4cda-ae44-f916cbc0a7a4","year":2006},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.102038Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:852f18295229ddc4faca38c0eca9b2a094b90b7c75a5e5fb26df9b3aacbfc425","observation_id":"ae98cfff-470e-412d-89c8-e35fe2e9578f","resolution":{"observed_at":"2026-08-10T23:30:25.399829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.384189Z","title":"A new weighted metric: the relative metric I.,J","venue":null,"work_id":"54075eb4-2301-43da-9be6-c2800d4ea484","year":2002},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.105674Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:558ce4115b0982761996fd07412300dfb47edf112ba02e04680b14555f680d4c","observation_id":"71f11e41-4b5a-45aa-8f93-5da173706824","resolution":{"observed_at":"2026-08-10T23:30:25.388335Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.372411Z","title":"Isometries of the half-Apollonian metric","venue":null,"work_id":"6e393823-8dab-4afe-b544-1d0808e3c33c","year":2004},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.109524Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:53294a39ae42134eb1e86fb880f878477e4f67f9926864a29016abafe11f949b","observation_id":"d03357c1-3955-419e-818c-a6cfeb445d84","resolution":{"observed_at":"2026-08-10T23:30:25.376343Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.359836Z","title":"Quasiconformal maps in metric spaces with controlled geometry, Acta Math., 1998, 1811, 1-61","venue":null,"work_id":"71fe901b-3c0e-4719-aca8-b07cb467d59e","year":1998},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.114531Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:70d88c76e8e8bb77df0e6064bf996c45d4b406f8a11032d052438aa73088ab69","observation_id":"f7fac29d-832b-4105-8750-bee6dfcec983","resolution":{"observed_at":"2026-08-10T23:30:25.364430Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.347700Z","title":"Hyperbolizing metric spaces","venue":null,"work_id":"4ea038bc-16bd-4f1e-86b4-c0ed1ade7075","year":2011},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.118243Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:c34bf6ddd36989b505366fa3148827fac59b658e9821ca591a6c3f5b387d31a8","observation_id":"f6015b62-0310-413b-8331-2e05f2cdb420","resolution":{"observed_at":"2026-08-10T23:30:25.351544Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.335034Z","title":"The Cassinian metric of a domain in Rn","venue":null,"work_id":"5a3664c0-b37e-497a-b506-1226c9ea2f48","year":2009},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.121930Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:f2d293f64c17800564755007de2bbd4b1d0b660855a4f807e0569123bfaed013","observation_id":"def5db56-41d5-4365-8060-4c50ec48c1f5","resolution":{"observed_at":"2026-08-10T23:30:25.339662Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.321668Z","title":"The visual angle me tric and M¨ obius transfor- mations","venue":null,"work_id":"e1c5e067-8364-4b49-b0f9-bb37de18a179","year":2014},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.125501Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:fa7b717a39d65bc981b430ed6e3b052fe62290516b4148642d0e1431cd5e099d","observation_id":"d513848b-c8f0-42a8-9f2e-a718ff12f3b9","resolution":{"observed_at":"2026-08-10T23:30:25.326102Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.309589Z","title":null,"venue":null,"work_id":"b485d392-1e91-40dc-afda-ad9e734ba5b0","year":2007},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.129457Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:689d7c426df155df7d614ffeb7f77c17f5dbe93481a87f83e3b11ccb361eed56","observation_id":"36fd3114-a743-418c-b01d-ba4310c3d521","resolution":{"observed_at":"2026-08-10T23:30:25.313758Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.297768Z","title":"Hyperbolic-type metrics","venue":null,"work_id":"7767149a-5344-4044-b497-d19b5cce1604","year":2007},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.133083Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:9f3580465867a7a25afcfe21a5308d5105e547a314c243ec16c40f53acaad79d","observation_id":"ccf187ba-f697-409e-8b23-48ed715385eb","resolution":{"observed_at":"2026-08-10T23:30:25.301730Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.286176Z","title":": The Nikolov–Andreev Metr ic and Gromov Hyper- bolicity","venue":null,"work_id":"dd527046-acff-4ccf-861f-f986d59f0e69","year":2024},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.136867Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:36b873510e93cb6960b4459f14237ee7388b53d2d8095ce34142b1c43045e1ef","observation_id":"4ef5dbfc-7411-4e90-acdd-790a2cf3ad63","resolution":{"observed_at":"2026-08-10T23:30:25.290451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.273413Z","title":"Estimates of the Kobayashi and quasi- hyperbolic distances","venue":null,"work_id":"e620bf05-e623-4516-a642-b79d945a145a","year":2017},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.140687Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:0edf6b48b773b8029806117a3124091ad7e0e68be9c1e8356e3173e11a192a03","observation_id":"6dca8855-711b-400a-9e3f-6840cffd8248","resolution":{"observed_at":"2026-08-10T23:30:25.278012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.259351Z","title":"Gromov hyperbolic spaces,Expo","venue":null,"work_id":"74862412-88f2-4584-8d7d-b8f048394f68","year":2005},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.144257Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:64a9f16f7ac76b78add8f707bb45ded24f9fc2fe1f75f3e84e866ca17ff5f91b","observation_id":"4a5501fd-353f-4da2-9c0e-0321d7aa673b","resolution":{"observed_at":"2026-08-10T23:30:25.264274Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.245519Z","title":"Conformal invariants and quasiregular mappings, J","venue":null,"work_id":"c45ac560-f781-44e7-a8a7-0c077b3614e4","year":1985},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.147806Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:6e373d70dc6dd66c826dd1c0d9478a63ab657314982d97a44305c1073e2f19b4","observation_id":"0a1bdf84-b406-426d-9010-9258acaf5819","resolution":{"observed_at":"2026-08-10T23:30:25.249982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.232817Z","title":"Conformal geometry and quasiregular mappings","venue":null,"work_id":"7783036e-487c-42ab-ace8-5925f981b4f0","year":1988},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.151380Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:76b72eb03956c13caf205cb27123ea137047955618213a9345ddf61b6c2261d5","observation_id":"4fb37e71-42a1-4b6c-aa27-daa3536ff5a9","resolution":{"observed_at":"2026-08-10T23:30:25.237080Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.221036Z","title":"Strongly hyperbolic metrics on Ptolemy spaces , J","venue":null,"work_id":"6d0c81bc-a98e-49e3-b78d-421574c866da","year":2019},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.155051Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:a283a75f068a1feacf9f694dcb7ff71b8c600b380d282b14725c4cc44b7eb7e8","observation_id":"134fcccf-d422-4f02-9fc7-59c1e1d54dac","resolution":{"observed_at":"2026-08-10T23:30:25.224961Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T23:30:25.209533Z","title":"Dovgoshey–Hariri– Vuorinen’s metric and Gro- mov hyperbolicity","venue":null,"work_id":"3b9d4e30-e093-4ae0-b726-9e99a69cba21","year":2004},"citing_paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T23:30:25.159428Z"},"links":{"citing_paper":"/paper/2412.20560"},"observation_digest":"sha256:249d760c7253df72cf23e1a41658c6f24d5cd711c2b11f94906b21f54f6444ef","observation_id":"82ecf5ee-6596-491c-9328-0a814787c69b","resolution":{"observed_at":"2026-08-10T23:30:25.213381Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.20560","last_updated":"2024-12-29T19:53:34Z","latest_version":1,"primary_category":"math.CV","snapshot_observed_at":"2026-08-11T05:59:36.896416Z","submitted_at":"2024-12-29T19:53:34Z","title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":1,"verified_fuzzy":23},"total_outbound_references":26},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"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."}