{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:XZTVGEQFE2VGOCQY4MQVGISSHT","short_pith_number":"pith:XZTVGEQF","schema_version":"1.0","canonical_sha256":"be6753120526aa670a18e3215322523ce4488a9eec217f3e1f44379cec89cef9","source":{"kind":"arxiv","id":"2412.20560","version":1},"attestation_state":"computed","paper":{"title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Marcelina Mocanu","submitted_at":"2024-12-29T19:53:34Z","abstract_excerpt":"We study in the setting of a metric space $\\left( X,d\\right) $ some generalizations of four hyperbolic-type metrics defined on open sets $G$ with nonempty boundary in the $n-$dimensional Euclidean space, namely Gehring-Osgood metric, Dovgoshey- Hariri-Vuorinen metric, Nikolov-Andreev metric and Ibragimov metric. In the definitions of these generalizations, the boundary $\\partial G$ of $G$ and the distance from a point $x$ of $G$ to $\\partial G$ are replaced by a nonempty proper closed subset $M$ of $X$ and by a $1-$Lipschitz function positive on $X\\setminus M$, respectively. For each generaliz"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.20560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2024-12-29T19:53:34Z","cross_cats_sorted":[],"title_canon_sha256":"3c6e42d1ac82937aa53b754010e4e1c9729ec2c2404b908f71d4749adc3178ce","abstract_canon_sha256":"35c0a36d2229d1b3edf3df3019087478ff29718bd73d1635aa5d08a2caa0d324"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:19.015000Z","signature_b64":"CBW9XAs1Eg7oRYVi71MBSJFwAImEi0oMf9sJ9PRVLT3v57j52FfMQ9RuQmNMs/NEFF/poQAqWfpmQq6PNYUsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be6753120526aa670a18e3215322523ce4488a9eec217f3e1f44379cec89cef9","last_reissued_at":"2026-07-05T09:55:19.014565Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:19.014565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalizations of four hyperbolic-type metrics and Gromov hyperbolicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Marcelina Mocanu","submitted_at":"2024-12-29T19:53:34Z","abstract_excerpt":"We study in the setting of a metric space $\\left( X,d\\right) $ some generalizations of four hyperbolic-type metrics defined on open sets $G$ with nonempty boundary in the $n-$dimensional Euclidean space, namely Gehring-Osgood metric, Dovgoshey- Hariri-Vuorinen metric, Nikolov-Andreev metric and Ibragimov metric. In the definitions of these generalizations, the boundary $\\partial G$ of $G$ and the distance from a point $x$ of $G$ to $\\partial G$ are replaced by a nonempty proper closed subset $M$ of $X$ and by a $1-$Lipschitz function positive on $X\\setminus M$, respectively. For each generaliz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.20560","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.20560/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.20560","created_at":"2026-07-05T09:55:19.014621+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.20560v1","created_at":"2026-07-05T09:55:19.014621+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.20560","created_at":"2026-07-05T09:55:19.014621+00:00"},{"alias_kind":"pith_short_12","alias_value":"XZTVGEQFE2VG","created_at":"2026-07-05T09:55:19.014621+00:00"},{"alias_kind":"pith_short_16","alias_value":"XZTVGEQFE2VGOCQY","created_at":"2026-07-05T09:55:19.014621+00:00"},{"alias_kind":"pith_short_8","alias_value":"XZTVGEQF","created_at":"2026-07-05T09:55:19.014621+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XZTVGEQFE2VGOCQY4MQVGISSHT","json":"https://pith.science/pith/XZTVGEQFE2VGOCQY4MQVGISSHT.json","graph_json":"https://pith.science/api/pith-number/XZTVGEQFE2VGOCQY4MQVGISSHT/graph.json","events_json":"https://pith.science/api/pith-number/XZTVGEQFE2VGOCQY4MQVGISSHT/events.json","paper":"https://pith.science/paper/XZTVGEQF"},"agent_actions":{"view_html":"https://pith.science/pith/XZTVGEQFE2VGOCQY4MQVGISSHT","download_json":"https://pith.science/pith/XZTVGEQFE2VGOCQY4MQVGISSHT.json","view_paper":"https://pith.science/paper/XZTVGEQF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.20560&json=true","fetch_graph":"https://pith.science/api/pith-number/XZTVGEQFE2VGOCQY4MQVGISSHT/graph.json","fetch_events":"https://pith.science/api/pith-number/XZTVGEQFE2VGOCQY4MQVGISSHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XZTVGEQFE2VGOCQY4MQVGISSHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XZTVGEQFE2VGOCQY4MQVGISSHT/action/storage_attestation","attest_author":"https://pith.science/pith/XZTVGEQFE2VGOCQY4MQVGISSHT/action/author_attestation","sign_citation":"https://pith.science/pith/XZTVGEQFE2VGOCQY4MQVGISSHT/action/citation_signature","submit_replication":"https://pith.science/pith/XZTVGEQFE2VGOCQY4MQVGISSHT/action/replication_record"}},"created_at":"2026-07-05T09:55:19.014621+00:00","updated_at":"2026-07-05T09:55:19.014621+00:00"}