{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2ZISFBMUTCO5G4OKHFZVOF5JKW","short_pith_number":"pith:2ZISFBMU","schema_version":"1.0","canonical_sha256":"d651228594989dd371ca39735717a955b41d7ef37b1fb7823c938acb4736ca8e","source":{"kind":"arxiv","id":"1701.00500","version":1},"attestation_state":"computed","paper":{"title":"A characterization of Gromov hyperbolicity via quasigeodesic subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Thomas Weighill","submitted_at":"2017-01-02T19:10:56Z","abstract_excerpt":"By a geodesic subspace of a metric space $X$ we mean a subset $A$ of $X$ such that any two points in $A$ can be connected by a geodesic in $A$. It is easy to check that a geodesic metric space $X$ is an $\\mathbb{R}$-tree (that is, a $0$-hyperbolic space in the sense of Gromov) if and only if the union of any two intersecting geodesic subspaces is again a geodesic subspace. In this paper, we prove an analogous characterization of general Gromov hyperbolic spaces, where we replace geodesic subspaces by quasigeodesic subspaces."},"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":"1701.00500","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-01-02T19:10:56Z","cross_cats_sorted":[],"title_canon_sha256":"4ec0b2c51da6fe9de512e380980bea47a252387c237bf2d8f8f5a31744b53a55","abstract_canon_sha256":"d51c21652416bfa2f58de5753c127294ef3efe16d60d2fdaa4fdb5b144a59064"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:29.108894Z","signature_b64":"vsko4AaJ0d0w1CPeKZpKa/IxqFfY3ifyyWxWS8cOpBySCKwAFDDNAH7byalg83NJxVAM6XoUXIw+9zWVid2VCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d651228594989dd371ca39735717a955b41d7ef37b1fb7823c938acb4736ca8e","last_reissued_at":"2026-05-18T00:53:29.108511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:29.108511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterization of Gromov hyperbolicity via quasigeodesic subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Thomas Weighill","submitted_at":"2017-01-02T19:10:56Z","abstract_excerpt":"By a geodesic subspace of a metric space $X$ we mean a subset $A$ of $X$ such that any two points in $A$ can be connected by a geodesic in $A$. It is easy to check that a geodesic metric space $X$ is an $\\mathbb{R}$-tree (that is, a $0$-hyperbolic space in the sense of Gromov) if and only if the union of any two intersecting geodesic subspaces is again a geodesic subspace. In this paper, we prove an analogous characterization of general Gromov hyperbolic spaces, where we replace geodesic subspaces by quasigeodesic subspaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00500","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":""},"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":"1701.00500","created_at":"2026-05-18T00:53:29.108571+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.00500v1","created_at":"2026-05-18T00:53:29.108571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00500","created_at":"2026-05-18T00:53:29.108571+00:00"},{"alias_kind":"pith_short_12","alias_value":"2ZISFBMUTCO5","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2ZISFBMUTCO5G4OK","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2ZISFBMU","created_at":"2026-05-18T12:30:55.937587+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/2ZISFBMUTCO5G4OKHFZVOF5JKW","json":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW.json","graph_json":"https://pith.science/api/pith-number/2ZISFBMUTCO5G4OKHFZVOF5JKW/graph.json","events_json":"https://pith.science/api/pith-number/2ZISFBMUTCO5G4OKHFZVOF5JKW/events.json","paper":"https://pith.science/paper/2ZISFBMU"},"agent_actions":{"view_html":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW","download_json":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW.json","view_paper":"https://pith.science/paper/2ZISFBMU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.00500&json=true","fetch_graph":"https://pith.science/api/pith-number/2ZISFBMUTCO5G4OKHFZVOF5JKW/graph.json","fetch_events":"https://pith.science/api/pith-number/2ZISFBMUTCO5G4OKHFZVOF5JKW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW/action/storage_attestation","attest_author":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW/action/author_attestation","sign_citation":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW/action/citation_signature","submit_replication":"https://pith.science/pith/2ZISFBMUTCO5G4OKHFZVOF5JKW/action/replication_record"}},"created_at":"2026-05-18T00:53:29.108571+00:00","updated_at":"2026-05-18T00:53:29.108571+00:00"}