{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MCI2DWLAMIW5RLZXVNHEVZW5E7","short_pith_number":"pith:MCI2DWLA","schema_version":"1.0","canonical_sha256":"6091a1d960622dd8af37ab4e4ae6dd27cd68f294b72f88bb92d975d7e99b0dff","source":{"kind":"arxiv","id":"1503.01340","version":1},"attestation_state":"computed","paper":{"title":"Bounds on Gromov Hyperbolicity Constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Domingo Pestana, Jose M. Rodriguez, Veronica Hernandez","submitted_at":"2015-03-04T15:23:27Z","abstract_excerpt":"If $X$ is a geodesic metric space and $x_{1},x_{2},x_{3} \\in X$, a geodesic triangle  $T=\\{x_{1},x_{2},x_{3}\\}$ is the union of the three geodesics $[x_{1}x_{2}]$, $[x_{2}x_{3}]$ and $[x_{3}x_{1}]$ in $X$. The space $X$ is $\\delta$-hyperbolic in the Gromov sense if any side of $T$ is contained in a $\\delta$-neighborhood of the union of the two   other sides, for every geodesic triangle $T$ in $X$.\n  If $X$ is hyperbolic, we denote by  $\\delta(X)$ the sharp hyperbolicity constant of $X$, i.e. $\\delta(X) =\\inf \\{ \\delta\\geq 0:{0.3cm}$ X ${0.2cm}$ $\\text{is} {0.2cm} \\delta \\text{-hyperbolic} \\}.$"},"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":"1503.01340","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-04T15:23:27Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"e683aabb5d148f4df40cb53836f1ef5863fc7127dc0ef67445be72eb5bd5d9ed","abstract_canon_sha256":"4bbd8576b7e210a2ca6a4ba9d5c04e30c6d2babdcf56a0b2678334c55111e636"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:34.758406Z","signature_b64":"bGwJ0A8zA2zE4g5WX/U/RqSgoyGouFuF7IHuCJUOnJD76TlqMus2Jdi9ded3niBasAcAdVepRwyHk5MkRmZlDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6091a1d960622dd8af37ab4e4ae6dd27cd68f294b72f88bb92d975d7e99b0dff","last_reissued_at":"2026-05-18T02:25:34.757940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:34.757940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds on Gromov Hyperbolicity Constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Domingo Pestana, Jose M. Rodriguez, Veronica Hernandez","submitted_at":"2015-03-04T15:23:27Z","abstract_excerpt":"If $X$ is a geodesic metric space and $x_{1},x_{2},x_{3} \\in X$, a geodesic triangle  $T=\\{x_{1},x_{2},x_{3}\\}$ is the union of the three geodesics $[x_{1}x_{2}]$, $[x_{2}x_{3}]$ and $[x_{3}x_{1}]$ in $X$. The space $X$ is $\\delta$-hyperbolic in the Gromov sense if any side of $T$ is contained in a $\\delta$-neighborhood of the union of the two   other sides, for every geodesic triangle $T$ in $X$.\n  If $X$ is hyperbolic, we denote by  $\\delta(X)$ the sharp hyperbolicity constant of $X$, i.e. $\\delta(X) =\\inf \\{ \\delta\\geq 0:{0.3cm}$ X ${0.2cm}$ $\\text{is} {0.2cm} \\delta \\text{-hyperbolic} \\}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01340","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":"1503.01340","created_at":"2026-05-18T02:25:34.758022+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.01340v1","created_at":"2026-05-18T02:25:34.758022+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01340","created_at":"2026-05-18T02:25:34.758022+00:00"},{"alias_kind":"pith_short_12","alias_value":"MCI2DWLAMIW5","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MCI2DWLAMIW5RLZX","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MCI2DWLA","created_at":"2026-05-18T12:29:32.376354+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/MCI2DWLAMIW5RLZXVNHEVZW5E7","json":"https://pith.science/pith/MCI2DWLAMIW5RLZXVNHEVZW5E7.json","graph_json":"https://pith.science/api/pith-number/MCI2DWLAMIW5RLZXVNHEVZW5E7/graph.json","events_json":"https://pith.science/api/pith-number/MCI2DWLAMIW5RLZXVNHEVZW5E7/events.json","paper":"https://pith.science/paper/MCI2DWLA"},"agent_actions":{"view_html":"https://pith.science/pith/MCI2DWLAMIW5RLZXVNHEVZW5E7","download_json":"https://pith.science/pith/MCI2DWLAMIW5RLZXVNHEVZW5E7.json","view_paper":"https://pith.science/paper/MCI2DWLA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.01340&json=true","fetch_graph":"https://pith.science/api/pith-number/MCI2DWLAMIW5RLZXVNHEVZW5E7/graph.json","fetch_events":"https://pith.science/api/pith-number/MCI2DWLAMIW5RLZXVNHEVZW5E7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MCI2DWLAMIW5RLZXVNHEVZW5E7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MCI2DWLAMIW5RLZXVNHEVZW5E7/action/storage_attestation","attest_author":"https://pith.science/pith/MCI2DWLAMIW5RLZXVNHEVZW5E7/action/author_attestation","sign_citation":"https://pith.science/pith/MCI2DWLAMIW5RLZXVNHEVZW5E7/action/citation_signature","submit_replication":"https://pith.science/pith/MCI2DWLAMIW5RLZXVNHEVZW5E7/action/replication_record"}},"created_at":"2026-05-18T02:25:34.758022+00:00","updated_at":"2026-05-18T02:25:34.758022+00:00"}