{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CQBOV7CVTBIWWOZWIMM5D7C6UE","short_pith_number":"pith:CQBOV7CV","schema_version":"1.0","canonical_sha256":"1402eafc5598516b3b364319d1fc5ea12f692be566324ea67a1853ff0849952f","source":{"kind":"arxiv","id":"1605.03059","version":2},"attestation_state":"computed","paper":{"title":"Core congestion is inherent in hyperbolic networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"cs.DS","authors_text":"Feodor F. Dragan, Victor Chepoi, Yann Vax\\`es","submitted_at":"2016-05-10T15:32:02Z","abstract_excerpt":"We investigate the impact the negative curvature has on the traffic congestion in large-scale networks. We prove that every Gromov hyperbolic network $G$ admits a core, thus answering in the positive a conjecture by Jonckheere, Lou, Bonahon, and Baryshnikov, Internet Mathematics, 7 (2011) which is based on the experimental observation by Narayan and Saniee, Physical Review E, 84 (2011) that real-world networks with small hyperbolicity have a core congestion. Namely, we prove that for every subset $X$ of vertices of a $\\delta$-hyperbolic graph $G$ there exists a vertex $m$ of $G$ such that the "},"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":"1605.03059","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-05-10T15:32:02Z","cross_cats_sorted":["math.CO","math.MG"],"title_canon_sha256":"96a471863f361fa8275cbe372a3d7fbf077661a236f2b5581393d761726fc041","abstract_canon_sha256":"be30ba86c672b22a46e08ea5d616d97616fa33554c84bcb64dbae23d4b17b674"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:07.959062Z","signature_b64":"vQs0XCP+/PXnc7y08iMQhc3WYHHZuOstncodKVlhl7FjV3NcMSV7uOyPc3QAq65KvOA6Zv7tRnzYbim13s/vCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1402eafc5598516b3b364319d1fc5ea12f692be566324ea67a1853ff0849952f","last_reissued_at":"2026-05-18T01:11:07.958467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:07.958467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Core congestion is inherent in hyperbolic networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"cs.DS","authors_text":"Feodor F. Dragan, Victor Chepoi, Yann Vax\\`es","submitted_at":"2016-05-10T15:32:02Z","abstract_excerpt":"We investigate the impact the negative curvature has on the traffic congestion in large-scale networks. We prove that every Gromov hyperbolic network $G$ admits a core, thus answering in the positive a conjecture by Jonckheere, Lou, Bonahon, and Baryshnikov, Internet Mathematics, 7 (2011) which is based on the experimental observation by Narayan and Saniee, Physical Review E, 84 (2011) that real-world networks with small hyperbolicity have a core congestion. Namely, we prove that for every subset $X$ of vertices of a $\\delta$-hyperbolic graph $G$ there exists a vertex $m$ of $G$ such that the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03059","kind":"arxiv","version":2},"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":"1605.03059","created_at":"2026-05-18T01:11:07.958553+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.03059v2","created_at":"2026-05-18T01:11:07.958553+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03059","created_at":"2026-05-18T01:11:07.958553+00:00"},{"alias_kind":"pith_short_12","alias_value":"CQBOV7CVTBIW","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CQBOV7CVTBIWWOZW","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CQBOV7CV","created_at":"2026-05-18T12:30:09.641336+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/CQBOV7CVTBIWWOZWIMM5D7C6UE","json":"https://pith.science/pith/CQBOV7CVTBIWWOZWIMM5D7C6UE.json","graph_json":"https://pith.science/api/pith-number/CQBOV7CVTBIWWOZWIMM5D7C6UE/graph.json","events_json":"https://pith.science/api/pith-number/CQBOV7CVTBIWWOZWIMM5D7C6UE/events.json","paper":"https://pith.science/paper/CQBOV7CV"},"agent_actions":{"view_html":"https://pith.science/pith/CQBOV7CVTBIWWOZWIMM5D7C6UE","download_json":"https://pith.science/pith/CQBOV7CVTBIWWOZWIMM5D7C6UE.json","view_paper":"https://pith.science/paper/CQBOV7CV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.03059&json=true","fetch_graph":"https://pith.science/api/pith-number/CQBOV7CVTBIWWOZWIMM5D7C6UE/graph.json","fetch_events":"https://pith.science/api/pith-number/CQBOV7CVTBIWWOZWIMM5D7C6UE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CQBOV7CVTBIWWOZWIMM5D7C6UE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CQBOV7CVTBIWWOZWIMM5D7C6UE/action/storage_attestation","attest_author":"https://pith.science/pith/CQBOV7CVTBIWWOZWIMM5D7C6UE/action/author_attestation","sign_citation":"https://pith.science/pith/CQBOV7CVTBIWWOZWIMM5D7C6UE/action/citation_signature","submit_replication":"https://pith.science/pith/CQBOV7CVTBIWWOZWIMM5D7C6UE/action/replication_record"}},"created_at":"2026-05-18T01:11:07.958553+00:00","updated_at":"2026-05-18T01:11:07.958553+00:00"}