{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:NCVK3TBEE6BC633IRIS4PH5DOH","short_pith_number":"pith:NCVK3TBE","schema_version":"1.0","canonical_sha256":"68aaadcc2427822f6f688a25c79fa371d4a51a1ec36cd9e4170c638144f9332e","source":{"kind":"arxiv","id":"physics/0610281","version":1},"attestation_state":"computed","paper":{"title":"Vertex labeling and routing in expanded Apollonian networks","license":"","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Andr\\'e Raspaud, Francesc Comellas, Guillaume Fertin, Lili Rong, Shuigeng Zhou, Zhongzhi Zhang","submitted_at":"2006-10-31T09:20:16Z","abstract_excerpt":"We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their vertices that allows to determine a shortest path routing between any two vertices of the network based only on the labels."},"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":"physics/0610281","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"physics.soc-ph","submitted_at":"2006-10-31T09:20:16Z","cross_cats_sorted":[],"title_canon_sha256":"724b620c59606af7f0798da1b7756c24fe7df4ae3371cfd7d8d17af4d34f3119","abstract_canon_sha256":"06b51f1715430a1739ab7ea92bfb3b48c03aedcd7985ec2df5530a607a2290b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:52.594187Z","signature_b64":"YMBzzCE09hgrqCuLMo31svDXnBPPkzBsUV9ZlSzaMiLJ/QY5kk4zEplXSaUvKwcYXtin3PoA+7DmcnLiQNpTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68aaadcc2427822f6f688a25c79fa371d4a51a1ec36cd9e4170c638144f9332e","last_reissued_at":"2026-05-18T04:08:52.593560Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:52.593560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vertex labeling and routing in expanded Apollonian networks","license":"","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Andr\\'e Raspaud, Francesc Comellas, Guillaume Fertin, Lili Rong, Shuigeng Zhou, Zhongzhi Zhang","submitted_at":"2006-10-31T09:20:16Z","abstract_excerpt":"We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their vertices that allows to determine a shortest path routing between any two vertices of the network based only on the labels."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0610281","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":"physics/0610281","created_at":"2026-05-18T04:08:52.593649+00:00"},{"alias_kind":"arxiv_version","alias_value":"physics/0610281v1","created_at":"2026-05-18T04:08:52.593649+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0610281","created_at":"2026-05-18T04:08:52.593649+00:00"},{"alias_kind":"pith_short_12","alias_value":"NCVK3TBEE6BC","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"NCVK3TBEE6BC633I","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"NCVK3TBE","created_at":"2026-05-18T12:25:54.717736+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/NCVK3TBEE6BC633IRIS4PH5DOH","json":"https://pith.science/pith/NCVK3TBEE6BC633IRIS4PH5DOH.json","graph_json":"https://pith.science/api/pith-number/NCVK3TBEE6BC633IRIS4PH5DOH/graph.json","events_json":"https://pith.science/api/pith-number/NCVK3TBEE6BC633IRIS4PH5DOH/events.json","paper":"https://pith.science/paper/NCVK3TBE"},"agent_actions":{"view_html":"https://pith.science/pith/NCVK3TBEE6BC633IRIS4PH5DOH","download_json":"https://pith.science/pith/NCVK3TBEE6BC633IRIS4PH5DOH.json","view_paper":"https://pith.science/paper/NCVK3TBE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=physics/0610281&json=true","fetch_graph":"https://pith.science/api/pith-number/NCVK3TBEE6BC633IRIS4PH5DOH/graph.json","fetch_events":"https://pith.science/api/pith-number/NCVK3TBEE6BC633IRIS4PH5DOH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NCVK3TBEE6BC633IRIS4PH5DOH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NCVK3TBEE6BC633IRIS4PH5DOH/action/storage_attestation","attest_author":"https://pith.science/pith/NCVK3TBEE6BC633IRIS4PH5DOH/action/author_attestation","sign_citation":"https://pith.science/pith/NCVK3TBEE6BC633IRIS4PH5DOH/action/citation_signature","submit_replication":"https://pith.science/pith/NCVK3TBEE6BC633IRIS4PH5DOH/action/replication_record"}},"created_at":"2026-05-18T04:08:52.593649+00:00","updated_at":"2026-05-18T04:08:52.593649+00:00"}