{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:KAJIXKZWKSMVZGCAPY3KTJ6UQN","short_pith_number":"pith:KAJIXKZW","schema_version":"1.0","canonical_sha256":"50128bab3654995c98407e36a9a7d48353cf659d89e0215e4d7fb1e0aef6b9e4","source":{"kind":"arxiv","id":"cond-mat/0503316","version":2},"attestation_state":"computed","paper":{"title":"High Dimensional Apollonian Networks","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.other","authors_text":"Francesc Comellas, Guillaume Fertin, Lili Rong, Zhongzhi Zhang","submitted_at":"2005-03-13T22:13:50Z","abstract_excerpt":"We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the networks, which are determined by their dimension."},"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":"cond-mat/0503316","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cond-mat.other","submitted_at":"2005-03-13T22:13:50Z","cross_cats_sorted":[],"title_canon_sha256":"b40f22bcc34948d264a731ed22d7e29435d0982702117c991a494fac6191d0d1","abstract_canon_sha256":"ff38fb6ec70465e4c9b942b9fe7505c2999256164decb6c0d4f018849534a4da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:53.560958Z","signature_b64":"QqyqSp23RdlfMKhlKRXtQPjydmARKbfvD7n0c1ytKxw4KmaMa241lRvNn/BYfdkM43xfBlE1ZYsy0JYkQrzVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50128bab3654995c98407e36a9a7d48353cf659d89e0215e4d7fb1e0aef6b9e4","last_reissued_at":"2026-05-18T01:39:53.560294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:53.560294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"High Dimensional Apollonian Networks","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.other","authors_text":"Francesc Comellas, Guillaume Fertin, Lili Rong, Zhongzhi Zhang","submitted_at":"2005-03-13T22:13:50Z","abstract_excerpt":"We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. We derive analytical expressions for the degree distribution, the clustering coefficient and the diameter of the networks, which are determined by their dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0503316","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":"cond-mat/0503316","created_at":"2026-05-18T01:39:53.560408+00:00"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0503316v2","created_at":"2026-05-18T01:39:53.560408+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0503316","created_at":"2026-05-18T01:39:53.560408+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAJIXKZWKSMV","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAJIXKZWKSMVZGCA","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAJIXKZW","created_at":"2026-05-18T12:25:53.335082+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/KAJIXKZWKSMVZGCAPY3KTJ6UQN","json":"https://pith.science/pith/KAJIXKZWKSMVZGCAPY3KTJ6UQN.json","graph_json":"https://pith.science/api/pith-number/KAJIXKZWKSMVZGCAPY3KTJ6UQN/graph.json","events_json":"https://pith.science/api/pith-number/KAJIXKZWKSMVZGCAPY3KTJ6UQN/events.json","paper":"https://pith.science/paper/KAJIXKZW"},"agent_actions":{"view_html":"https://pith.science/pith/KAJIXKZWKSMVZGCAPY3KTJ6UQN","download_json":"https://pith.science/pith/KAJIXKZWKSMVZGCAPY3KTJ6UQN.json","view_paper":"https://pith.science/paper/KAJIXKZW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cond-mat/0503316&json=true","fetch_graph":"https://pith.science/api/pith-number/KAJIXKZWKSMVZGCAPY3KTJ6UQN/graph.json","fetch_events":"https://pith.science/api/pith-number/KAJIXKZWKSMVZGCAPY3KTJ6UQN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAJIXKZWKSMVZGCAPY3KTJ6UQN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAJIXKZWKSMVZGCAPY3KTJ6UQN/action/storage_attestation","attest_author":"https://pith.science/pith/KAJIXKZWKSMVZGCAPY3KTJ6UQN/action/author_attestation","sign_citation":"https://pith.science/pith/KAJIXKZWKSMVZGCAPY3KTJ6UQN/action/citation_signature","submit_replication":"https://pith.science/pith/KAJIXKZWKSMVZGCAPY3KTJ6UQN/action/replication_record"}},"created_at":"2026-05-18T01:39:53.560408+00:00","updated_at":"2026-05-18T01:39:53.560408+00:00"}