{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:KAJIXKZWKSMVZGCAPY3KTJ6UQN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ff38fb6ec70465e4c9b942b9fe7505c2999256164decb6c0d4f018849534a4da","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.other","submitted_at":"2005-03-13T22:13:50Z","title_canon_sha256":"b40f22bcc34948d264a731ed22d7e29435d0982702117c991a494fac6191d0d1"},"schema_version":"1.0","source":{"id":"cond-mat/0503316","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0503316","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0503316v2","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0503316","created_at":"2026-05-18T01:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"KAJIXKZWKSMV","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"KAJIXKZWKSMVZGCA","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"KAJIXKZW","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:3079eeb3e94ae999c9149e368b697343fb11bb61f6345dc2e1112aa95aa1fe1c","target":"graph","created_at":"2026-05-18T01:39:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Francesc Comellas, Guillaume Fertin, Lili Rong, Zhongzhi Zhang","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.other","submitted_at":"2005-03-13T22:13:50Z","title":"High Dimensional Apollonian Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0503316","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6cdd54b59e63dbe7534425af4b3e92589aebde42679963c85b119a30fae094f1","target":"record","created_at":"2026-05-18T01:39:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ff38fb6ec70465e4c9b942b9fe7505c2999256164decb6c0d4f018849534a4da","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.other","submitted_at":"2005-03-13T22:13:50Z","title_canon_sha256":"b40f22bcc34948d264a731ed22d7e29435d0982702117c991a494fac6191d0d1"},"schema_version":"1.0","source":{"id":"cond-mat/0503316","kind":"arxiv","version":2}},"canonical_sha256":"50128bab3654995c98407e36a9a7d48353cf659d89e0215e4d7fb1e0aef6b9e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50128bab3654995c98407e36a9a7d48353cf659d89e0215e4d7fb1e0aef6b9e4","first_computed_at":"2026-05-18T01:39:53.560294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:53.560294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QqyqSp23RdlfMKhlKRXtQPjydmARKbfvD7n0c1ytKxw4KmaMa241lRvNn/BYfdkM43xfBlE1ZYsy0JYkQrzVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:53.560958Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0503316","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cdd54b59e63dbe7534425af4b3e92589aebde42679963c85b119a30fae094f1","sha256:3079eeb3e94ae999c9149e368b697343fb11bb61f6345dc2e1112aa95aa1fe1c"],"state_sha256":"0d0c83df23b582abd5d5bf434a44eef12fb3b4e5a8c7e7ad2d38070d6d6da090"}