{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3Z45BZ5NK6ABKBFVQBL4AMVCOH","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":"048a9345286e5af43a83d4146ebabbe967cb2bc9f6921bdb61cb580fdae9edfb","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2012-04-13T14:31:47Z","title_canon_sha256":"3f80d4dc1bc142bf03e5455fae5700f1ce198f72e4af3fe5a86d4ffd2b705823"},"schema_version":"1.0","source":{"id":"1204.3010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3010","created_at":"2026-05-18T01:57:52Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3010v1","created_at":"2026-05-18T01:57:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3010","created_at":"2026-05-18T01:57:52Z"},{"alias_kind":"pith_short_12","alias_value":"3Z45BZ5NK6AB","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3Z45BZ5NK6ABKBFV","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3Z45BZ5N","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:c55329cddb8d8ebd0f900de4a87bfa965d034b8febc9f79bd2c33d7d10993930","target":"graph","created_at":"2026-05-18T01:57:52Z","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":"The self-similarity of complex networks is typically investigated through computational algorithms the primary task of which is to cover the structure with a minimal number of boxes. Here we introduce a box-covering algorithm that not only outperforms previous ones, but also finds optimal solutions. For the two benchmark cases tested, namely, the E. Coli and the WWW networks, our results show that the improvement can be rather substantial, reaching up to 15% in the case of the WWW network.","authors_text":"Christian M. Schneider, Hans J. Herrmann, Jose S. Andrade Jr., Tobias A. Kesselring","cross_cats":["cs.SI","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2012-04-13T14:31:47Z","title":"Optimal box-covering algorithm for fractal dimension of complex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3010","kind":"arxiv","version":1},"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:dc7bebe35e74397ff9e8dd134cfdee3df31f91e9a9ec496063cbaa51f879dc36","target":"record","created_at":"2026-05-18T01:57:52Z","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":"048a9345286e5af43a83d4146ebabbe967cb2bc9f6921bdb61cb580fdae9edfb","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2012-04-13T14:31:47Z","title_canon_sha256":"3f80d4dc1bc142bf03e5455fae5700f1ce198f72e4af3fe5a86d4ffd2b705823"},"schema_version":"1.0","source":{"id":"1204.3010","kind":"arxiv","version":1}},"canonical_sha256":"de79d0e7ad57801504b58057c032a271dffa0c258707441eec3a6e9bcaacabfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de79d0e7ad57801504b58057c032a271dffa0c258707441eec3a6e9bcaacabfa","first_computed_at":"2026-05-18T01:57:52.708920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:52.708920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bADyL89zbW+3QQdKFi7uSDHPF1EjiAdJ8o0nWXcaQymWseZJhs6d8Gpb5P9cVCdGm/MnHvHmolzdyvf9YWq6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:52.709432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc7bebe35e74397ff9e8dd134cfdee3df31f91e9a9ec496063cbaa51f879dc36","sha256:c55329cddb8d8ebd0f900de4a87bfa965d034b8febc9f79bd2c33d7d10993930"],"state_sha256":"2d643db11988386731a1e10c4e920f4edc304203b2c19e4d05ae2470e60a5d10"}