{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:SUI4B64PSBYXXRCNRO6DQYKWTV","short_pith_number":"pith:SUI4B64P","schema_version":"1.0","canonical_sha256":"9511c0fb8f90717bc44d8bbc3861569d60518ac8c0aeb7502df51925015a8759","source":{"kind":"arxiv","id":"0810.3313","version":3},"attestation_state":"computed","paper":{"title":"Mapping Koch curves into scale-free small-world networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hongjuan Zhang, Jihong Guan, Lichao Chen, Shuigeng Zhou, Shuyang Gao, Zhongzhi Zhang","submitted_at":"2008-10-18T13:06:47Z","abstract_excerpt":"The class of Koch fractals is one of the most interesting families of fractals, and the study of complex networks is a central issue in the scientific community. In this paper, inspired by the famous Koch fractals, we propose a mapping technique converting Koch fractals into a family of deterministic networks, called Koch networks. This novel class of networks incorporates some key properties characterizing a majority of real-life networked systems---a power-law distribution with exponent in the range between 2 and 3, a high clustering coefficient, small diameter and average path length, and d"},"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":"0810.3313","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-10-18T13:06:47Z","cross_cats_sorted":["math-ph","math.MP","physics.soc-ph"],"title_canon_sha256":"a04ee6d3ba69c3b03c0812be01f037e991d375cccae17c75bf9c2063384142c3","abstract_canon_sha256":"f441e342d4c2c5c1eed39b31f99441543c1fafba09970eb67244b067f3e7538d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:35.123624Z","signature_b64":"E/dHZMw8s2J6eMb2aP+Zceednbx/O51eZDqehQcNalDDWiPIFg/94ZiB8/V7lHDfqN7z8l9z2VaNrt595sEECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9511c0fb8f90717bc44d8bbc3861569d60518ac8c0aeb7502df51925015a8759","last_reissued_at":"2026-05-18T04:41:35.123119Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:35.123119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mapping Koch curves into scale-free small-world networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Hongjuan Zhang, Jihong Guan, Lichao Chen, Shuigeng Zhou, Shuyang Gao, Zhongzhi Zhang","submitted_at":"2008-10-18T13:06:47Z","abstract_excerpt":"The class of Koch fractals is one of the most interesting families of fractals, and the study of complex networks is a central issue in the scientific community. In this paper, inspired by the famous Koch fractals, we propose a mapping technique converting Koch fractals into a family of deterministic networks, called Koch networks. This novel class of networks incorporates some key properties characterizing a majority of real-life networked systems---a power-law distribution with exponent in the range between 2 and 3, a high clustering coefficient, small diameter and average path length, and d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.3313","kind":"arxiv","version":3},"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":"0810.3313","created_at":"2026-05-18T04:41:35.123185+00:00"},{"alias_kind":"arxiv_version","alias_value":"0810.3313v3","created_at":"2026-05-18T04:41:35.123185+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.3313","created_at":"2026-05-18T04:41:35.123185+00:00"},{"alias_kind":"pith_short_12","alias_value":"SUI4B64PSBYX","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"SUI4B64PSBYXXRCN","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"SUI4B64P","created_at":"2026-05-18T12:25:58.018023+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/SUI4B64PSBYXXRCNRO6DQYKWTV","json":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV.json","graph_json":"https://pith.science/api/pith-number/SUI4B64PSBYXXRCNRO6DQYKWTV/graph.json","events_json":"https://pith.science/api/pith-number/SUI4B64PSBYXXRCNRO6DQYKWTV/events.json","paper":"https://pith.science/paper/SUI4B64P"},"agent_actions":{"view_html":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV","download_json":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV.json","view_paper":"https://pith.science/paper/SUI4B64P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0810.3313&json=true","fetch_graph":"https://pith.science/api/pith-number/SUI4B64PSBYXXRCNRO6DQYKWTV/graph.json","fetch_events":"https://pith.science/api/pith-number/SUI4B64PSBYXXRCNRO6DQYKWTV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV/action/storage_attestation","attest_author":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV/action/author_attestation","sign_citation":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV/action/citation_signature","submit_replication":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV/action/replication_record"}},"created_at":"2026-05-18T04:41:35.123185+00:00","updated_at":"2026-05-18T04:41:35.123185+00:00"}