{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:SUI4B64PSBYXXRCNRO6DQYKWTV","short_pith_number":"pith:SUI4B64P","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"},"canonical_sha256":"9511c0fb8f90717bc44d8bbc3861569d60518ac8c0aeb7502df51925015a8759","source":{"kind":"arxiv","id":"0810.3313","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.3313","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"arxiv_version","alias_value":"0810.3313v3","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.3313","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"pith_short_12","alias_value":"SUI4B64PSBYX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"SUI4B64PSBYXXRCN","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"SUI4B64P","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:SUI4B64PSBYXXRCNRO6DQYKWTV","target":"record","payload":{"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"},"canonical_sha256":"9511c0fb8f90717bc44d8bbc3861569d60518ac8c0aeb7502df51925015a8759","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"},"source_kind":"arxiv","source_id":"0810.3313","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9o4pbcRicCRolzZ4nCab5rsCKRdzjhq1z6fEoR93I9cVONMaVCS2L2wGMvrzvy4CAZpSkmF3oTqmbJdXCUNXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:50:04.093424Z"},"content_sha256":"02feb27237cc302375454741af0ea487d1d620c57be8168bd870db326d80bacb","schema_version":"1.0","event_id":"sha256:02feb27237cc302375454741af0ea487d1d620c57be8168bd870db326d80bacb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:SUI4B64PSBYXXRCNRO6DQYKWTV","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WBy8ITdRv+0UuTB0xc2fzoo+u7nugn1TBKbklPuHiniSJ3F6kmM4BZLq5gpOfrh1MMuPT0SLty56FjbtJ6v0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:50:04.093783Z"},"content_sha256":"05ddc6f28ea50b8379ad50fae00a2690a57f8cd78864b7006bb4067cb9e0f3b9","schema_version":"1.0","event_id":"sha256:05ddc6f28ea50b8379ad50fae00a2690a57f8cd78864b7006bb4067cb9e0f3b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV/bundle.json","state_url":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SUI4B64PSBYXXRCNRO6DQYKWTV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T07:50:04Z","links":{"resolver":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV","bundle":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV/bundle.json","state":"https://pith.science/pith/SUI4B64PSBYXXRCNRO6DQYKWTV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SUI4B64PSBYXXRCNRO6DQYKWTV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:SUI4B64PSBYXXRCNRO6DQYKWTV","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":"f441e342d4c2c5c1eed39b31f99441543c1fafba09970eb67244b067f3e7538d","cross_cats_sorted":["math-ph","math.MP","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-10-18T13:06:47Z","title_canon_sha256":"a04ee6d3ba69c3b03c0812be01f037e991d375cccae17c75bf9c2063384142c3"},"schema_version":"1.0","source":{"id":"0810.3313","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.3313","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"arxiv_version","alias_value":"0810.3313v3","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.3313","created_at":"2026-05-18T04:41:35Z"},{"alias_kind":"pith_short_12","alias_value":"SUI4B64PSBYX","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"SUI4B64PSBYXXRCN","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"SUI4B64P","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:05ddc6f28ea50b8379ad50fae00a2690a57f8cd78864b7006bb4067cb9e0f3b9","target":"graph","created_at":"2026-05-18T04:41:35Z","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 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","authors_text":"Hongjuan Zhang, Jihong Guan, Lichao Chen, Shuigeng Zhou, Shuyang Gao, Zhongzhi Zhang","cross_cats":["math-ph","math.MP","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-10-18T13:06:47Z","title":"Mapping Koch curves into scale-free small-world networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.3313","kind":"arxiv","version":3},"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":"sha256:02feb27237cc302375454741af0ea487d1d620c57be8168bd870db326d80bacb","target":"record","created_at":"2026-05-18T04:41:35Z","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":"f441e342d4c2c5c1eed39b31f99441543c1fafba09970eb67244b067f3e7538d","cross_cats_sorted":["math-ph","math.MP","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2008-10-18T13:06:47Z","title_canon_sha256":"a04ee6d3ba69c3b03c0812be01f037e991d375cccae17c75bf9c2063384142c3"},"schema_version":"1.0","source":{"id":"0810.3313","kind":"arxiv","version":3}},"canonical_sha256":"9511c0fb8f90717bc44d8bbc3861569d60518ac8c0aeb7502df51925015a8759","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9511c0fb8f90717bc44d8bbc3861569d60518ac8c0aeb7502df51925015a8759","first_computed_at":"2026-05-18T04:41:35.123119Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:35.123119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E/dHZMw8s2J6eMb2aP+Zceednbx/O51eZDqehQcNalDDWiPIFg/94ZiB8/V7lHDfqN7z8l9z2VaNrt595sEECQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:35.123624Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.3313","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02feb27237cc302375454741af0ea487d1d620c57be8168bd870db326d80bacb","sha256:05ddc6f28ea50b8379ad50fae00a2690a57f8cd78864b7006bb4067cb9e0f3b9"],"state_sha256":"af0cb48c9c8f921037532273b5d53771d0cb766d224b7122480b4e81020900b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F3nDbbvMAouk3Q/YYFX+/ou1GeYKZkLW4V/7jlwyBQHN/wqI2lN4vvCb5khkQQ2xUYahi6PJXmtyfXd+TTt1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:50:04.096283Z","bundle_sha256":"5c6609880f09360e54cf66fb68bb823d9d96c80dbc368e60f1c2c0600712c982"}}