{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:74GTEZP7ULI354ERQI3WLFVYIM","short_pith_number":"pith:74GTEZP7","canonical_record":{"source":{"id":"1212.0207","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-12-02T13:41:44Z","cross_cats_sorted":["math-ph","math.MP","nlin.AO","physics.soc-ph"],"title_canon_sha256":"e8e153a376f23c9b890ec1908ee59e3d540e729fcd6e081c3eea4a0ba0052ccb","abstract_canon_sha256":"4d5be0348c1855817b63af03e7a7f83fa7fde4d04cbb49068a8f3c14a8093a81"},"schema_version":"1.0"},"canonical_sha256":"ff0d3265ffa2d1bef09182376596b8431082c9b7d2c962c0db7a46a9d5db5a5d","source":{"kind":"arxiv","id":"1212.0207","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0207","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0207v1","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0207","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"pith_short_12","alias_value":"74GTEZP7ULI3","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"74GTEZP7ULI354ER","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"74GTEZP7","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:74GTEZP7ULI354ERQI3WLFVYIM","target":"record","payload":{"canonical_record":{"source":{"id":"1212.0207","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-12-02T13:41:44Z","cross_cats_sorted":["math-ph","math.MP","nlin.AO","physics.soc-ph"],"title_canon_sha256":"e8e153a376f23c9b890ec1908ee59e3d540e729fcd6e081c3eea4a0ba0052ccb","abstract_canon_sha256":"4d5be0348c1855817b63af03e7a7f83fa7fde4d04cbb49068a8f3c14a8093a81"},"schema_version":"1.0"},"canonical_sha256":"ff0d3265ffa2d1bef09182376596b8431082c9b7d2c962c0db7a46a9d5db5a5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:26.868282Z","signature_b64":"nJs87sh0CSANrDTUyfUn7AkaTD7r4iY0vnOfz/tBCbWGsBAOiiZjHZ17LVlk2bkIk7RGhMe9gEssRlYJqVNsDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff0d3265ffa2d1bef09182376596b8431082c9b7d2c962c0db7a46a9d5db5a5d","last_reissued_at":"2026-05-18T03:39:26.867639Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:26.867639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.0207","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5BXWMi1nnIdEKCsh32oq5WWi8PoPVu9YiVh3obsMc/LDGeSArkgeqcBOYKmuIH+z9M+QkTpnmKZ6PpruKe7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T21:34:29.786587Z"},"content_sha256":"cac825b4215866892d3cbc66e367b48fdb6e331c442b72aa1d540349ff45fd7a","schema_version":"1.0","event_id":"sha256:cac825b4215866892d3cbc66e367b48fdb6e331c442b72aa1d540349ff45fd7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:74GTEZP7ULI354ERQI3WLFVYIM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modelling Multi-Trait Scale-free Networks by Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.AO","physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Bojin Zheng, Hongrun Wu, Jun Qin, Wenfei Lan, Wenhua Du","submitted_at":"2012-12-02T13:41:44Z","abstract_excerpt":"Recently, one paper in Nature(Papadopoulos, 2012) raised an old debate on the origin of the scale-free property of complex networks, which focuses on whether the scale-free property origins from the optimization or not. Because the real-world complex networks often have multiple traits, any explanation on the scale-free property of complex networks should be capable of explaining the other traits as well. This paper proposed a framework which can model multi-trait scale-free networks based on optimization, and used three examples to demonstrate its effectiveness. The results suggested that the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0207","kind":"arxiv","version":1},"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":"2026-05-18T03:39:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWSF3RNr5BKS/r7hV++sk8Av4VpT9Fdkp1GX2cMXgCu+ex6SwgQC77A58ipr0KJobcQ2uRPfr28rNz+gmnY+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T21:34:29.786935Z"},"content_sha256":"393dce3c9af56e9228e4011790c8abffd290cc67e33170c9a49bf6c2b4e5e896","schema_version":"1.0","event_id":"sha256:393dce3c9af56e9228e4011790c8abffd290cc67e33170c9a49bf6c2b4e5e896"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/74GTEZP7ULI354ERQI3WLFVYIM/bundle.json","state_url":"https://pith.science/pith/74GTEZP7ULI354ERQI3WLFVYIM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/74GTEZP7ULI354ERQI3WLFVYIM/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":"2026-05-21T21:34:29Z","links":{"resolver":"https://pith.science/pith/74GTEZP7ULI354ERQI3WLFVYIM","bundle":"https://pith.science/pith/74GTEZP7ULI354ERQI3WLFVYIM/bundle.json","state":"https://pith.science/pith/74GTEZP7ULI354ERQI3WLFVYIM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/74GTEZP7ULI354ERQI3WLFVYIM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:74GTEZP7ULI354ERQI3WLFVYIM","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":"4d5be0348c1855817b63af03e7a7f83fa7fde4d04cbb49068a8f3c14a8093a81","cross_cats_sorted":["math-ph","math.MP","nlin.AO","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-12-02T13:41:44Z","title_canon_sha256":"e8e153a376f23c9b890ec1908ee59e3d540e729fcd6e081c3eea4a0ba0052ccb"},"schema_version":"1.0","source":{"id":"1212.0207","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.0207","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"arxiv_version","alias_value":"1212.0207v1","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.0207","created_at":"2026-05-18T03:39:26Z"},{"alias_kind":"pith_short_12","alias_value":"74GTEZP7ULI3","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"74GTEZP7ULI354ER","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"74GTEZP7","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:393dce3c9af56e9228e4011790c8abffd290cc67e33170c9a49bf6c2b4e5e896","target":"graph","created_at":"2026-05-18T03:39:26Z","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":"Recently, one paper in Nature(Papadopoulos, 2012) raised an old debate on the origin of the scale-free property of complex networks, which focuses on whether the scale-free property origins from the optimization or not. Because the real-world complex networks often have multiple traits, any explanation on the scale-free property of complex networks should be capable of explaining the other traits as well. This paper proposed a framework which can model multi-trait scale-free networks based on optimization, and used three examples to demonstrate its effectiveness. The results suggested that the","authors_text":"Bojin Zheng, Hongrun Wu, Jun Qin, Wenfei Lan, Wenhua Du","cross_cats":["math-ph","math.MP","nlin.AO","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-12-02T13:41:44Z","title":"Modelling Multi-Trait Scale-free Networks by Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0207","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:cac825b4215866892d3cbc66e367b48fdb6e331c442b72aa1d540349ff45fd7a","target":"record","created_at":"2026-05-18T03:39:26Z","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":"4d5be0348c1855817b63af03e7a7f83fa7fde4d04cbb49068a8f3c14a8093a81","cross_cats_sorted":["math-ph","math.MP","nlin.AO","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2012-12-02T13:41:44Z","title_canon_sha256":"e8e153a376f23c9b890ec1908ee59e3d540e729fcd6e081c3eea4a0ba0052ccb"},"schema_version":"1.0","source":{"id":"1212.0207","kind":"arxiv","version":1}},"canonical_sha256":"ff0d3265ffa2d1bef09182376596b8431082c9b7d2c962c0db7a46a9d5db5a5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff0d3265ffa2d1bef09182376596b8431082c9b7d2c962c0db7a46a9d5db5a5d","first_computed_at":"2026-05-18T03:39:26.867639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:26.867639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nJs87sh0CSANrDTUyfUn7AkaTD7r4iY0vnOfz/tBCbWGsBAOiiZjHZ17LVlk2bkIk7RGhMe9gEssRlYJqVNsDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:26.868282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.0207","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cac825b4215866892d3cbc66e367b48fdb6e331c442b72aa1d540349ff45fd7a","sha256:393dce3c9af56e9228e4011790c8abffd290cc67e33170c9a49bf6c2b4e5e896"],"state_sha256":"840154bbdebca4deae11357475d2c860cd291a3ab19ba27aecd5d8d5211c051c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CVp8FyfXzfk76Xwvd2EjFP32FPAtLYxoQg2hl+X2JE5RY5et1DWF1LwikkI8l/LYzl1/0xzJoKWQY4rzZyX8Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T21:34:29.788953Z","bundle_sha256":"031220fd8d5553f95523588ea13e4079925fda5788de2e076e25dea754f4b472"}}