{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:3NNEHUKZWJY72EZP4L3DAVNSF3","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":"cb1f0a904bc7fc042963046376b3fbe3eabb1d4c43bde2e2d58fee9f509bf9f3","cross_cats_sorted":["cond-mat.stat-mech","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2009-08-31T11:57:02Z","title_canon_sha256":"780a8f94d6c5dbf2b3bc170e3d9daee8611a5ebc4584a9c6364ad7acef0b4d02"},"schema_version":"1.0","source":{"id":"0908.4509","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.4509","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"0908.4509v1","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.4509","created_at":"2026-05-18T03:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"3NNEHUKZWJY7","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"3NNEHUKZWJY72EZP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"3NNEHUKZ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:d3ca593f22536841f7bf306df00c06fed933b00f872cafcdf6223dde15cb5bcb","target":"graph","created_at":"2026-05-18T03:02:57Z","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":"In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension. The proposed framework defines an unifying general theory of fractal networks able to unravel some hidden mechanisms responsible for the emergence of fractal structures in Nature.","authors_text":"Simone Righi, Timoteo Carletti","cross_cats":["cond-mat.stat-mech","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2009-08-31T11:57:02Z","title":"Weighted Fractal Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.4509","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":"sha256:376a4a08e860bcab9366851f9a3558e033901dc3c0c157548022ffc46620e51f","target":"record","created_at":"2026-05-18T03:02:57Z","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":"cb1f0a904bc7fc042963046376b3fbe3eabb1d4c43bde2e2d58fee9f509bf9f3","cross_cats_sorted":["cond-mat.stat-mech","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.other","submitted_at":"2009-08-31T11:57:02Z","title_canon_sha256":"780a8f94d6c5dbf2b3bc170e3d9daee8611a5ebc4584a9c6364ad7acef0b4d02"},"schema_version":"1.0","source":{"id":"0908.4509","kind":"arxiv","version":1}},"canonical_sha256":"db5a43d159b271fd132fe2f63055b22ed3b440161e30c0ae890dd26718acdb2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db5a43d159b271fd132fe2f63055b22ed3b440161e30c0ae890dd26718acdb2a","first_computed_at":"2026-05-18T03:02:57.627122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:57.627122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E3LGIUXs3TqyVOqivBxjND/6XovjQyohWhGuVyrG0qBb5zfp4/lfO9kuM2/LaYnQq7cX1lJIDk8DO0JYify2Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:57.627719Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.4509","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:376a4a08e860bcab9366851f9a3558e033901dc3c0c157548022ffc46620e51f","sha256:d3ca593f22536841f7bf306df00c06fed933b00f872cafcdf6223dde15cb5bcb"],"state_sha256":"c185eeea0536330d858de40f152ff6868982f4257d5cb7c3ba94bc1aafdeae19"}