{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DGCOBC7SBMC3CN5WE2WRPFLOBQ","short_pith_number":"pith:DGCOBC7S","canonical_record":{"source":{"id":"1109.5454","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"nlin.AO","submitted_at":"2011-09-26T06:52:21Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"27cea7cd26892f3256e26cdba96bb0a61dd1656b63f1304cad9f7abf90a60501","abstract_canon_sha256":"2b999add61b2538929de2d426b9ac098311f19cd339097a129214eca0570a377"},"schema_version":"1.0"},"canonical_sha256":"1984e08bf20b05b137b626ad17956e0c202a2c066037bb9ac06c741583e0bd0f","source":{"kind":"arxiv","id":"1109.5454","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5454","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5454v1","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5454","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"DGCOBC7SBMC3","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DGCOBC7SBMC3CN5W","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DGCOBC7S","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DGCOBC7SBMC3CN5WE2WRPFLOBQ","target":"record","payload":{"canonical_record":{"source":{"id":"1109.5454","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"nlin.AO","submitted_at":"2011-09-26T06:52:21Z","cross_cats_sorted":["cs.SI","physics.soc-ph"],"title_canon_sha256":"27cea7cd26892f3256e26cdba96bb0a61dd1656b63f1304cad9f7abf90a60501","abstract_canon_sha256":"2b999add61b2538929de2d426b9ac098311f19cd339097a129214eca0570a377"},"schema_version":"1.0"},"canonical_sha256":"1984e08bf20b05b137b626ad17956e0c202a2c066037bb9ac06c741583e0bd0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:19.781121Z","signature_b64":"HjY2rDo1M9nUcEFC9FvBrm3SwzHgcSTiKff7UFW8zi6/6kd5i+9M0cgsN/m2sy0XE2/IuJSRiT6+2iiJy4c3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1984e08bf20b05b137b626ad17956e0c202a2c066037bb9ac06c741583e0bd0f","last_reissued_at":"2026-05-18T04:12:19.780572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:19.780572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.5454","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":"2026-05-18T04:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q5bA020QtVKrWVlhhJmfEGzOboU2iJjCiMD3yodo49NV6V4q8wk+1RIMlD5g7NpN5JMT5Hu/g0TjS/ddv4OzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:19:52.813921Z"},"content_sha256":"8d4ec660549b11b961a637dd20e37b0b26720b604a44cc1f1e307382655ac81a","schema_version":"1.0","event_id":"sha256:8d4ec660549b11b961a637dd20e37b0b26720b604a44cc1f1e307382655ac81a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DGCOBC7SBMC3CN5WE2WRPFLOBQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The ubiquity of small-world networks","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["cs.SI","physics.soc-ph"],"primary_cat":"nlin.AO","authors_text":"Jonathan H. Burdette, Karen E. Joyce, Paul J. Laurienti, Qawi K. Telesford, Satoru Hayasaka","submitted_at":"2011-09-26T06:52:21Z","abstract_excerpt":"Small-world networks by Watts and Strogatz are a class of networks that are highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. These characteristics result in networks with unique properties of regional specialization with efficient information transfer. Social networks are intuitive examples of this organization with cliques or clusters of friends being interconnected, but each person is really only 5-6 people away from anyone else. While this qualitative definition has prevailed in network science theory, in application, the standard quan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5454","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":"2026-05-18T04:12:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sWWlg4DCDohbcCjVA/u3q0M74P5UmeMOxmfhWBqVmF9KseZGcaHb34We2u9geza2EQ3qSZzGXtSPUb996Gn6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:19:52.814294Z"},"content_sha256":"2a08e77e5000424ee2016f448e7a0434540547c4d85babf723ef376fdd3c1133","schema_version":"1.0","event_id":"sha256:2a08e77e5000424ee2016f448e7a0434540547c4d85babf723ef376fdd3c1133"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DGCOBC7SBMC3CN5WE2WRPFLOBQ/bundle.json","state_url":"https://pith.science/pith/DGCOBC7SBMC3CN5WE2WRPFLOBQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DGCOBC7SBMC3CN5WE2WRPFLOBQ/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":"2026-06-22T23:19:52Z","links":{"resolver":"https://pith.science/pith/DGCOBC7SBMC3CN5WE2WRPFLOBQ","bundle":"https://pith.science/pith/DGCOBC7SBMC3CN5WE2WRPFLOBQ/bundle.json","state":"https://pith.science/pith/DGCOBC7SBMC3CN5WE2WRPFLOBQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DGCOBC7SBMC3CN5WE2WRPFLOBQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DGCOBC7SBMC3CN5WE2WRPFLOBQ","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":"2b999add61b2538929de2d426b9ac098311f19cd339097a129214eca0570a377","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"nlin.AO","submitted_at":"2011-09-26T06:52:21Z","title_canon_sha256":"27cea7cd26892f3256e26cdba96bb0a61dd1656b63f1304cad9f7abf90a60501"},"schema_version":"1.0","source":{"id":"1109.5454","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5454","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5454v1","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5454","created_at":"2026-05-18T04:12:19Z"},{"alias_kind":"pith_short_12","alias_value":"DGCOBC7SBMC3","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DGCOBC7SBMC3CN5W","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DGCOBC7S","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:2a08e77e5000424ee2016f448e7a0434540547c4d85babf723ef376fdd3c1133","target":"graph","created_at":"2026-05-18T04:12:19Z","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":"Small-world networks by Watts and Strogatz are a class of networks that are highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. These characteristics result in networks with unique properties of regional specialization with efficient information transfer. Social networks are intuitive examples of this organization with cliques or clusters of friends being interconnected, but each person is really only 5-6 people away from anyone else. While this qualitative definition has prevailed in network science theory, in application, the standard quan","authors_text":"Jonathan H. Burdette, Karen E. Joyce, Paul J. Laurienti, Qawi K. Telesford, Satoru Hayasaka","cross_cats":["cs.SI","physics.soc-ph"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"nlin.AO","submitted_at":"2011-09-26T06:52:21Z","title":"The ubiquity of small-world networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5454","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":"sha256:8d4ec660549b11b961a637dd20e37b0b26720b604a44cc1f1e307382655ac81a","target":"record","created_at":"2026-05-18T04:12:19Z","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":"2b999add61b2538929de2d426b9ac098311f19cd339097a129214eca0570a377","cross_cats_sorted":["cs.SI","physics.soc-ph"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"nlin.AO","submitted_at":"2011-09-26T06:52:21Z","title_canon_sha256":"27cea7cd26892f3256e26cdba96bb0a61dd1656b63f1304cad9f7abf90a60501"},"schema_version":"1.0","source":{"id":"1109.5454","kind":"arxiv","version":1}},"canonical_sha256":"1984e08bf20b05b137b626ad17956e0c202a2c066037bb9ac06c741583e0bd0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1984e08bf20b05b137b626ad17956e0c202a2c066037bb9ac06c741583e0bd0f","first_computed_at":"2026-05-18T04:12:19.780572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:19.780572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HjY2rDo1M9nUcEFC9FvBrm3SwzHgcSTiKff7UFW8zi6/6kd5i+9M0cgsN/m2sy0XE2/IuJSRiT6+2iiJy4c3BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:19.781121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5454","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d4ec660549b11b961a637dd20e37b0b26720b604a44cc1f1e307382655ac81a","sha256:2a08e77e5000424ee2016f448e7a0434540547c4d85babf723ef376fdd3c1133"],"state_sha256":"da9c8b86470326d484cc3b101c44301f56b9129465f45c48d8418154184a057f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hh86I9yUf+yi9CuSnAQdZCTP/YSyEuSLR4IIyOwreEkUdxc/J4nfqsCrjM/TTl/y5kO81I1VPiQr1jHMnDrQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:19:52.816216Z","bundle_sha256":"65ef632d4dbf1ddbc73b7b9089d8bde4dbe16ac1df9ad26e6a3567ac9a32a59c"}}