{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ZUP3NXELSROBIFT6MPXFAFORM3","short_pith_number":"pith:ZUP3NXEL","canonical_record":{"source":{"id":"1209.3307","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-09-14T20:00:06Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","nlin.AO"],"title_canon_sha256":"adffff9acbbfbf1e8ca8e0e699ef5e4f2d108aa8f5658ec7dedf012f4b1a87b2","abstract_canon_sha256":"f2d67611d2d82a216acdae23744472604fd9bc08d34c885de6e905134a27651b"},"schema_version":"1.0"},"canonical_sha256":"cd1fb6dc8b945c14167e63ee5015d166dda036831969099ea3188d686bc7849d","source":{"kind":"arxiv","id":"1209.3307","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3307","created_at":"2026-05-18T03:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3307v3","created_at":"2026-05-18T03:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3307","created_at":"2026-05-18T03:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZUP3NXELSROB","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZUP3NXELSROBIFT6","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZUP3NXEL","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ZUP3NXELSROBIFT6MPXFAFORM3","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3307","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-09-14T20:00:06Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","nlin.AO"],"title_canon_sha256":"adffff9acbbfbf1e8ca8e0e699ef5e4f2d108aa8f5658ec7dedf012f4b1a87b2","abstract_canon_sha256":"f2d67611d2d82a216acdae23744472604fd9bc08d34c885de6e905134a27651b"},"schema_version":"1.0"},"canonical_sha256":"cd1fb6dc8b945c14167e63ee5015d166dda036831969099ea3188d686bc7849d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:06.652868Z","signature_b64":"MgvUoU+d9p5NULt26YqJYfg7RbapotfiLGjlRRoJPn3JN6YExGYJk2LAnPfzREGDgydJKttbPVGsj/QlSRpfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd1fb6dc8b945c14167e63ee5015d166dda036831969099ea3188d686bc7849d","last_reissued_at":"2026-05-18T03:20:06.652207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:06.652207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3307","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":"2026-05-18T03:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqhbDPE8KgDg4BRTsDdkfeAOGA8Ag/EC7P6pP67b5dBzVOURNf1r6wf9aIU9HkqQHjoXZhHi1F+xNVmnd561Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:45:33.733385Z"},"content_sha256":"dd83af69345c25a8a6d70ed64b4d0694b326a2fc3751cf9cde2b0f6c7073bd38","schema_version":"1.0","event_id":"sha256:dd83af69345c25a8a6d70ed64b4d0694b326a2fc3751cf9cde2b0f6c7073bd38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ZUP3NXELSROBIFT6MPXFAFORM3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Natural emergence of clusters and bursts in network evolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI","nlin.AO"],"primary_cat":"physics.soc-ph","authors_text":"Dirk Brockmann, James P. Bagrow","submitted_at":"2012-09-14T20:00:06Z","abstract_excerpt":"Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced where nodes attach proportionally to arbitrary fitness functions. However, in these models, attaching to a node always increases the ability of that node to gain more links in the future. We study network growth where nodes attach proportionally to the clustering coefficients, or local densities of triangles, of existing nodes. Attaching to a node typically "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3307","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":"2026-05-18T03:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EPassUxekB3zkdu5yc5T4/tjAeR9RfFpIBIUt6MaxhQs5xApJAYsE+74zjsqtmCzTfNZ/vPutVVlqciOVAX5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:45:33.734098Z"},"content_sha256":"bd155c9fe8813d2fbc84862b8ef30a8f2a138671c9b96d758b71f4bd01ee80cc","schema_version":"1.0","event_id":"sha256:bd155c9fe8813d2fbc84862b8ef30a8f2a138671c9b96d758b71f4bd01ee80cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZUP3NXELSROBIFT6MPXFAFORM3/bundle.json","state_url":"https://pith.science/pith/ZUP3NXELSROBIFT6MPXFAFORM3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZUP3NXELSROBIFT6MPXFAFORM3/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":"2026-05-25T21:45:33Z","links":{"resolver":"https://pith.science/pith/ZUP3NXELSROBIFT6MPXFAFORM3","bundle":"https://pith.science/pith/ZUP3NXELSROBIFT6MPXFAFORM3/bundle.json","state":"https://pith.science/pith/ZUP3NXELSROBIFT6MPXFAFORM3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZUP3NXELSROBIFT6MPXFAFORM3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ZUP3NXELSROBIFT6MPXFAFORM3","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":"f2d67611d2d82a216acdae23744472604fd9bc08d34c885de6e905134a27651b","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-09-14T20:00:06Z","title_canon_sha256":"adffff9acbbfbf1e8ca8e0e699ef5e4f2d108aa8f5658ec7dedf012f4b1a87b2"},"schema_version":"1.0","source":{"id":"1209.3307","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3307","created_at":"2026-05-18T03:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3307v3","created_at":"2026-05-18T03:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3307","created_at":"2026-05-18T03:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"ZUP3NXELSROB","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"ZUP3NXELSROBIFT6","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"ZUP3NXEL","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:bd155c9fe8813d2fbc84862b8ef30a8f2a138671c9b96d758b71f4bd01ee80cc","target":"graph","created_at":"2026-05-18T03:20:06Z","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":"Network models with preferential attachment, where new nodes are injected into the network and form links with existing nodes proportional to their current connectivity, have been well studied for some time. Extensions have been introduced where nodes attach proportionally to arbitrary fitness functions. However, in these models, attaching to a node always increases the ability of that node to gain more links in the future. We study network growth where nodes attach proportionally to the clustering coefficients, or local densities of triangles, of existing nodes. Attaching to a node typically ","authors_text":"Dirk Brockmann, James P. Bagrow","cross_cats":["cond-mat.stat-mech","cs.SI","nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-09-14T20:00:06Z","title":"Natural emergence of clusters and bursts in network evolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3307","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:dd83af69345c25a8a6d70ed64b4d0694b326a2fc3751cf9cde2b0f6c7073bd38","target":"record","created_at":"2026-05-18T03:20:06Z","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":"f2d67611d2d82a216acdae23744472604fd9bc08d34c885de6e905134a27651b","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2012-09-14T20:00:06Z","title_canon_sha256":"adffff9acbbfbf1e8ca8e0e699ef5e4f2d108aa8f5658ec7dedf012f4b1a87b2"},"schema_version":"1.0","source":{"id":"1209.3307","kind":"arxiv","version":3}},"canonical_sha256":"cd1fb6dc8b945c14167e63ee5015d166dda036831969099ea3188d686bc7849d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd1fb6dc8b945c14167e63ee5015d166dda036831969099ea3188d686bc7849d","first_computed_at":"2026-05-18T03:20:06.652207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:06.652207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MgvUoU+d9p5NULt26YqJYfg7RbapotfiLGjlRRoJPn3JN6YExGYJk2LAnPfzREGDgydJKttbPVGsj/QlSRpfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:06.652868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3307","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd83af69345c25a8a6d70ed64b4d0694b326a2fc3751cf9cde2b0f6c7073bd38","sha256:bd155c9fe8813d2fbc84862b8ef30a8f2a138671c9b96d758b71f4bd01ee80cc"],"state_sha256":"f3feb977fbc1b21baf1be123298e2460915e7b22aabdd251a182640eb421fa10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aEmhIIXYdA30H6lPfNNGWwWI7X3fkJX1VyqrhObaxVQndDaqrZ3wsg2MWoOECZVF1A4GBlge6tkrLowcqeyeBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:45:33.737707Z","bundle_sha256":"ad73b802ba0a9591557656552e770bfcf87d178d6c3a5937cb8a326dfd69d4f3"}}