{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CT324DATTMCE5IT5XGXA77E33W","short_pith_number":"pith:CT324DAT","canonical_record":{"source":{"id":"1504.07981","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-29T19:58:35Z","cross_cats_sorted":["cs.SI","math-ph","math.MP"],"title_canon_sha256":"c820a32e11d326e092f1684c790624f5c7c182788981c86a75de9c5d1d5b9614","abstract_canon_sha256":"36d720dbc1aa5278f1716946fd0552b7c3c4a7cfe1f98631b6387665a87cfa70"},"schema_version":"1.0"},"canonical_sha256":"14f7ae0c139b044ea27db9ae0ffc9bdd98713b3d5080412b517045d293eb108a","source":{"kind":"arxiv","id":"1504.07981","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07981","created_at":"2026-05-18T01:21:37Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07981v2","created_at":"2026-05-18T01:21:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07981","created_at":"2026-05-18T01:21:37Z"},{"alias_kind":"pith_short_12","alias_value":"CT324DATTMCE","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CT324DATTMCE5IT5","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CT324DAT","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CT324DATTMCE5IT5XGXA77E33W","target":"record","payload":{"canonical_record":{"source":{"id":"1504.07981","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-29T19:58:35Z","cross_cats_sorted":["cs.SI","math-ph","math.MP"],"title_canon_sha256":"c820a32e11d326e092f1684c790624f5c7c182788981c86a75de9c5d1d5b9614","abstract_canon_sha256":"36d720dbc1aa5278f1716946fd0552b7c3c4a7cfe1f98631b6387665a87cfa70"},"schema_version":"1.0"},"canonical_sha256":"14f7ae0c139b044ea27db9ae0ffc9bdd98713b3d5080412b517045d293eb108a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:37.495825Z","signature_b64":"silRiX51Dl0bDa/Eda/XV/iQsUylDcAiDVWYqBIKMQw9U+R/vfTW0ka/wsBW0ABG4ps/jfUXM6ge2N9JM5ZKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14f7ae0c139b044ea27db9ae0ffc9bdd98713b3d5080412b517045d293eb108a","last_reissued_at":"2026-05-18T01:21:37.495325Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:37.495325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.07981","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WzOLfbD0L+3aV4DsbVM/KDiZWjn2opNvX1PsUA6Z3i92pLMuMSO+keeBOz/N4D4YLTQxkkeWRuEW8iISynquCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T12:23:10.198104Z"},"content_sha256":"35268f9e47c73ad5a4f6370572605a3046dc7158e3e00887fe29cbb9a0a73cb4","schema_version":"1.0","event_id":"sha256:35268f9e47c73ad5a4f6370572605a3046dc7158e3e00887fe29cbb9a0a73cb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CT324DATTMCE5IT5XGXA77E33W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamiltonian Dynamics of Preferential Attachment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","math-ph","math.MP"],"primary_cat":"physics.soc-ph","authors_text":"Dmitri Krioukov, Fragkiskos Papadopoulos, Konstantin Zuev","submitted_at":"2015-04-29T19:58:35Z","abstract_excerpt":"Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment, known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07981","kind":"arxiv","version":2},"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":"2026-05-18T01:21:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1AMSQBSDvTqmMDE+cy9cZQ6EV9KNyA24XXFRvr9O7h+IShqQpsydxfZNA3aRhmX4sKicvKiPjrKMcKnaRb6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T12:23:10.198507Z"},"content_sha256":"18c074cd1fcc5af3b1434f325f23fde1acdad3edfc3850ddd4a93f77003b1e4e","schema_version":"1.0","event_id":"sha256:18c074cd1fcc5af3b1434f325f23fde1acdad3edfc3850ddd4a93f77003b1e4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CT324DATTMCE5IT5XGXA77E33W/bundle.json","state_url":"https://pith.science/pith/CT324DATTMCE5IT5XGXA77E33W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CT324DATTMCE5IT5XGXA77E33W/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":"2026-05-20T12:23:10Z","links":{"resolver":"https://pith.science/pith/CT324DATTMCE5IT5XGXA77E33W","bundle":"https://pith.science/pith/CT324DATTMCE5IT5XGXA77E33W/bundle.json","state":"https://pith.science/pith/CT324DATTMCE5IT5XGXA77E33W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CT324DATTMCE5IT5XGXA77E33W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CT324DATTMCE5IT5XGXA77E33W","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":"36d720dbc1aa5278f1716946fd0552b7c3c4a7cfe1f98631b6387665a87cfa70","cross_cats_sorted":["cs.SI","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-29T19:58:35Z","title_canon_sha256":"c820a32e11d326e092f1684c790624f5c7c182788981c86a75de9c5d1d5b9614"},"schema_version":"1.0","source":{"id":"1504.07981","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07981","created_at":"2026-05-18T01:21:37Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07981v2","created_at":"2026-05-18T01:21:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07981","created_at":"2026-05-18T01:21:37Z"},{"alias_kind":"pith_short_12","alias_value":"CT324DATTMCE","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CT324DATTMCE5IT5","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CT324DAT","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:18c074cd1fcc5af3b1434f325f23fde1acdad3edfc3850ddd4a93f77003b1e4e","target":"graph","created_at":"2026-05-18T01:21:37Z","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":"Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment, known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evol","authors_text":"Dmitri Krioukov, Fragkiskos Papadopoulos, Konstantin Zuev","cross_cats":["cs.SI","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-29T19:58:35Z","title":"Hamiltonian Dynamics of Preferential Attachment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07981","kind":"arxiv","version":2},"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":"sha256:35268f9e47c73ad5a4f6370572605a3046dc7158e3e00887fe29cbb9a0a73cb4","target":"record","created_at":"2026-05-18T01:21:37Z","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":"36d720dbc1aa5278f1716946fd0552b7c3c4a7cfe1f98631b6387665a87cfa70","cross_cats_sorted":["cs.SI","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-29T19:58:35Z","title_canon_sha256":"c820a32e11d326e092f1684c790624f5c7c182788981c86a75de9c5d1d5b9614"},"schema_version":"1.0","source":{"id":"1504.07981","kind":"arxiv","version":2}},"canonical_sha256":"14f7ae0c139b044ea27db9ae0ffc9bdd98713b3d5080412b517045d293eb108a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14f7ae0c139b044ea27db9ae0ffc9bdd98713b3d5080412b517045d293eb108a","first_computed_at":"2026-05-18T01:21:37.495325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:37.495325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"silRiX51Dl0bDa/Eda/XV/iQsUylDcAiDVWYqBIKMQw9U+R/vfTW0ka/wsBW0ABG4ps/jfUXM6ge2N9JM5ZKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:37.495825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.07981","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35268f9e47c73ad5a4f6370572605a3046dc7158e3e00887fe29cbb9a0a73cb4","sha256:18c074cd1fcc5af3b1434f325f23fde1acdad3edfc3850ddd4a93f77003b1e4e"],"state_sha256":"42504cf1f9e8eff535ee01a7ae34822ac9a50b047d19c31c670a5476a7bc6b28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VwCjh0V4r0N1ihBMH8Wf9hBo1WtDdZEqV3xZuoTEe6HsdqTFSDORlrQ6flHSP//pNxNpaYNxmwoc4jV5Ay4ZDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T12:23:10.200673Z","bundle_sha256":"08899cb11e32d6dbac0b2c4c376801da46431541a469e6e28d0852316d8d38ce"}}