{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NNB7IFSRZYRFBFEP6UAUNAIY6J","short_pith_number":"pith:NNB7IFSR","canonical_record":{"source":{"id":"1908.07376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2019-08-16T22:16:48Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"title_canon_sha256":"9aa34ab50b9c629cf61acbc10ee09fa6226cdcda3aa559e337b22f797d273db7","abstract_canon_sha256":"0425d502b2e52a53286eda632bba6e9aa696782273f357561e94c027ff3ea298"},"schema_version":"1.0"},"canonical_sha256":"6b43f41651ce2250948ff501468118f279f3013c97bd071129ef4c56d7e73e1a","source":{"kind":"arxiv","id":"1908.07376","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07376","created_at":"2026-07-04T23:58:33Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07376v1","created_at":"2026-07-04T23:58:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07376","created_at":"2026-07-04T23:58:33Z"},{"alias_kind":"pith_short_12","alias_value":"NNB7IFSRZYRF","created_at":"2026-07-04T23:58:33Z"},{"alias_kind":"pith_short_16","alias_value":"NNB7IFSRZYRFBFEP","created_at":"2026-07-04T23:58:33Z"},{"alias_kind":"pith_short_8","alias_value":"NNB7IFSR","created_at":"2026-07-04T23:58:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NNB7IFSRZYRFBFEP6UAUNAIY6J","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2019-08-16T22:16:48Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"title_canon_sha256":"9aa34ab50b9c629cf61acbc10ee09fa6226cdcda3aa559e337b22f797d273db7","abstract_canon_sha256":"0425d502b2e52a53286eda632bba6e9aa696782273f357561e94c027ff3ea298"},"schema_version":"1.0"},"canonical_sha256":"6b43f41651ce2250948ff501468118f279f3013c97bd071129ef4c56d7e73e1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:33.792952Z","signature_b64":"s6ee1aoM8fZOxo/yP4rNpVU9TaFWU+Zpn2+wNlPtEbdEqOFdxOpVm7vQzlHUmAfp6u6C1YNCIhGmRQgEYbnwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b43f41651ce2250948ff501468118f279f3013c97bd071129ef4c56d7e73e1a","last_reissued_at":"2026-07-04T23:58:33.792592Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:33.792592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07376","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":"2026-07-04T23:58:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q7qLifrpLxCcA0wL1K89pnToVxFA6LKwwRY3iK5RkusNisyuX6+TrYhVlrCLVwKrbIVUpLt9B9nF/F/8fRD3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:57:57.079211Z"},"content_sha256":"c7a670c6ce59894beac12241ade9d1adc4e6eb0247c79d602841324f8c0c2820","schema_version":"1.0","event_id":"sha256:c7a670c6ce59894beac12241ade9d1adc4e6eb0247c79d602841324f8c0c2820"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NNB7IFSRZYRFBFEP6UAUNAIY6J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytical results for the distribution of shortest path lengths in directed random networks that grow by node duplication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech"],"primary_cat":"physics.soc-ph","authors_text":"Chanania Steinbock, Eytan Katzav, Ofer Biham","submitted_at":"2019-08-16T22:16:48Z","abstract_excerpt":"We present exact analytical results for the distribution of shortest path lengths (DSPL) in a directed network model that grows by node duplication. Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific citation networks. Starting from an initial seed network, at each time step a random node, referred to as a mother node, is selected for duplication. Its daughter node is added to the network and duplicates each outgoing link of the mother node with probability $p$. In addition, the daughter node forms a directed link to the mother n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07376","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07376/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:58:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N8yyh7u276MdZrApo4s+EcAkWoSVLZASdCfWb2olyNyWFncahBYFa/M7BPqcoPvpiYLR9XEFqFHWhHWnuCPODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:57:57.079982Z"},"content_sha256":"6e1521a22b1150c233dae545e7a0886f32c3aaf1c52461dad2b259f1e4ce0ad7","schema_version":"1.0","event_id":"sha256:6e1521a22b1150c233dae545e7a0886f32c3aaf1c52461dad2b259f1e4ce0ad7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNB7IFSRZYRFBFEP6UAUNAIY6J/bundle.json","state_url":"https://pith.science/pith/NNB7IFSRZYRFBFEP6UAUNAIY6J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNB7IFSRZYRFBFEP6UAUNAIY6J/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":"2026-08-17T02:57:57Z","links":{"resolver":"https://pith.science/pith/NNB7IFSRZYRFBFEP6UAUNAIY6J","bundle":"https://pith.science/pith/NNB7IFSRZYRFBFEP6UAUNAIY6J/bundle.json","state":"https://pith.science/pith/NNB7IFSRZYRFBFEP6UAUNAIY6J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNB7IFSRZYRFBFEP6UAUNAIY6J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NNB7IFSRZYRFBFEP6UAUNAIY6J","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":"0425d502b2e52a53286eda632bba6e9aa696782273f357561e94c027ff3ea298","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2019-08-16T22:16:48Z","title_canon_sha256":"9aa34ab50b9c629cf61acbc10ee09fa6226cdcda3aa559e337b22f797d273db7"},"schema_version":"1.0","source":{"id":"1908.07376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07376","created_at":"2026-07-04T23:58:33Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07376v1","created_at":"2026-07-04T23:58:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07376","created_at":"2026-07-04T23:58:33Z"},{"alias_kind":"pith_short_12","alias_value":"NNB7IFSRZYRF","created_at":"2026-07-04T23:58:33Z"},{"alias_kind":"pith_short_16","alias_value":"NNB7IFSRZYRFBFEP","created_at":"2026-07-04T23:58:33Z"},{"alias_kind":"pith_short_8","alias_value":"NNB7IFSR","created_at":"2026-07-04T23:58:33Z"}],"graph_snapshots":[{"event_id":"sha256:6e1521a22b1150c233dae545e7a0886f32c3aaf1c52461dad2b259f1e4ce0ad7","target":"graph","created_at":"2026-07-04T23:58:33Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07376/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present exact analytical results for the distribution of shortest path lengths (DSPL) in a directed network model that grows by node duplication. Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific citation networks. Starting from an initial seed network, at each time step a random node, referred to as a mother node, is selected for duplication. Its daughter node is added to the network and duplicates each outgoing link of the mother node with probability $p$. In addition, the daughter node forms a directed link to the mother n","authors_text":"Chanania Steinbock, Eytan Katzav, Ofer Biham","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2019-08-16T22:16:48Z","title":"Analytical results for the distribution of shortest path lengths in directed random networks that grow by node duplication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07376","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:c7a670c6ce59894beac12241ade9d1adc4e6eb0247c79d602841324f8c0c2820","target":"record","created_at":"2026-07-04T23:58:33Z","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":"0425d502b2e52a53286eda632bba6e9aa696782273f357561e94c027ff3ea298","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2019-08-16T22:16:48Z","title_canon_sha256":"9aa34ab50b9c629cf61acbc10ee09fa6226cdcda3aa559e337b22f797d273db7"},"schema_version":"1.0","source":{"id":"1908.07376","kind":"arxiv","version":1}},"canonical_sha256":"6b43f41651ce2250948ff501468118f279f3013c97bd071129ef4c56d7e73e1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b43f41651ce2250948ff501468118f279f3013c97bd071129ef4c56d7e73e1a","first_computed_at":"2026-07-04T23:58:33.792592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:33.792592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s6ee1aoM8fZOxo/yP4rNpVU9TaFWU+Zpn2+wNlPtEbdEqOFdxOpVm7vQzlHUmAfp6u6C1YNCIhGmRQgEYbnwAg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:33.792952Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7a670c6ce59894beac12241ade9d1adc4e6eb0247c79d602841324f8c0c2820","sha256:6e1521a22b1150c233dae545e7a0886f32c3aaf1c52461dad2b259f1e4ce0ad7"],"state_sha256":"d47bb2828ff4f4b0e2012a8b6a608a0a513378a89b3f86e56a04404cc2451fc3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"shPAezeAgderqN3g1hJxWLJhIarjzqdrSII72Xc+J4GMGDUqJqS8vkfkcD0RCTy2tcq1q+L58vRkhPNwSLVDAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T02:57:57.087772Z","bundle_sha256":"2713e17c0390ec912947bdf0f09d3d4d6877fae457133798a8a5a891fc9038f0"}}