{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7I63DJYEGKS5D3PLA4QG2I67NK","short_pith_number":"pith:7I63DJYE","canonical_record":{"source":{"id":"1312.7843","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-12-30T20:04:51Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"f99bd0cbe8c05ab9819943bb4ba8ae75e91d6d47de76ba3bbef8c383f040afb7","abstract_canon_sha256":"b1d10c7bedc40623282bf0b4c1f7150b22ca29cbc13a00186610bd7fa0525518"},"schema_version":"1.0"},"canonical_sha256":"fa3db1a70432a5d1edeb07206d23df6a8b860f2794f54bc7e6b8518530087603","source":{"kind":"arxiv","id":"1312.7843","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7843","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7843v3","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7843","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"7I63DJYEGKS5","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7I63DJYEGKS5D3PL","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7I63DJYE","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7I63DJYEGKS5D3PLA4QG2I67NK","target":"record","payload":{"canonical_record":{"source":{"id":"1312.7843","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-12-30T20:04:51Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"f99bd0cbe8c05ab9819943bb4ba8ae75e91d6d47de76ba3bbef8c383f040afb7","abstract_canon_sha256":"b1d10c7bedc40623282bf0b4c1f7150b22ca29cbc13a00186610bd7fa0525518"},"schema_version":"1.0"},"canonical_sha256":"fa3db1a70432a5d1edeb07206d23df6a8b860f2794f54bc7e6b8518530087603","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:39.259730Z","signature_b64":"rYbH+KohJtR2LhgcTVssOb9Si8q7EG7O+YjalhGkt+vkV7yq4UgU8+uF57jSlWTXLEPHGSmJCS9k8QK5CRPBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa3db1a70432a5d1edeb07206d23df6a8b860f2794f54bc7e6b8518530087603","last_reissued_at":"2026-05-18T02:46:39.259037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:39.259037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.7843","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":"2026-05-18T02:46:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AiXVdR6iRM7UFDEuTmzRl5+t2wjJKN4LMUfwkLA0mRWg68th1tTRN7CJach1IF4CSprCiWmXAfCBHvcxzB6iCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:48:08.047755Z"},"content_sha256":"ce9fbdf90b2d7f854b003bccf7878e76024e61ca4c41fa067e3ce1ba175dcbc1","schema_version":"1.0","event_id":"sha256:ce9fbdf90b2d7f854b003bccf7878e76024e61ca4c41fa067e3ce1ba175dcbc1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7I63DJYEGKS5D3PLA4QG2I67NK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Highly Dispersed Networks Generated by Enhanced Redirection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alan Gabel, P. L. Krapivsky, S. Redner","submitted_at":"2013-12-30T20:04:51Z","abstract_excerpt":"We analyze growing networks that are built by enhanced redirection. Nodes are sequentially added and each incoming node attaches to a randomly chosen 'target' node with probability 1-r, or to the parent of the target node with probability r. When the redirection probability r is an increasing function of the degree of the parent node, with r-->1 as the parent degree diverges, networks grown via this enhanced redirection mechanism exhibit unusual properties, including: (i) multiple macrohubs---nodes with degrees proportional to the number of network nodes N; (ii) non-extensivity of the degree d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7843","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":"2026-05-18T02:46:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dJyn187eP/lUEPuSUsPeBRHzsQZoTXs9riVypiUfTvevP3/6u07LPx8ktHQ8vu7oB1XYw6bREyCnjJIsl10IAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:48:08.048097Z"},"content_sha256":"1a33fd99a4de24eb4bc3a68796583e44890138412bfb6b52a2368ee05ff21027","schema_version":"1.0","event_id":"sha256:1a33fd99a4de24eb4bc3a68796583e44890138412bfb6b52a2368ee05ff21027"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7I63DJYEGKS5D3PLA4QG2I67NK/bundle.json","state_url":"https://pith.science/pith/7I63DJYEGKS5D3PLA4QG2I67NK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7I63DJYEGKS5D3PLA4QG2I67NK/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":"2026-06-04T21:48:08Z","links":{"resolver":"https://pith.science/pith/7I63DJYEGKS5D3PLA4QG2I67NK","bundle":"https://pith.science/pith/7I63DJYEGKS5D3PLA4QG2I67NK/bundle.json","state":"https://pith.science/pith/7I63DJYEGKS5D3PLA4QG2I67NK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7I63DJYEGKS5D3PLA4QG2I67NK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7I63DJYEGKS5D3PLA4QG2I67NK","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":"b1d10c7bedc40623282bf0b4c1f7150b22ca29cbc13a00186610bd7fa0525518","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-12-30T20:04:51Z","title_canon_sha256":"f99bd0cbe8c05ab9819943bb4ba8ae75e91d6d47de76ba3bbef8c383f040afb7"},"schema_version":"1.0","source":{"id":"1312.7843","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.7843","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"1312.7843v3","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7843","created_at":"2026-05-18T02:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"7I63DJYEGKS5","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7I63DJYEGKS5D3PL","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7I63DJYE","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:1a33fd99a4de24eb4bc3a68796583e44890138412bfb6b52a2368ee05ff21027","target":"graph","created_at":"2026-05-18T02:46:39Z","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":"We analyze growing networks that are built by enhanced redirection. Nodes are sequentially added and each incoming node attaches to a randomly chosen 'target' node with probability 1-r, or to the parent of the target node with probability r. When the redirection probability r is an increasing function of the degree of the parent node, with r-->1 as the parent degree diverges, networks grown via this enhanced redirection mechanism exhibit unusual properties, including: (i) multiple macrohubs---nodes with degrees proportional to the number of network nodes N; (ii) non-extensivity of the degree d","authors_text":"Alan Gabel, P. L. Krapivsky, S. Redner","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-12-30T20:04:51Z","title":"Highly Dispersed Networks Generated by Enhanced Redirection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7843","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:ce9fbdf90b2d7f854b003bccf7878e76024e61ca4c41fa067e3ce1ba175dcbc1","target":"record","created_at":"2026-05-18T02:46:39Z","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":"b1d10c7bedc40623282bf0b4c1f7150b22ca29cbc13a00186610bd7fa0525518","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-12-30T20:04:51Z","title_canon_sha256":"f99bd0cbe8c05ab9819943bb4ba8ae75e91d6d47de76ba3bbef8c383f040afb7"},"schema_version":"1.0","source":{"id":"1312.7843","kind":"arxiv","version":3}},"canonical_sha256":"fa3db1a70432a5d1edeb07206d23df6a8b860f2794f54bc7e6b8518530087603","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa3db1a70432a5d1edeb07206d23df6a8b860f2794f54bc7e6b8518530087603","first_computed_at":"2026-05-18T02:46:39.259037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:39.259037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rYbH+KohJtR2LhgcTVssOb9Si8q7EG7O+YjalhGkt+vkV7yq4UgU8+uF57jSlWTXLEPHGSmJCS9k8QK5CRPBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:39.259730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.7843","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce9fbdf90b2d7f854b003bccf7878e76024e61ca4c41fa067e3ce1ba175dcbc1","sha256:1a33fd99a4de24eb4bc3a68796583e44890138412bfb6b52a2368ee05ff21027"],"state_sha256":"2b9c0499f8d4df83d452da8730cf66592a7f86b62d516290dc94193461e672dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wCP8T5C1fsj4mUrnCnttDGsDlscU0Wxu33cZmUFmWXONvx7GjOaNw83+Ps3FTxdF23orL8A16amlwrQycWEIBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:48:08.050098Z","bundle_sha256":"f5b6cb2e18dfd6ea0e4d66052829231f0a1c71dc6054b06f772a18faafbcbc94"}}