{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:6MYNKKSA7XTB5PJJH5V37H44RR","short_pith_number":"pith:6MYNKKSA","canonical_record":{"source":{"id":"0909.0605","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-09-03T09:07:13Z","cross_cats_sorted":[],"title_canon_sha256":"2c2eb79ed447fefa2c23b84a1f493d70ce80280de6a2913013aa873c72d0a393","abstract_canon_sha256":"643a08accb3cac58ad680494eafa262da363c2ae86635244a1d420768bb76bab"},"schema_version":"1.0"},"canonical_sha256":"f330d52a40fde61ebd293f6bbf9f9c8c48d6b07a61408a1706ec1e8706c19b7c","source":{"kind":"arxiv","id":"0909.0605","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0605","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0605v4","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0605","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"6MYNKKSA7XTB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6MYNKKSA7XTB5PJJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6MYNKKSA","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:6MYNKKSA7XTB5PJJH5V37H44RR","target":"record","payload":{"canonical_record":{"source":{"id":"0909.0605","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-09-03T09:07:13Z","cross_cats_sorted":[],"title_canon_sha256":"2c2eb79ed447fefa2c23b84a1f493d70ce80280de6a2913013aa873c72d0a393","abstract_canon_sha256":"643a08accb3cac58ad680494eafa262da363c2ae86635244a1d420768bb76bab"},"schema_version":"1.0"},"canonical_sha256":"f330d52a40fde61ebd293f6bbf9f9c8c48d6b07a61408a1706ec1e8706c19b7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:26.694816Z","signature_b64":"cW0snA6TxFx6Qmal2p+D9RGm1s6SjW8a3JTapMbEJVEsytykJllpW4vP0avvD1uakyjHAzvcwEwK0myaGiCIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f330d52a40fde61ebd293f6bbf9f9c8c48d6b07a61408a1706ec1e8706c19b7c","last_reissued_at":"2026-05-18T03:35:26.693918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:26.693918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.0605","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0CMY7Q+E+8ffoBmRqBaDpTwBmH0j3wSVcSM8t3LwSkB9WK7n4Kumn8FaI2XJ2liZE2KSfxyuYLPedyQsG/l4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:31:03.928589Z"},"content_sha256":"9b8c09ccfbf2018ccc1d8d15646398163e1921d0458e4dd9248499fbf70f738e","schema_version":"1.0","event_id":"sha256:9b8c09ccfbf2018ccc1d8d15646398163e1921d0458e4dd9248499fbf70f738e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:6MYNKKSA7XTB5PJJH5V37H44RR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic analysis of first passage time in complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Hon Wai Lau, Kwok Yip Szeto","submitted_at":"2009-09-03T09:07:13Z","abstract_excerpt":"The first passage time (FPT) distribution for random walk in complex networks is calculated through an asymptotic analysis. For network with size $N$ and short relaxation time $\\tau\\ll N$, the computed mean first passage time (MFPT), which is inverse of the decay rate of FPT distribution, is inversely proportional to the degree of the destination. These results are verified numerically for the paradigmatic networks with excellent agreement. We show that the range of validity of the analytical results covers networks that have short relaxation time and high mean degree, which turn out to be val"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0605","kind":"arxiv","version":4},"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":"2026-05-18T03:35:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S4CjDip+3+PhKbWNtk2graJqmp8xkj8+Dy0j2HclyywudjU42mGvX84aBi82zsn7uAfI1mZkT+b1+KygByDCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:31:03.928936Z"},"content_sha256":"20b843ed3ae0ed9591a8848c5eb40358d4701ac1f6aaee38bd66eea718a6a4f8","schema_version":"1.0","event_id":"sha256:20b843ed3ae0ed9591a8848c5eb40358d4701ac1f6aaee38bd66eea718a6a4f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6MYNKKSA7XTB5PJJH5V37H44RR/bundle.json","state_url":"https://pith.science/pith/6MYNKKSA7XTB5PJJH5V37H44RR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6MYNKKSA7XTB5PJJH5V37H44RR/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":"2026-06-22T14:31:03Z","links":{"resolver":"https://pith.science/pith/6MYNKKSA7XTB5PJJH5V37H44RR","bundle":"https://pith.science/pith/6MYNKKSA7XTB5PJJH5V37H44RR/bundle.json","state":"https://pith.science/pith/6MYNKKSA7XTB5PJJH5V37H44RR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6MYNKKSA7XTB5PJJH5V37H44RR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6MYNKKSA7XTB5PJJH5V37H44RR","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":"643a08accb3cac58ad680494eafa262da363c2ae86635244a1d420768bb76bab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-09-03T09:07:13Z","title_canon_sha256":"2c2eb79ed447fefa2c23b84a1f493d70ce80280de6a2913013aa873c72d0a393"},"schema_version":"1.0","source":{"id":"0909.0605","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0605","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0605v4","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0605","created_at":"2026-05-18T03:35:26Z"},{"alias_kind":"pith_short_12","alias_value":"6MYNKKSA7XTB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6MYNKKSA7XTB5PJJ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6MYNKKSA","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:20b843ed3ae0ed9591a8848c5eb40358d4701ac1f6aaee38bd66eea718a6a4f8","target":"graph","created_at":"2026-05-18T03:35:26Z","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":"The first passage time (FPT) distribution for random walk in complex networks is calculated through an asymptotic analysis. For network with size $N$ and short relaxation time $\\tau\\ll N$, the computed mean first passage time (MFPT), which is inverse of the decay rate of FPT distribution, is inversely proportional to the degree of the destination. These results are verified numerically for the paradigmatic networks with excellent agreement. We show that the range of validity of the analytical results covers networks that have short relaxation time and high mean degree, which turn out to be val","authors_text":"Hon Wai Lau, Kwok Yip Szeto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-09-03T09:07:13Z","title":"Asymptotic analysis of first passage time in complex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0605","kind":"arxiv","version":4},"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":"sha256:9b8c09ccfbf2018ccc1d8d15646398163e1921d0458e4dd9248499fbf70f738e","target":"record","created_at":"2026-05-18T03:35:26Z","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":"643a08accb3cac58ad680494eafa262da363c2ae86635244a1d420768bb76bab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-09-03T09:07:13Z","title_canon_sha256":"2c2eb79ed447fefa2c23b84a1f493d70ce80280de6a2913013aa873c72d0a393"},"schema_version":"1.0","source":{"id":"0909.0605","kind":"arxiv","version":4}},"canonical_sha256":"f330d52a40fde61ebd293f6bbf9f9c8c48d6b07a61408a1706ec1e8706c19b7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f330d52a40fde61ebd293f6bbf9f9c8c48d6b07a61408a1706ec1e8706c19b7c","first_computed_at":"2026-05-18T03:35:26.693918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:26.693918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cW0snA6TxFx6Qmal2p+D9RGm1s6SjW8a3JTapMbEJVEsytykJllpW4vP0avvD1uakyjHAzvcwEwK0myaGiCIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:26.694816Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.0605","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b8c09ccfbf2018ccc1d8d15646398163e1921d0458e4dd9248499fbf70f738e","sha256:20b843ed3ae0ed9591a8848c5eb40358d4701ac1f6aaee38bd66eea718a6a4f8"],"state_sha256":"78fb2976e9dd0374d6c074beed472dca5f78205e2bac89fdd949078692349767"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ca0ZaX7RLBZIJy6gDf+6OZ/EY9zz5rluUUD7jjbFo62Cg5jlBZLVITbBzQNbDl3lUG0vZtf46GZNGvYnWBqrCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:31:03.930882Z","bundle_sha256":"620b677fa814684491ad1951f265c1d896d178bcceb8e94e3e30975bbba7ebb5"}}