{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MIJL4QS365B4JK6KSN6M7LR4CG","short_pith_number":"pith:MIJL4QS3","canonical_record":{"source":{"id":"1406.3680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-06-14T03:47:59Z","cross_cats_sorted":[],"title_canon_sha256":"7fae705cf0dc3f7f703cdead28bf28f5f43b83752e162bdac3002825b999078b","abstract_canon_sha256":"7ba788ffed4718fc0aac399bb854da8c8d11ba7991be87f5b6391a73eb85048c"},"schema_version":"1.0"},"canonical_sha256":"6212be425bf743c4abca937ccfae3c11b533ddba5e3c537d7753ffe0b42388eb","source":{"kind":"arxiv","id":"1406.3680","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3680","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3680v1","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3680","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"MIJL4QS365B4","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MIJL4QS365B4JK6K","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MIJL4QS3","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MIJL4QS365B4JK6KSN6M7LR4CG","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-06-14T03:47:59Z","cross_cats_sorted":[],"title_canon_sha256":"7fae705cf0dc3f7f703cdead28bf28f5f43b83752e162bdac3002825b999078b","abstract_canon_sha256":"7ba788ffed4718fc0aac399bb854da8c8d11ba7991be87f5b6391a73eb85048c"},"schema_version":"1.0"},"canonical_sha256":"6212be425bf743c4abca937ccfae3c11b533ddba5e3c537d7753ffe0b42388eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:45.240509Z","signature_b64":"O5jZjgGBB1QkE4odfbPRvYa1rt3eB5JX7MHXWQuzbq3Mfvx4gQVbHhLIuQq68yGej1AAlwnC22xEwI8iCYABCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6212be425bf743c4abca937ccfae3c11b533ddba5e3c537d7753ffe0b42388eb","last_reissued_at":"2026-05-18T02:49:45.240115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:45.240115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3680","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":"2026-05-18T02:49:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EewjYVbTw0X5J1BxLHCOI5gPcHlR03okDIx9RXFZMhd3P8JsPCV0vkir2NVFMOZfxS4T31Kace21CMynMRw4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:41:25.525377Z"},"content_sha256":"9a15c699cee8cb205d0ed7f5a80325ceaa82d70977ad3c8089d5509a2cfece70","schema_version":"1.0","event_id":"sha256:9a15c699cee8cb205d0ed7f5a80325ceaa82d70977ad3c8089d5509a2cfece70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MIJL4QS365B4JK6KSN6M7LR4CG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean first-passage time for maximal-entropy random walks in complex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Yuan Lin, Zhongzhi Zhang","submitted_at":"2014-06-14T03:47:59Z","abstract_excerpt":"We perform an in-depth study for mean first-passage time (MFPT)---a primary quantity for random walks with numerous applications---of maximal-entropy random walks (MERW) performed in complex networks. For MERW in a general network, we derive an explicit expression of MFPT in terms of the eigenvalues and eigenvectors of the adjacency matrix associated with the network. For MERW in uncorrelated networks, we also provide a theoretical formula of MFPT at the mean-field level, based on which we further evaluate the dominant scalings of MFPT to different targets for MERW in uncorrelated scale-free n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3680","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":""},"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":"2026-05-18T02:49:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cmdFLr3KSADg6636YEOKKd4LeQK0rnG1BXloPMeGFdGGbP65VhpcyJK4dq3IW/3L7O/TNvsBvUwucqfcuHZvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:41:25.525816Z"},"content_sha256":"f50aafeebc6b1a0e473cdb75400160d55ea4ecc747919c5fc9c953093f803b59","schema_version":"1.0","event_id":"sha256:f50aafeebc6b1a0e473cdb75400160d55ea4ecc747919c5fc9c953093f803b59"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIJL4QS365B4JK6KSN6M7LR4CG/bundle.json","state_url":"https://pith.science/pith/MIJL4QS365B4JK6KSN6M7LR4CG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIJL4QS365B4JK6KSN6M7LR4CG/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":"2026-05-26T02:41:25Z","links":{"resolver":"https://pith.science/pith/MIJL4QS365B4JK6KSN6M7LR4CG","bundle":"https://pith.science/pith/MIJL4QS365B4JK6KSN6M7LR4CG/bundle.json","state":"https://pith.science/pith/MIJL4QS365B4JK6KSN6M7LR4CG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIJL4QS365B4JK6KSN6M7LR4CG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MIJL4QS365B4JK6KSN6M7LR4CG","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":"7ba788ffed4718fc0aac399bb854da8c8d11ba7991be87f5b6391a73eb85048c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-06-14T03:47:59Z","title_canon_sha256":"7fae705cf0dc3f7f703cdead28bf28f5f43b83752e162bdac3002825b999078b"},"schema_version":"1.0","source":{"id":"1406.3680","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3680","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3680v1","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3680","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"MIJL4QS365B4","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MIJL4QS365B4JK6K","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MIJL4QS3","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:f50aafeebc6b1a0e473cdb75400160d55ea4ecc747919c5fc9c953093f803b59","target":"graph","created_at":"2026-05-18T02:49:45Z","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 perform an in-depth study for mean first-passage time (MFPT)---a primary quantity for random walks with numerous applications---of maximal-entropy random walks (MERW) performed in complex networks. For MERW in a general network, we derive an explicit expression of MFPT in terms of the eigenvalues and eigenvectors of the adjacency matrix associated with the network. For MERW in uncorrelated networks, we also provide a theoretical formula of MFPT at the mean-field level, based on which we further evaluate the dominant scalings of MFPT to different targets for MERW in uncorrelated scale-free n","authors_text":"Yuan Lin, Zhongzhi Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-06-14T03:47:59Z","title":"Mean first-passage time for maximal-entropy random walks in complex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3680","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":"sha256:9a15c699cee8cb205d0ed7f5a80325ceaa82d70977ad3c8089d5509a2cfece70","target":"record","created_at":"2026-05-18T02:49:45Z","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":"7ba788ffed4718fc0aac399bb854da8c8d11ba7991be87f5b6391a73eb85048c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-06-14T03:47:59Z","title_canon_sha256":"7fae705cf0dc3f7f703cdead28bf28f5f43b83752e162bdac3002825b999078b"},"schema_version":"1.0","source":{"id":"1406.3680","kind":"arxiv","version":1}},"canonical_sha256":"6212be425bf743c4abca937ccfae3c11b533ddba5e3c537d7753ffe0b42388eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6212be425bf743c4abca937ccfae3c11b533ddba5e3c537d7753ffe0b42388eb","first_computed_at":"2026-05-18T02:49:45.240115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:45.240115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O5jZjgGBB1QkE4odfbPRvYa1rt3eB5JX7MHXWQuzbq3Mfvx4gQVbHhLIuQq68yGej1AAlwnC22xEwI8iCYABCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:45.240509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3680","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a15c699cee8cb205d0ed7f5a80325ceaa82d70977ad3c8089d5509a2cfece70","sha256:f50aafeebc6b1a0e473cdb75400160d55ea4ecc747919c5fc9c953093f803b59"],"state_sha256":"e484db36c2cc17b46535dae6eb68b7172dabdb8bcdd730502c8a62782a08cfb3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5sxrMNZVb31kBMJmRbL3XB8FNzb4GrD4s9e+MUJHFtd3p0my1zC7mg8D9M6w/0tdMasM1YyWBDENlXR+BtAVCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T02:41:25.529253Z","bundle_sha256":"e193f6a61c7a042acdacc7b82fec3c816f5542d008b2811ec53d19c0996ba93d"}}