{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:5IM76P3YGNP5OCIGP64TZEGPUT","short_pith_number":"pith:5IM76P3Y","schema_version":"1.0","canonical_sha256":"ea19ff3f78335fd709067fb93c90cfa4fa3bcb656d252390cb28415adb995431","source":{"kind":"arxiv","id":"1004.3667","version":1},"attestation_state":"computed","paper":{"title":"The various facets of random walk entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"B. Waclaw, J. Duda, J.M. Luck, Z. Burda","submitted_at":"2010-04-21T10:06:00Z","abstract_excerpt":"We review various features of the statistics of random paths on graphs. The relationship between path statistics and Quantum Mechanics (QM) leads to two canonical ways of defining random walk on a graph, which have different statistics and hence different entropies. Generic random walk (GRW) is in correspondence with the field-theoretical formalism, whereas maximal entropy random walk (MERW), introduced by us in a recent work, is motivated by the Feynman path-integral formulation of QM. GRW maximizes entropy locally (neighbors are chosen with equal probabilities), in contrast to MERW which doe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1004.3667","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-04-21T10:06:00Z","cross_cats_sorted":[],"title_canon_sha256":"5c8d9d64b282fa71aa03b55331af63e5745a2b791e44ee3b72b0c74764ab887f","abstract_canon_sha256":"a0a2196e4ca1ae0b44923fb15be51c1236e0ad76bba2535b7ade1aac2bb9ea24"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:43.205988Z","signature_b64":"uFwWzkrJ10Pk1l0vqU7KThkTeOXmm2Ri5slPkoVoLgCGs2KrLi3uCp6hD1Gw4tOzOMt7JuNBS9eZJkd82aLEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea19ff3f78335fd709067fb93c90cfa4fa3bcb656d252390cb28415adb995431","last_reissued_at":"2026-05-18T04:42:43.205622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:43.205622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The various facets of random walk entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"B. Waclaw, J. Duda, J.M. Luck, Z. Burda","submitted_at":"2010-04-21T10:06:00Z","abstract_excerpt":"We review various features of the statistics of random paths on graphs. The relationship between path statistics and Quantum Mechanics (QM) leads to two canonical ways of defining random walk on a graph, which have different statistics and hence different entropies. Generic random walk (GRW) is in correspondence with the field-theoretical formalism, whereas maximal entropy random walk (MERW), introduced by us in a recent work, is motivated by the Feynman path-integral formulation of QM. GRW maximizes entropy locally (neighbors are chosen with equal probabilities), in contrast to MERW which doe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3667","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1004.3667","created_at":"2026-05-18T04:42:43.205676+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.3667v1","created_at":"2026-05-18T04:42:43.205676+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3667","created_at":"2026-05-18T04:42:43.205676+00:00"},{"alias_kind":"pith_short_12","alias_value":"5IM76P3YGNP5","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"5IM76P3YGNP5OCIG","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"5IM76P3Y","created_at":"2026-05-18T12:26:04.259169+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.12536","citing_title":"Information as Maximum-Caliber Deviation: A bridge between Integrated Information Theory and the Free Energy Principle","ref_index":223,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5IM76P3YGNP5OCIGP64TZEGPUT","json":"https://pith.science/pith/5IM76P3YGNP5OCIGP64TZEGPUT.json","graph_json":"https://pith.science/api/pith-number/5IM76P3YGNP5OCIGP64TZEGPUT/graph.json","events_json":"https://pith.science/api/pith-number/5IM76P3YGNP5OCIGP64TZEGPUT/events.json","paper":"https://pith.science/paper/5IM76P3Y"},"agent_actions":{"view_html":"https://pith.science/pith/5IM76P3YGNP5OCIGP64TZEGPUT","download_json":"https://pith.science/pith/5IM76P3YGNP5OCIGP64TZEGPUT.json","view_paper":"https://pith.science/paper/5IM76P3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.3667&json=true","fetch_graph":"https://pith.science/api/pith-number/5IM76P3YGNP5OCIGP64TZEGPUT/graph.json","fetch_events":"https://pith.science/api/pith-number/5IM76P3YGNP5OCIGP64TZEGPUT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5IM76P3YGNP5OCIGP64TZEGPUT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5IM76P3YGNP5OCIGP64TZEGPUT/action/storage_attestation","attest_author":"https://pith.science/pith/5IM76P3YGNP5OCIGP64TZEGPUT/action/author_attestation","sign_citation":"https://pith.science/pith/5IM76P3YGNP5OCIGP64TZEGPUT/action/citation_signature","submit_replication":"https://pith.science/pith/5IM76P3YGNP5OCIGP64TZEGPUT/action/replication_record"}},"created_at":"2026-05-18T04:42:43.205676+00:00","updated_at":"2026-05-18T04:42:43.205676+00:00"}