{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JEL6R6L4HKY73NXBF425LW7N4U","short_pith_number":"pith:JEL6R6L4","schema_version":"1.0","canonical_sha256":"4917e8f97c3ab1fdb6e12f35d5dbede51dbc168bd815e10e1b7ea90b46b7a13e","source":{"kind":"arxiv","id":"1201.3607","version":2},"attestation_state":"computed","paper":{"title":"Derivation of the particle dynamics from kinetic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"A. S. Trushechkin","submitted_at":"2012-01-17T20:13:51Z","abstract_excerpt":"We consider the microscopic solutions of the Boltzmann-Enskog equation discovered by Bogolyubov. The fact that the time-irreversible kinetic equation has time-reversible microscopic solutions is rather surprising. We analyze this paradox and show that the reversibility or irreversibility property of the Boltzmann-Enskog equation depends on the considered class of solutions. If the considered solutions have the form of sums of delta-functions, then the equation is reversible. If the considered solutions belong to the class of continuously differentiable functions, then the equation is irreversi"},"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":"1201.3607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-01-17T20:13:51Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"70e68fb537bc6fed70332563999e98b59b117c00a1382595110a5b2a23971d14","abstract_canon_sha256":"1efd72a6f2281ad8be3c436ee617962b3ab712ffe8f473764680326f587c5633"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:23.238872Z","signature_b64":"0IBEdRDD5N86a1Lo8u3ndTbDtO2qv9WdKB7UcS8Hz8cw8S36PcbcrtP7FoOhbOnx+43+BkdaRCp7LEDUhNwjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4917e8f97c3ab1fdb6e12f35d5dbede51dbc168bd815e10e1b7ea90b46b7a13e","last_reissued_at":"2026-05-18T03:27:23.238194Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:23.238194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Derivation of the particle dynamics from kinetic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"A. S. Trushechkin","submitted_at":"2012-01-17T20:13:51Z","abstract_excerpt":"We consider the microscopic solutions of the Boltzmann-Enskog equation discovered by Bogolyubov. The fact that the time-irreversible kinetic equation has time-reversible microscopic solutions is rather surprising. We analyze this paradox and show that the reversibility or irreversibility property of the Boltzmann-Enskog equation depends on the considered class of solutions. If the considered solutions have the form of sums of delta-functions, then the equation is reversible. If the considered solutions belong to the class of continuously differentiable functions, then the equation is irreversi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3607","kind":"arxiv","version":2},"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":"1201.3607","created_at":"2026-05-18T03:27:23.238323+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.3607v2","created_at":"2026-05-18T03:27:23.238323+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3607","created_at":"2026-05-18T03:27:23.238323+00:00"},{"alias_kind":"pith_short_12","alias_value":"JEL6R6L4HKY7","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JEL6R6L4HKY73NXB","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JEL6R6L4","created_at":"2026-05-18T12:27:11.947152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JEL6R6L4HKY73NXBF425LW7N4U","json":"https://pith.science/pith/JEL6R6L4HKY73NXBF425LW7N4U.json","graph_json":"https://pith.science/api/pith-number/JEL6R6L4HKY73NXBF425LW7N4U/graph.json","events_json":"https://pith.science/api/pith-number/JEL6R6L4HKY73NXBF425LW7N4U/events.json","paper":"https://pith.science/paper/JEL6R6L4"},"agent_actions":{"view_html":"https://pith.science/pith/JEL6R6L4HKY73NXBF425LW7N4U","download_json":"https://pith.science/pith/JEL6R6L4HKY73NXBF425LW7N4U.json","view_paper":"https://pith.science/paper/JEL6R6L4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.3607&json=true","fetch_graph":"https://pith.science/api/pith-number/JEL6R6L4HKY73NXBF425LW7N4U/graph.json","fetch_events":"https://pith.science/api/pith-number/JEL6R6L4HKY73NXBF425LW7N4U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JEL6R6L4HKY73NXBF425LW7N4U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JEL6R6L4HKY73NXBF425LW7N4U/action/storage_attestation","attest_author":"https://pith.science/pith/JEL6R6L4HKY73NXBF425LW7N4U/action/author_attestation","sign_citation":"https://pith.science/pith/JEL6R6L4HKY73NXBF425LW7N4U/action/citation_signature","submit_replication":"https://pith.science/pith/JEL6R6L4HKY73NXBF425LW7N4U/action/replication_record"}},"created_at":"2026-05-18T03:27:23.238323+00:00","updated_at":"2026-05-18T03:27:23.238323+00:00"}