{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DD6E6YXWBITBIND2UTOQMVUPY7","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":"e41457e32937d08d183b5ed067ae2d6f2280e8f426b14fdb455f2cac36268bce","cross_cats_sorted":["math.MP","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-06T09:43:16Z","title_canon_sha256":"ba5bd0bb9649d6f1eab8b8daa65de70f9ae0c4b7ce96c8b5e5706e5e29301aaa"},"schema_version":"1.0","source":{"id":"1212.1270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1270","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1270v1","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1270","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"pith_short_12","alias_value":"DD6E6YXWBITB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"DD6E6YXWBITBIND2","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"DD6E6YXW","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:5ab63281d7ae02a1737c8db6faaabed9768b35e7dd94b389e1f9f05f74b46cad","target":"graph","created_at":"2026-05-18T03:39:04Z","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 Kramers problem for quantum Bose-gases with specular-diffuse boundary conditions of the kinetic theory is considered. On an example of Kramers' problem the new generalized method of a source of the decision of the boundary problems from the kinetic theory is developed. The method allows to receive the decision with any degree of accuracy. At the basis of a method lays the idea of representation of a boundary condition on distribution function in the form of a source in the kinetic equation. By means of integrals Fourier the kinetic equation with a source is reduced to the integral equation","authors_text":"A. V. Latyshev, E. A. Bedrikova","cross_cats":["math.MP","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-06T09:43:16Z","title":"The Kramers problem for quantum bose-gases with constant collision frequency and specular-diffusive boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1270","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:af14431f6adbe5ac66dbf73cb9900d4b5e2bcaf358462d47d47caac4701c72ed","target":"record","created_at":"2026-05-18T03:39:04Z","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":"e41457e32937d08d183b5ed067ae2d6f2280e8f426b14fdb455f2cac36268bce","cross_cats_sorted":["math.MP","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-12-06T09:43:16Z","title_canon_sha256":"ba5bd0bb9649d6f1eab8b8daa65de70f9ae0c4b7ce96c8b5e5706e5e29301aaa"},"schema_version":"1.0","source":{"id":"1212.1270","kind":"arxiv","version":1}},"canonical_sha256":"18fc4f62f60a2614347aa4dd06568fc7f86c01e848c6ce871fc16ad8d09dce37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18fc4f62f60a2614347aa4dd06568fc7f86c01e848c6ce871fc16ad8d09dce37","first_computed_at":"2026-05-18T03:39:04.384723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:04.384723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BcZLzupkEgqSG3WFbsPyClCSSLzvjhKSe43QsGkUFrFsott6xZJRWL8iW8hdr3i6r6keiWRcsAyGtFD6UzuNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:04.385253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af14431f6adbe5ac66dbf73cb9900d4b5e2bcaf358462d47d47caac4701c72ed","sha256:5ab63281d7ae02a1737c8db6faaabed9768b35e7dd94b389e1f9f05f74b46cad"],"state_sha256":"8973a33533e897530e80b066d8ea06a6f9896c171a1c428ed6d69509d86c990d"}