{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RDTXOEHIYQPMLXMM6XN3BOT6RU","short_pith_number":"pith:RDTXOEHI","canonical_record":{"source":{"id":"1112.1283","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-06T14:18:59Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"11d2d4d0b740d8f8c1d67a473d328f468d9de156ab6238a742883c23ebd93372","abstract_canon_sha256":"60c8314e31fe222bd32c06675736fafad9cd05ef7dbb5a2100f5089581a9edf4"},"schema_version":"1.0"},"canonical_sha256":"88e77710e8c41ec5dd8cf5dbb0ba7e8d1eee809e9324159b06481f46576ba836","source":{"kind":"arxiv","id":"1112.1283","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1283","created_at":"2026-05-18T04:06:55Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1283v1","created_at":"2026-05-18T04:06:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1283","created_at":"2026-05-18T04:06:55Z"},{"alias_kind":"pith_short_12","alias_value":"RDTXOEHIYQPM","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RDTXOEHIYQPMLXMM","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RDTXOEHI","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RDTXOEHIYQPMLXMM6XN3BOT6RU","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1283","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-06T14:18:59Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"11d2d4d0b740d8f8c1d67a473d328f468d9de156ab6238a742883c23ebd93372","abstract_canon_sha256":"60c8314e31fe222bd32c06675736fafad9cd05ef7dbb5a2100f5089581a9edf4"},"schema_version":"1.0"},"canonical_sha256":"88e77710e8c41ec5dd8cf5dbb0ba7e8d1eee809e9324159b06481f46576ba836","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:55.812836Z","signature_b64":"kThB4EJaviRcj/u1d2mO8bm7pbFJJn0KG/dKrwM4IHTwbon2GkWGPP+VAPMWcKKOXHTRSdzKhxRHrDVOj7sOAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88e77710e8c41ec5dd8cf5dbb0ba7e8d1eee809e9324159b06481f46576ba836","last_reissued_at":"2026-05-18T04:06:55.812017Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:55.812017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1283","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":"2026-05-18T04:06:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E9n2gBD0Xw/faot6ouLzjeM5yc1GqsZG0f42PMPIngPD97SZxo6IbjDNZG4nl+DRZ3dJLOubENgebSqosMjSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T11:08:31.871293Z"},"content_sha256":"9889f65fb16f9fc2b828ca104582b2df5d96c9c18cb92b42396acd1967902604","schema_version":"1.0","event_id":"sha256:9889f65fb16f9fc2b828ca104582b2df5d96c9c18cb92b42396acd1967902604"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RDTXOEHIYQPMLXMM6XN3BOT6RU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytical Solution of Second Stokes Problem on Behavior of Gas over Oscillation Surface. Part III: Solving of Problem and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. A. Yushkanov, A. V. Latyshev, V. A. Akimova","submitted_at":"2011-12-06T14:18:59Z","abstract_excerpt":"The second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane, limiting half-space, makes harmonious oscillations in the plane. The kinetic equation with model integral of collisions in the form $ \\tau $ - model is used. The case of diffusive reflection of molecules of gas from a wall is considered. There are eigen solutions (continuous modes) the initial kinetic equation, corresponding to the continuous spectrum. Properties of dispersion function are studied. The discrete spectrum of this problem consisting of zeroes of dispersion function in complex "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1283","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":"2026-05-18T04:06:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EtP8nRyltg2MrfKp8tAVck5Myy+CzOC4kcgZEfY5BGgF+CAGc1GtKoc+vsAaEw8aTquFd1LQ5QtOSX/WPhrgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T11:08:31.871655Z"},"content_sha256":"a11d9ecf920382cf2aa8db96a2e6c3c2bc017d86bf633cf7d19c8256bec353ce","schema_version":"1.0","event_id":"sha256:a11d9ecf920382cf2aa8db96a2e6c3c2bc017d86bf633cf7d19c8256bec353ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RDTXOEHIYQPMLXMM6XN3BOT6RU/bundle.json","state_url":"https://pith.science/pith/RDTXOEHIYQPMLXMM6XN3BOT6RU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RDTXOEHIYQPMLXMM6XN3BOT6RU/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":"2026-07-01T11:08:31Z","links":{"resolver":"https://pith.science/pith/RDTXOEHIYQPMLXMM6XN3BOT6RU","bundle":"https://pith.science/pith/RDTXOEHIYQPMLXMM6XN3BOT6RU/bundle.json","state":"https://pith.science/pith/RDTXOEHIYQPMLXMM6XN3BOT6RU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RDTXOEHIYQPMLXMM6XN3BOT6RU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RDTXOEHIYQPMLXMM6XN3BOT6RU","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":"60c8314e31fe222bd32c06675736fafad9cd05ef7dbb5a2100f5089581a9edf4","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-06T14:18:59Z","title_canon_sha256":"11d2d4d0b740d8f8c1d67a473d328f468d9de156ab6238a742883c23ebd93372"},"schema_version":"1.0","source":{"id":"1112.1283","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1283","created_at":"2026-05-18T04:06:55Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1283v1","created_at":"2026-05-18T04:06:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1283","created_at":"2026-05-18T04:06:55Z"},{"alias_kind":"pith_short_12","alias_value":"RDTXOEHIYQPM","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RDTXOEHIYQPMLXMM","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RDTXOEHI","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:a11d9ecf920382cf2aa8db96a2e6c3c2bc017d86bf633cf7d19c8256bec353ce","target":"graph","created_at":"2026-05-18T04:06:55Z","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 second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane, limiting half-space, makes harmonious oscillations in the plane. The kinetic equation with model integral of collisions in the form $ \\tau $ - model is used. The case of diffusive reflection of molecules of gas from a wall is considered. There are eigen solutions (continuous modes) the initial kinetic equation, corresponding to the continuous spectrum. Properties of dispersion function are studied. The discrete spectrum of this problem consisting of zeroes of dispersion function in complex ","authors_text":"A. A. Yushkanov, A. V. Latyshev, V. A. Akimova","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-06T14:18:59Z","title":"Analytical Solution of Second Stokes Problem on Behavior of Gas over Oscillation Surface. Part III: Solving of Problem and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1283","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":"sha256:9889f65fb16f9fc2b828ca104582b2df5d96c9c18cb92b42396acd1967902604","target":"record","created_at":"2026-05-18T04:06:55Z","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":"60c8314e31fe222bd32c06675736fafad9cd05ef7dbb5a2100f5089581a9edf4","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-06T14:18:59Z","title_canon_sha256":"11d2d4d0b740d8f8c1d67a473d328f468d9de156ab6238a742883c23ebd93372"},"schema_version":"1.0","source":{"id":"1112.1283","kind":"arxiv","version":1}},"canonical_sha256":"88e77710e8c41ec5dd8cf5dbb0ba7e8d1eee809e9324159b06481f46576ba836","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88e77710e8c41ec5dd8cf5dbb0ba7e8d1eee809e9324159b06481f46576ba836","first_computed_at":"2026-05-18T04:06:55.812017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:55.812017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kThB4EJaviRcj/u1d2mO8bm7pbFJJn0KG/dKrwM4IHTwbon2GkWGPP+VAPMWcKKOXHTRSdzKhxRHrDVOj7sOAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:55.812836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1283","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9889f65fb16f9fc2b828ca104582b2df5d96c9c18cb92b42396acd1967902604","sha256:a11d9ecf920382cf2aa8db96a2e6c3c2bc017d86bf633cf7d19c8256bec353ce"],"state_sha256":"08065b84d64f063f684adec45c139699ae26a9246b5bb1b0b7940e52cd0df7a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+ng/w/1Jsc266aL30te/Y55/wPr1xudF/BR50CETDP3meY558mCUa/cyOwWyPFtSV141ybXV0JX1t3mp+DmAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T11:08:31.873580Z","bundle_sha256":"20bebac0029e0cad31bb54c3b1de1f1cd2bc24889525958762517780f5f4efe6"}}