{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2WVFSUGYNJ3KZ6FAOE5YDZDA2H","short_pith_number":"pith:2WVFSUGY","canonical_record":{"source":{"id":"1112.3019","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-13T20:19:27Z","cross_cats_sorted":["math.MP","physics.ao-ph","physics.flu-dyn"],"title_canon_sha256":"37c099ed79312d13b86bcd56f798b127d4d896e766bdda7139c6779b4be4ecef","abstract_canon_sha256":"fead3fc0bcfdec01ed3d5bf87a3c9b1059732d377a61066d2f622341f29a5edf"},"schema_version":"1.0"},"canonical_sha256":"d5aa5950d86a76acf8a0713b81e460d1f2d4dd8665349c2c0a79bc822f9655d8","source":{"kind":"arxiv","id":"1112.3019","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3019","created_at":"2026-05-18T01:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3019v2","created_at":"2026-05-18T01:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3019","created_at":"2026-05-18T01:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"2WVFSUGYNJ3K","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2WVFSUGYNJ3KZ6FA","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2WVFSUGY","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2WVFSUGYNJ3KZ6FAOE5YDZDA2H","target":"record","payload":{"canonical_record":{"source":{"id":"1112.3019","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-13T20:19:27Z","cross_cats_sorted":["math.MP","physics.ao-ph","physics.flu-dyn"],"title_canon_sha256":"37c099ed79312d13b86bcd56f798b127d4d896e766bdda7139c6779b4be4ecef","abstract_canon_sha256":"fead3fc0bcfdec01ed3d5bf87a3c9b1059732d377a61066d2f622341f29a5edf"},"schema_version":"1.0"},"canonical_sha256":"d5aa5950d86a76acf8a0713b81e460d1f2d4dd8665349c2c0a79bc822f9655d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:10.635289Z","signature_b64":"DO2SNTG/mYHNNYE08iWgO/rmenUlfPkhKRRg5r36ke0JtxyLWTym+np6Ew5EQ1LF9Bs0YehP7VQScllEcFO5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5aa5950d86a76acf8a0713b81e460d1f2d4dd8665349c2c0a79bc822f9655d8","last_reissued_at":"2026-05-18T01:59:10.634540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:10.634540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.3019","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NlNWoNRQGenzMDPTBGRrYjgS2Zu2tjqZ6wB1gMGg4hiEo1wWE565Sk/l9Z/9jCfA/d+LSXez5FypiS4Nr4sKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:51:51.701659Z"},"content_sha256":"eb0fdb7fb2003ac7149a96fa749ca4d44bcfbfd40cdaa5f97fcf262ea0b3b5a2","schema_version":"1.0","event_id":"sha256:eb0fdb7fb2003ac7149a96fa749ca4d44bcfbfd40cdaa5f97fcf262ea0b3b5a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2WVFSUGYNJ3KZ6FAOE5YDZDA2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lie reduction and exact solutions of vorticity equation on rotating sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.ao-ph","physics.flu-dyn"],"primary_cat":"math-ph","authors_text":"Alexander Bihlo, Roman O. Popovych","submitted_at":"2011-12-13T20:19:27Z","abstract_excerpt":"Following our paper [J. Math. Phys. 50 (2009) 123102], we systematically carry out Lie symmetry analysis for the barotropic vorticity equation on the rotating sphere. All finite-dimensional subalgebras of the corresponding maximal Lie invariance algebra, which is infinite-dimensional, are classified. Appropriate subalgebras are then used to exhaustively determine Lie reductions of the equation under consideration. The relevance of the constructed exact solutions for the description of real-world physical processes is discussed. It is shown that the results of the above paper are directly relat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3019","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QYuPNyPwR+11LlKpqt044ZsMryfxxjolIE9XpSQ75mpKvALn/q1nNk6TN4dT0OIM80Gr9s608yjofZ4mgPqkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:51:51.702301Z"},"content_sha256":"ea957371c3449ebd3a60d36eeb28ce159bc6686e9de727acb4ac533d43d0fef9","schema_version":"1.0","event_id":"sha256:ea957371c3449ebd3a60d36eeb28ce159bc6686e9de727acb4ac533d43d0fef9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2WVFSUGYNJ3KZ6FAOE5YDZDA2H/bundle.json","state_url":"https://pith.science/pith/2WVFSUGYNJ3KZ6FAOE5YDZDA2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2WVFSUGYNJ3KZ6FAOE5YDZDA2H/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":"2026-05-27T07:51:51Z","links":{"resolver":"https://pith.science/pith/2WVFSUGYNJ3KZ6FAOE5YDZDA2H","bundle":"https://pith.science/pith/2WVFSUGYNJ3KZ6FAOE5YDZDA2H/bundle.json","state":"https://pith.science/pith/2WVFSUGYNJ3KZ6FAOE5YDZDA2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2WVFSUGYNJ3KZ6FAOE5YDZDA2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2WVFSUGYNJ3KZ6FAOE5YDZDA2H","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":"fead3fc0bcfdec01ed3d5bf87a3c9b1059732d377a61066d2f622341f29a5edf","cross_cats_sorted":["math.MP","physics.ao-ph","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-13T20:19:27Z","title_canon_sha256":"37c099ed79312d13b86bcd56f798b127d4d896e766bdda7139c6779b4be4ecef"},"schema_version":"1.0","source":{"id":"1112.3019","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3019","created_at":"2026-05-18T01:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3019v2","created_at":"2026-05-18T01:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3019","created_at":"2026-05-18T01:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"2WVFSUGYNJ3K","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2WVFSUGYNJ3KZ6FA","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2WVFSUGY","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:ea957371c3449ebd3a60d36eeb28ce159bc6686e9de727acb4ac533d43d0fef9","target":"graph","created_at":"2026-05-18T01:59:10Z","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":"Following our paper [J. Math. Phys. 50 (2009) 123102], we systematically carry out Lie symmetry analysis for the barotropic vorticity equation on the rotating sphere. All finite-dimensional subalgebras of the corresponding maximal Lie invariance algebra, which is infinite-dimensional, are classified. Appropriate subalgebras are then used to exhaustively determine Lie reductions of the equation under consideration. The relevance of the constructed exact solutions for the description of real-world physical processes is discussed. It is shown that the results of the above paper are directly relat","authors_text":"Alexander Bihlo, Roman O. Popovych","cross_cats":["math.MP","physics.ao-ph","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-13T20:19:27Z","title":"Lie reduction and exact solutions of vorticity equation on rotating sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3019","kind":"arxiv","version":2},"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:eb0fdb7fb2003ac7149a96fa749ca4d44bcfbfd40cdaa5f97fcf262ea0b3b5a2","target":"record","created_at":"2026-05-18T01:59:10Z","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":"fead3fc0bcfdec01ed3d5bf87a3c9b1059732d377a61066d2f622341f29a5edf","cross_cats_sorted":["math.MP","physics.ao-ph","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-13T20:19:27Z","title_canon_sha256":"37c099ed79312d13b86bcd56f798b127d4d896e766bdda7139c6779b4be4ecef"},"schema_version":"1.0","source":{"id":"1112.3019","kind":"arxiv","version":2}},"canonical_sha256":"d5aa5950d86a76acf8a0713b81e460d1f2d4dd8665349c2c0a79bc822f9655d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5aa5950d86a76acf8a0713b81e460d1f2d4dd8665349c2c0a79bc822f9655d8","first_computed_at":"2026-05-18T01:59:10.634540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:10.634540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DO2SNTG/mYHNNYE08iWgO/rmenUlfPkhKRRg5r36ke0JtxyLWTym+np6Ew5EQ1LF9Bs0YehP7VQScllEcFO5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:10.635289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3019","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb0fdb7fb2003ac7149a96fa749ca4d44bcfbfd40cdaa5f97fcf262ea0b3b5a2","sha256:ea957371c3449ebd3a60d36eeb28ce159bc6686e9de727acb4ac533d43d0fef9"],"state_sha256":"7eea3edfe8dc75e18bb94a3fb8ef7b990fa8ae5d6b13c031538380816195974a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ySwafPk9iXyn96okE0D1xobHkB1kDqgxs9cVVapuhpeOUsi2QLWeaDnDU8em9njQgafZUi9NtZ5DeZsrHpGqBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:51:51.705600Z","bundle_sha256":"201bc8d0b0530d27bbf3d89c12d9177433cdd874d7f4b2045288a3d33ee0f6db"}}