{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LRGFWHKRPQWZAPGACAUSIBSY42","short_pith_number":"pith:LRGFWHKR","canonical_record":{"source":{"id":"1409.7040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-24T18:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"aaa7fae28ee361ca8a0f76f67897fa0b1710d126e028bf4aef3f5103e9627755","abstract_canon_sha256":"e6775357a8f58139a4d7d3807e3e21755f1af106333c4db473033e0c16b8a436"},"schema_version":"1.0"},"canonical_sha256":"5c4c5b1d517c2d903cc01029240658e695604189924fbdfd26e9106ab94fff54","source":{"kind":"arxiv","id":"1409.7040","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7040","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7040v2","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7040","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"LRGFWHKRPQWZ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LRGFWHKRPQWZAPGA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LRGFWHKR","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LRGFWHKRPQWZAPGACAUSIBSY42","target":"record","payload":{"canonical_record":{"source":{"id":"1409.7040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-24T18:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"aaa7fae28ee361ca8a0f76f67897fa0b1710d126e028bf4aef3f5103e9627755","abstract_canon_sha256":"e6775357a8f58139a4d7d3807e3e21755f1af106333c4db473033e0c16b8a436"},"schema_version":"1.0"},"canonical_sha256":"5c4c5b1d517c2d903cc01029240658e695604189924fbdfd26e9106ab94fff54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:44.259345Z","signature_b64":"Hra6PbIOaKKrGeYfbcF1Knt60uc8OAQvR5lujfzZ493ORgwJbeMbex1fICK24XwkVcf3O8VDcUK+c70kvv32Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c4c5b1d517c2d903cc01029240658e695604189924fbdfd26e9106ab94fff54","last_reissued_at":"2026-05-18T01:17:44.258622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:44.258622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.7040","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":"2026-05-18T01:17:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tPM+boRVuzQooJYxhCgKHPeatAQOB+405miKhztmn6YT3uCzITiyBDNdJ1hHLqg62Ns0z9MNgrKtqJnP0NZwBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T12:32:28.787054Z"},"content_sha256":"58b5e879fd5548a0e2af2dcd64253d82ed62614ee4e9990e089c03b2b101ebd0","schema_version":"1.0","event_id":"sha256:58b5e879fd5548a0e2af2dcd64253d82ed62614ee4e9990e089c03b2b101ebd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LRGFWHKRPQWZAPGACAUSIBSY42","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angel Castro, Diego C\\'ordoba, Javier G\\'omez-Serrano","submitted_at":"2014-09-24T18:41:59Z","abstract_excerpt":"Motivated by the recent work of Hassainia and Hmidi [Z. Hassainia, T. Hmidi - On the {V}-states for the generalized quasi-geostrophic equations,arXiv preprint arXiv:1405.0858], we close the question of the existence of convex global rotating solutions for the generalized surface quasi-geostrophic equation for $\\alpha \\in [1,2)$. We also show $C^{\\infty}$ regularity of their boundary for all $\\alpha \\in (0,2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7040","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":"2026-05-18T01:17:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cMsG53kdDid12LqRt4Jxssyw9MEkmED+MKAQ968E8HAKuF26Z0THhTaUcseezwvUUjRkc5WIQnHnHDzW8q2MDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T12:32:28.787408Z"},"content_sha256":"ca06b6e3567a9da26d2e33355dfca00ea13fab9c57b9cd238ac66c1e242a0b4b","schema_version":"1.0","event_id":"sha256:ca06b6e3567a9da26d2e33355dfca00ea13fab9c57b9cd238ac66c1e242a0b4b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LRGFWHKRPQWZAPGACAUSIBSY42/bundle.json","state_url":"https://pith.science/pith/LRGFWHKRPQWZAPGACAUSIBSY42/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LRGFWHKRPQWZAPGACAUSIBSY42/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":"2026-07-03T12:32:28Z","links":{"resolver":"https://pith.science/pith/LRGFWHKRPQWZAPGACAUSIBSY42","bundle":"https://pith.science/pith/LRGFWHKRPQWZAPGACAUSIBSY42/bundle.json","state":"https://pith.science/pith/LRGFWHKRPQWZAPGACAUSIBSY42/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LRGFWHKRPQWZAPGACAUSIBSY42/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LRGFWHKRPQWZAPGACAUSIBSY42","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":"e6775357a8f58139a4d7d3807e3e21755f1af106333c4db473033e0c16b8a436","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-24T18:41:59Z","title_canon_sha256":"aaa7fae28ee361ca8a0f76f67897fa0b1710d126e028bf4aef3f5103e9627755"},"schema_version":"1.0","source":{"id":"1409.7040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7040","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7040v2","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7040","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"LRGFWHKRPQWZ","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LRGFWHKRPQWZAPGA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LRGFWHKR","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:ca06b6e3567a9da26d2e33355dfca00ea13fab9c57b9cd238ac66c1e242a0b4b","target":"graph","created_at":"2026-05-18T01:17:44Z","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":"Motivated by the recent work of Hassainia and Hmidi [Z. Hassainia, T. Hmidi - On the {V}-states for the generalized quasi-geostrophic equations,arXiv preprint arXiv:1405.0858], we close the question of the existence of convex global rotating solutions for the generalized surface quasi-geostrophic equation for $\\alpha \\in [1,2)$. We also show $C^{\\infty}$ regularity of their boundary for all $\\alpha \\in (0,2)$.","authors_text":"Angel Castro, Diego C\\'ordoba, Javier G\\'omez-Serrano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-24T18:41:59Z","title":"Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7040","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":"sha256:58b5e879fd5548a0e2af2dcd64253d82ed62614ee4e9990e089c03b2b101ebd0","target":"record","created_at":"2026-05-18T01:17:44Z","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":"e6775357a8f58139a4d7d3807e3e21755f1af106333c4db473033e0c16b8a436","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-24T18:41:59Z","title_canon_sha256":"aaa7fae28ee361ca8a0f76f67897fa0b1710d126e028bf4aef3f5103e9627755"},"schema_version":"1.0","source":{"id":"1409.7040","kind":"arxiv","version":2}},"canonical_sha256":"5c4c5b1d517c2d903cc01029240658e695604189924fbdfd26e9106ab94fff54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c4c5b1d517c2d903cc01029240658e695604189924fbdfd26e9106ab94fff54","first_computed_at":"2026-05-18T01:17:44.258622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:44.258622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hra6PbIOaKKrGeYfbcF1Knt60uc8OAQvR5lujfzZ493ORgwJbeMbex1fICK24XwkVcf3O8VDcUK+c70kvv32Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:44.259345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58b5e879fd5548a0e2af2dcd64253d82ed62614ee4e9990e089c03b2b101ebd0","sha256:ca06b6e3567a9da26d2e33355dfca00ea13fab9c57b9cd238ac66c1e242a0b4b"],"state_sha256":"7c65ce162286689d328f2684780dbb3dbb95ca85ad111deabf511a3a6e8e28da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hnNPa3MwPmupTP82XaEtibjzy5wAzWmevgrRSzOnVFL+BfVEgqzw375CyXPek0Og6D0ISsGx3WHk4Djhw5grBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T12:32:28.789216Z","bundle_sha256":"8d5b9a3a4cedfed645a399f9340618d1c5a2af6ab50d3c5144496dc692d9cd86"}}