{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BO3X3IBU2TJWSANAXBDLNJZIAY","short_pith_number":"pith:BO3X3IBU","canonical_record":{"source":{"id":"2504.09423","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-04-13T04:12:03Z","cross_cats_sorted":[],"title_canon_sha256":"eb888960da9b68ef6460a7f09209b938f2d7e679380483a1fcfd6ddb60ddbbe2","abstract_canon_sha256":"a51bc6404e5c6ae2d07f6b48aa839a5286e0917ec10e52e7b91c6762e3b05de8"},"schema_version":"1.0"},"canonical_sha256":"0bb77da034d4d36901a0b846b6a728062ef96431446efdecae7a22be3f8fc6b9","source":{"kind":"arxiv","id":"2504.09423","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.09423","created_at":"2026-05-26T02:05:00Z"},{"alias_kind":"arxiv_version","alias_value":"2504.09423v2","created_at":"2026-05-26T02:05:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09423","created_at":"2026-05-26T02:05:00Z"},{"alias_kind":"pith_short_12","alias_value":"BO3X3IBU2TJW","created_at":"2026-05-26T02:05:00Z"},{"alias_kind":"pith_short_16","alias_value":"BO3X3IBU2TJWSANA","created_at":"2026-05-26T02:05:00Z"},{"alias_kind":"pith_short_8","alias_value":"BO3X3IBU","created_at":"2026-05-26T02:05:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BO3X3IBU2TJWSANAXBDLNJZIAY","target":"record","payload":{"canonical_record":{"source":{"id":"2504.09423","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-04-13T04:12:03Z","cross_cats_sorted":[],"title_canon_sha256":"eb888960da9b68ef6460a7f09209b938f2d7e679380483a1fcfd6ddb60ddbbe2","abstract_canon_sha256":"a51bc6404e5c6ae2d07f6b48aa839a5286e0917ec10e52e7b91c6762e3b05de8"},"schema_version":"1.0"},"canonical_sha256":"0bb77da034d4d36901a0b846b6a728062ef96431446efdecae7a22be3f8fc6b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:05:00.163302Z","signature_b64":"gU8gknYqlZNZZJQyZwmiiJxDtOpDYHcWPvsR/ZUjvDGlO2nrXoFAnurvTRCvp8UdgyG7q/dvMOddruDiz+/HDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bb77da034d4d36901a0b846b6a728062ef96431446efdecae7a22be3f8fc6b9","last_reissued_at":"2026-05-26T02:05:00.162793Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:05:00.162793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.09423","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":"2026-05-26T02:05:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1khn+P08N1tdg8Q1vU2f0124CJWSyYTih1R6a6O/9Pjtse0/TkJk0VUBUmACmhqhlfTi0TGss9iEFRIjPk/SDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:41:59.836190Z"},"content_sha256":"6a7cd2fa8bae407ac407a85fb872dfae060c59ad0fc1648cd0f832ce777be85b","schema_version":"1.0","event_id":"sha256:6a7cd2fa8bae407ac407a85fb872dfae060c59ad0fc1648cd0f832ce777be85b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BO3X3IBU2TJWSANAXBDLNJZIAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some new Liouville type theorems for 3D steady tropical climate model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yan Fang, Yanyan Dong, Zhibing Zhang","submitted_at":"2025-04-13T04:12:03Z","abstract_excerpt":"In this paper, we establish two major classes of Liouville type results for the three-dimensional stationary tropical climate model. The first class is obtained under the assumptions imposed on $u,v,\\theta$ whereas the second one relies on the assumptions imposed on $u,v,\\nabla\\theta$. Using the energy method and an iteration argument, we obtain Liouville type theorems under the condition that Lebesgue norms of the smooth solutions on the annulus satisfy some power-law growth conditions. As a consequence, we show that a smooth solution is trivial provided that it belongs to some Lebesgue space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09423","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.09423/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-26T02:05:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QFX7fzb8urh8ty5Fni5P4b7787+4Exg53U4GR1CPy5aNsSXav4Bz6NLkJLQLkj0o/ewvFGnkG9qyNBdFUhYnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:41:59.836586Z"},"content_sha256":"1e1fb20025e21a32490ab70fdf01323b23d88b43a1993f9f6fd448f228d327a7","schema_version":"1.0","event_id":"sha256:1e1fb20025e21a32490ab70fdf01323b23d88b43a1993f9f6fd448f228d327a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BO3X3IBU2TJWSANAXBDLNJZIAY/bundle.json","state_url":"https://pith.science/pith/BO3X3IBU2TJWSANAXBDLNJZIAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BO3X3IBU2TJWSANAXBDLNJZIAY/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":"2026-06-22T23:41:59Z","links":{"resolver":"https://pith.science/pith/BO3X3IBU2TJWSANAXBDLNJZIAY","bundle":"https://pith.science/pith/BO3X3IBU2TJWSANAXBDLNJZIAY/bundle.json","state":"https://pith.science/pith/BO3X3IBU2TJWSANAXBDLNJZIAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BO3X3IBU2TJWSANAXBDLNJZIAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BO3X3IBU2TJWSANAXBDLNJZIAY","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":"a51bc6404e5c6ae2d07f6b48aa839a5286e0917ec10e52e7b91c6762e3b05de8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-04-13T04:12:03Z","title_canon_sha256":"eb888960da9b68ef6460a7f09209b938f2d7e679380483a1fcfd6ddb60ddbbe2"},"schema_version":"1.0","source":{"id":"2504.09423","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.09423","created_at":"2026-05-26T02:05:00Z"},{"alias_kind":"arxiv_version","alias_value":"2504.09423v2","created_at":"2026-05-26T02:05:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.09423","created_at":"2026-05-26T02:05:00Z"},{"alias_kind":"pith_short_12","alias_value":"BO3X3IBU2TJW","created_at":"2026-05-26T02:05:00Z"},{"alias_kind":"pith_short_16","alias_value":"BO3X3IBU2TJWSANA","created_at":"2026-05-26T02:05:00Z"},{"alias_kind":"pith_short_8","alias_value":"BO3X3IBU","created_at":"2026-05-26T02:05:00Z"}],"graph_snapshots":[{"event_id":"sha256:1e1fb20025e21a32490ab70fdf01323b23d88b43a1993f9f6fd448f228d327a7","target":"graph","created_at":"2026-05-26T02:05:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.09423/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we establish two major classes of Liouville type results for the three-dimensional stationary tropical climate model. The first class is obtained under the assumptions imposed on $u,v,\\theta$ whereas the second one relies on the assumptions imposed on $u,v,\\nabla\\theta$. Using the energy method and an iteration argument, we obtain Liouville type theorems under the condition that Lebesgue norms of the smooth solutions on the annulus satisfy some power-law growth conditions. As a consequence, we show that a smooth solution is trivial provided that it belongs to some Lebesgue space","authors_text":"Yan Fang, Yanyan Dong, Zhibing Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-04-13T04:12:03Z","title":"Some new Liouville type theorems for 3D steady tropical climate model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09423","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":"sha256:6a7cd2fa8bae407ac407a85fb872dfae060c59ad0fc1648cd0f832ce777be85b","target":"record","created_at":"2026-05-26T02:05:00Z","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":"a51bc6404e5c6ae2d07f6b48aa839a5286e0917ec10e52e7b91c6762e3b05de8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-04-13T04:12:03Z","title_canon_sha256":"eb888960da9b68ef6460a7f09209b938f2d7e679380483a1fcfd6ddb60ddbbe2"},"schema_version":"1.0","source":{"id":"2504.09423","kind":"arxiv","version":2}},"canonical_sha256":"0bb77da034d4d36901a0b846b6a728062ef96431446efdecae7a22be3f8fc6b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bb77da034d4d36901a0b846b6a728062ef96431446efdecae7a22be3f8fc6b9","first_computed_at":"2026-05-26T02:05:00.162793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:05:00.162793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gU8gknYqlZNZZJQyZwmiiJxDtOpDYHcWPvsR/ZUjvDGlO2nrXoFAnurvTRCvp8UdgyG7q/dvMOddruDiz+/HDQ==","signature_status":"signed_v1","signed_at":"2026-05-26T02:05:00.163302Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.09423","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a7cd2fa8bae407ac407a85fb872dfae060c59ad0fc1648cd0f832ce777be85b","sha256:1e1fb20025e21a32490ab70fdf01323b23d88b43a1993f9f6fd448f228d327a7"],"state_sha256":"925fa5b782f28c5ca754cef6e7ff2aa006196337e82ba70e8a0928d939eff8a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NXFWvnnfzQpDSYoJoxG+geLbhepdTK8dXBbCdsIUmdsHScTxRmoS7HbH7Ma2APh4A7Owybhb7s52gOCFYxN9AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:41:59.838694Z","bundle_sha256":"6599a34a7cbe7fadc26c757f1eaf96355a3e40635019531f4bcdb6c7ced8e8a1"}}