{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VHHRVMDGQURICZTMCNJM7H52VN","short_pith_number":"pith:VHHRVMDG","canonical_record":{"source":{"id":"2501.09956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-17T05:09:56Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"7c3ca7a01ba1997d0c812b8e84de26ced1f393c8fed697be0a8a7dd315e95036","abstract_canon_sha256":"fe56266921590492b85f73bfbac94a5fd29bf6f7747671a9947f491c1b30f298"},"schema_version":"1.0"},"canonical_sha256":"a9cf1ab066852281666c1352cf9fbaab640f6c8e99e1d0b333d9379faf3655a8","source":{"kind":"arxiv","id":"2501.09956","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.09956","created_at":"2026-07-05T10:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"2501.09956v1","created_at":"2026-07-05T10:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.09956","created_at":"2026-07-05T10:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"VHHRVMDGQURI","created_at":"2026-07-05T10:02:13Z"},{"alias_kind":"pith_short_16","alias_value":"VHHRVMDGQURICZTM","created_at":"2026-07-05T10:02:13Z"},{"alias_kind":"pith_short_8","alias_value":"VHHRVMDG","created_at":"2026-07-05T10:02:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VHHRVMDGQURICZTMCNJM7H52VN","target":"record","payload":{"canonical_record":{"source":{"id":"2501.09956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-17T05:09:56Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"7c3ca7a01ba1997d0c812b8e84de26ced1f393c8fed697be0a8a7dd315e95036","abstract_canon_sha256":"fe56266921590492b85f73bfbac94a5fd29bf6f7747671a9947f491c1b30f298"},"schema_version":"1.0"},"canonical_sha256":"a9cf1ab066852281666c1352cf9fbaab640f6c8e99e1d0b333d9379faf3655a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:02:13.906053Z","signature_b64":"NbyNCUPxb9PN5LV0aYtvOvoTMa3nbEbERUUzoOiEMR19tgH2vHKmaciXIExpXxs329RBYjrwpxZuL2os/UvDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9cf1ab066852281666c1352cf9fbaab640f6c8e99e1d0b333d9379faf3655a8","last_reissued_at":"2026-07-05T10:02:13.905613Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:02:13.905613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.09956","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":"2026-07-05T10:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gAyDirLbZethgKlODfflYos0CxiGRwp62C9fKcY03jfL8R8c1UaUo/ye8po5fthYYDw89TZK0/Che4JXUCc1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T16:44:37.308689Z"},"content_sha256":"b66e348e8fe2bd3a17afbe189887619eb82f2f89ac7a78c515ef06d84d0cd86d","schema_version":"1.0","event_id":"sha256:b66e348e8fe2bd3a17afbe189887619eb82f2f89ac7a78c515ef06d84d0cd86d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VHHRVMDGQURICZTMCNJM7H52VN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the local well-posedness of fractionally dissipated primitive equations with transport noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Quyuan Lin, Rongchang Liu, Ruimeng Hu","submitted_at":"2025-01-17T05:09:56Z","abstract_excerpt":"We investigate the three-dimensional fractionally dissipated primitive equations with transport noise, focusing on subcritical and critical dissipation regimes characterized by $ (-\\Delta)^{s/2} $ with $ s \\in (1,2)$ and $s = 1$, respectively. For $\\sigma>3$, we establish the local existence of unique pathwise solutions in Sobolev space $H^\\sigma$. This result applies to arbitrary initial data in the subcritical case ($s \\in(1,2)$), and to small initial data in the critical case ($s=1$). The analysis is particularly challenging due to the loss of horizontal derivatives in the nonlinear terms a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09956","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.09956/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":"2026-07-05T10:02:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cebmggTmgQYyguyBQB8cAxw4Zb0cGEUIGKesHVDx0esgWBAlHVJIt81Ehj2FynvDAUJRjuOy7R8SCzJ/RsZGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T16:44:37.309196Z"},"content_sha256":"116320699a20df3b8df2be7f9a411a11563a3f82b9bb1c0095b6622fba905310","schema_version":"1.0","event_id":"sha256:116320699a20df3b8df2be7f9a411a11563a3f82b9bb1c0095b6622fba905310"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VHHRVMDGQURICZTMCNJM7H52VN/bundle.json","state_url":"https://pith.science/pith/VHHRVMDGQURICZTMCNJM7H52VN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VHHRVMDGQURICZTMCNJM7H52VN/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":"2026-08-09T16:44:37Z","links":{"resolver":"https://pith.science/pith/VHHRVMDGQURICZTMCNJM7H52VN","bundle":"https://pith.science/pith/VHHRVMDGQURICZTMCNJM7H52VN/bundle.json","state":"https://pith.science/pith/VHHRVMDGQURICZTMCNJM7H52VN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VHHRVMDGQURICZTMCNJM7H52VN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VHHRVMDGQURICZTMCNJM7H52VN","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":"fe56266921590492b85f73bfbac94a5fd29bf6f7747671a9947f491c1b30f298","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-17T05:09:56Z","title_canon_sha256":"7c3ca7a01ba1997d0c812b8e84de26ced1f393c8fed697be0a8a7dd315e95036"},"schema_version":"1.0","source":{"id":"2501.09956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.09956","created_at":"2026-07-05T10:02:13Z"},{"alias_kind":"arxiv_version","alias_value":"2501.09956v1","created_at":"2026-07-05T10:02:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.09956","created_at":"2026-07-05T10:02:13Z"},{"alias_kind":"pith_short_12","alias_value":"VHHRVMDGQURI","created_at":"2026-07-05T10:02:13Z"},{"alias_kind":"pith_short_16","alias_value":"VHHRVMDGQURICZTM","created_at":"2026-07-05T10:02:13Z"},{"alias_kind":"pith_short_8","alias_value":"VHHRVMDG","created_at":"2026-07-05T10:02:13Z"}],"graph_snapshots":[{"event_id":"sha256:116320699a20df3b8df2be7f9a411a11563a3f82b9bb1c0095b6622fba905310","target":"graph","created_at":"2026-07-05T10:02:13Z","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/2501.09956/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the three-dimensional fractionally dissipated primitive equations with transport noise, focusing on subcritical and critical dissipation regimes characterized by $ (-\\Delta)^{s/2} $ with $ s \\in (1,2)$ and $s = 1$, respectively. For $\\sigma>3$, we establish the local existence of unique pathwise solutions in Sobolev space $H^\\sigma$. This result applies to arbitrary initial data in the subcritical case ($s \\in(1,2)$), and to small initial data in the critical case ($s=1$). The analysis is particularly challenging due to the loss of horizontal derivatives in the nonlinear terms a","authors_text":"Quyuan Lin, Rongchang Liu, Ruimeng Hu","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-17T05:09:56Z","title":"On the local well-posedness of fractionally dissipated primitive equations with transport noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09956","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:b66e348e8fe2bd3a17afbe189887619eb82f2f89ac7a78c515ef06d84d0cd86d","target":"record","created_at":"2026-07-05T10:02:13Z","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":"fe56266921590492b85f73bfbac94a5fd29bf6f7747671a9947f491c1b30f298","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-01-17T05:09:56Z","title_canon_sha256":"7c3ca7a01ba1997d0c812b8e84de26ced1f393c8fed697be0a8a7dd315e95036"},"schema_version":"1.0","source":{"id":"2501.09956","kind":"arxiv","version":1}},"canonical_sha256":"a9cf1ab066852281666c1352cf9fbaab640f6c8e99e1d0b333d9379faf3655a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9cf1ab066852281666c1352cf9fbaab640f6c8e99e1d0b333d9379faf3655a8","first_computed_at":"2026-07-05T10:02:13.905613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:02:13.905613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NbyNCUPxb9PN5LV0aYtvOvoTMa3nbEbERUUzoOiEMR19tgH2vHKmaciXIExpXxs329RBYjrwpxZuL2os/UvDDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:02:13.906053Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.09956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b66e348e8fe2bd3a17afbe189887619eb82f2f89ac7a78c515ef06d84d0cd86d","sha256:116320699a20df3b8df2be7f9a411a11563a3f82b9bb1c0095b6622fba905310"],"state_sha256":"8e9b8ec232220313197212ee1dc628e0ceba8d72a879f4a4297e9329fb471c0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qiyh77tAMgnTKAS9LMAbthdoShmO5LE5wOYpJM1gKQg7V+I7FVyoiTs/dmVPqESegZjWnrgQv2UkqzP6SsdLCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T16:44:37.313081Z","bundle_sha256":"344fe6a948af5cfbbe5f9a03aa9f42e7d35ed660e7ba7b0266b31fa3e683f4a4"}}