{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:D3AJU3GSCWUKW4C7YY2UHHEO5U","short_pith_number":"pith:D3AJU3GS","canonical_record":{"source":{"id":"2404.02541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-03T07:58:24Z","cross_cats_sorted":[],"title_canon_sha256":"492d2662fd9b2852963522c801e66bc40f98fc9d675adcefd7ec2b9c1a843875","abstract_canon_sha256":"def5a193aeb5f3c81728205c4ff80152789260c71ca6f3780db42412b192bedf"},"schema_version":"1.0"},"canonical_sha256":"1ec09a6cd215a8ab705fc635439c8eed1e8589502f932f162e7c659720c277d6","source":{"kind":"arxiv","id":"2404.02541","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.02541","created_at":"2026-07-05T08:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"2404.02541v1","created_at":"2026-07-05T08:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.02541","created_at":"2026-07-05T08:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"D3AJU3GSCWUK","created_at":"2026-07-05T08:03:57Z"},{"alias_kind":"pith_short_16","alias_value":"D3AJU3GSCWUKW4C7","created_at":"2026-07-05T08:03:57Z"},{"alias_kind":"pith_short_8","alias_value":"D3AJU3GS","created_at":"2026-07-05T08:03:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:D3AJU3GSCWUKW4C7YY2UHHEO5U","target":"record","payload":{"canonical_record":{"source":{"id":"2404.02541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-03T07:58:24Z","cross_cats_sorted":[],"title_canon_sha256":"492d2662fd9b2852963522c801e66bc40f98fc9d675adcefd7ec2b9c1a843875","abstract_canon_sha256":"def5a193aeb5f3c81728205c4ff80152789260c71ca6f3780db42412b192bedf"},"schema_version":"1.0"},"canonical_sha256":"1ec09a6cd215a8ab705fc635439c8eed1e8589502f932f162e7c659720c277d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:03:57.957583Z","signature_b64":"NloGz7TWy85exNGj7V//WWyDAhxN0ogXjAdCK0vPqKBvYr0SCLHvIcucaWhM0+z6nVo+4ArcqEJ+uMNydFEQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ec09a6cd215a8ab705fc635439c8eed1e8589502f932f162e7c659720c277d6","last_reissued_at":"2026-07-05T08:03:57.957153Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:03:57.957153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.02541","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":"2026-07-05T08:03:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I2jnCFUgBhxk4vzH3I2oZHuCCztjrJ7s3XeEZPG1uG2yH9q5qoJQRapuRAeXxggVxpIPwGHkyo/5RnxYOVpHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T12:37:42.828666Z"},"content_sha256":"cc04d10c99197629ff0c6819083175da9c7ff2d14f9d6f1905a9484c5601f60b","schema_version":"1.0","event_id":"sha256:cc04d10c99197629ff0c6819083175da9c7ff2d14f9d6f1905a9484c5601f60b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:D3AJU3GSCWUKW4C7YY2UHHEO5U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global well-posedness for 2D inhomogeneous viscous flows with rough data via dynamic interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"LJLL), Rapha\\\"el Danchin (LAMA","submitted_at":"2024-04-03T07:58:24Z","abstract_excerpt":"We consider the evolution of two-dimensional incompressible flows with variable density, only bounded and bounded away from zero. Assuming that the initial velocity belongs to a suitable critical subspace of L^2 , we prove a global-in-time existence and stability result for the initial (boundary) value problem. Our proof relies on new time decay estimates for finite energy weak solutions and on a 'dynamic interpolation' argument. We show that the constructed solutions have a uniformly C^1 flow, which ensures the propagation of geometrical structures in the fluid and guarantees that the Euleria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.02541","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/2404.02541/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":"2026-07-05T08:03:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x8YyPziQXIUfrBuI/g0+1QfDeOtN65DstwS4UrtmU6SyOQ4XrgB1CBYAkNnRg/Qjm7ngnU4wc7FwQ807Se3IBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T12:37:42.830598Z"},"content_sha256":"b896044e7d36001ba1a55d855dec48f3f0702c9e9338afe7cad1ea887d6d4267","schema_version":"1.0","event_id":"sha256:b896044e7d36001ba1a55d855dec48f3f0702c9e9338afe7cad1ea887d6d4267"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D3AJU3GSCWUKW4C7YY2UHHEO5U/bundle.json","state_url":"https://pith.science/pith/D3AJU3GSCWUKW4C7YY2UHHEO5U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D3AJU3GSCWUKW4C7YY2UHHEO5U/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":"2026-08-17T12:37:42Z","links":{"resolver":"https://pith.science/pith/D3AJU3GSCWUKW4C7YY2UHHEO5U","bundle":"https://pith.science/pith/D3AJU3GSCWUKW4C7YY2UHHEO5U/bundle.json","state":"https://pith.science/pith/D3AJU3GSCWUKW4C7YY2UHHEO5U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D3AJU3GSCWUKW4C7YY2UHHEO5U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:D3AJU3GSCWUKW4C7YY2UHHEO5U","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":"def5a193aeb5f3c81728205c4ff80152789260c71ca6f3780db42412b192bedf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-03T07:58:24Z","title_canon_sha256":"492d2662fd9b2852963522c801e66bc40f98fc9d675adcefd7ec2b9c1a843875"},"schema_version":"1.0","source":{"id":"2404.02541","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.02541","created_at":"2026-07-05T08:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"2404.02541v1","created_at":"2026-07-05T08:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.02541","created_at":"2026-07-05T08:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"D3AJU3GSCWUK","created_at":"2026-07-05T08:03:57Z"},{"alias_kind":"pith_short_16","alias_value":"D3AJU3GSCWUKW4C7","created_at":"2026-07-05T08:03:57Z"},{"alias_kind":"pith_short_8","alias_value":"D3AJU3GS","created_at":"2026-07-05T08:03:57Z"}],"graph_snapshots":[{"event_id":"sha256:b896044e7d36001ba1a55d855dec48f3f0702c9e9338afe7cad1ea887d6d4267","target":"graph","created_at":"2026-07-05T08:03:57Z","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/2404.02541/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the evolution of two-dimensional incompressible flows with variable density, only bounded and bounded away from zero. Assuming that the initial velocity belongs to a suitable critical subspace of L^2 , we prove a global-in-time existence and stability result for the initial (boundary) value problem. Our proof relies on new time decay estimates for finite energy weak solutions and on a 'dynamic interpolation' argument. We show that the constructed solutions have a uniformly C^1 flow, which ensures the propagation of geometrical structures in the fluid and guarantees that the Euleria","authors_text":"LJLL), Rapha\\\"el Danchin (LAMA","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-03T07:58:24Z","title":"Global well-posedness for 2D inhomogeneous viscous flows with rough data via dynamic interpolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.02541","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:cc04d10c99197629ff0c6819083175da9c7ff2d14f9d6f1905a9484c5601f60b","target":"record","created_at":"2026-07-05T08:03:57Z","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":"def5a193aeb5f3c81728205c4ff80152789260c71ca6f3780db42412b192bedf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-04-03T07:58:24Z","title_canon_sha256":"492d2662fd9b2852963522c801e66bc40f98fc9d675adcefd7ec2b9c1a843875"},"schema_version":"1.0","source":{"id":"2404.02541","kind":"arxiv","version":1}},"canonical_sha256":"1ec09a6cd215a8ab705fc635439c8eed1e8589502f932f162e7c659720c277d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ec09a6cd215a8ab705fc635439c8eed1e8589502f932f162e7c659720c277d6","first_computed_at":"2026-07-05T08:03:57.957153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:03:57.957153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NloGz7TWy85exNGj7V//WWyDAhxN0ogXjAdCK0vPqKBvYr0SCLHvIcucaWhM0+z6nVo+4ArcqEJ+uMNydFEQBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:03:57.957583Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.02541","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc04d10c99197629ff0c6819083175da9c7ff2d14f9d6f1905a9484c5601f60b","sha256:b896044e7d36001ba1a55d855dec48f3f0702c9e9338afe7cad1ea887d6d4267"],"state_sha256":"3d6ef5def079bbadc97878396269774ff2925e7e518153bee1a0b19d02f46324"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VkrnlPceJqcKIiXfHfSW5WsLpIukCjlsM7C+mP/x8Qt/cr8SiP+AHfo/IHPx1ANMhNrBeTavexk2RpynotZGAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T12:37:42.838260Z","bundle_sha256":"8a2c207c7577a7da356dd332ad5a600ce25f9893405de60d1350abc06d68c9b0"}}