{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:3JAIREDAN2IFVIJ6KI2LDWD2SF","short_pith_number":"pith:3JAIREDA","canonical_record":{"source":{"id":"2408.07934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-15T05:08:48Z","cross_cats_sorted":[],"title_canon_sha256":"9af51dedf26f09e96cff45b577efd35ca5d904929292b689ddfd1c6acd9a0c18","abstract_canon_sha256":"3936fc290dd3a112fe73087d91aa228b4da80bb80cbebb8d052999b3c9f11dfa"},"schema_version":"1.0"},"canonical_sha256":"da408890606e905aa13e5234b1d87a917bec5041dd35fbf873cdd2f6d239a466","source":{"kind":"arxiv","id":"2408.07934","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.07934","created_at":"2026-07-05T08:55:42Z"},{"alias_kind":"arxiv_version","alias_value":"2408.07934v1","created_at":"2026-07-05T08:55:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.07934","created_at":"2026-07-05T08:55:42Z"},{"alias_kind":"pith_short_12","alias_value":"3JAIREDAN2IF","created_at":"2026-07-05T08:55:42Z"},{"alias_kind":"pith_short_16","alias_value":"3JAIREDAN2IFVIJ6","created_at":"2026-07-05T08:55:42Z"},{"alias_kind":"pith_short_8","alias_value":"3JAIREDA","created_at":"2026-07-05T08:55:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:3JAIREDAN2IFVIJ6KI2LDWD2SF","target":"record","payload":{"canonical_record":{"source":{"id":"2408.07934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-15T05:08:48Z","cross_cats_sorted":[],"title_canon_sha256":"9af51dedf26f09e96cff45b577efd35ca5d904929292b689ddfd1c6acd9a0c18","abstract_canon_sha256":"3936fc290dd3a112fe73087d91aa228b4da80bb80cbebb8d052999b3c9f11dfa"},"schema_version":"1.0"},"canonical_sha256":"da408890606e905aa13e5234b1d87a917bec5041dd35fbf873cdd2f6d239a466","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:55:42.210114Z","signature_b64":"ThU0+13EvWN/7wzD2xDx8pvvs84PDe3CPiw9KNM/kUZTa+5+c8LNB43HHIFYecwqZRlXLv5TXY+tXxYoMspcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da408890606e905aa13e5234b1d87a917bec5041dd35fbf873cdd2f6d239a466","last_reissued_at":"2026-07-05T08:55:42.209634Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:55:42.209634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.07934","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":"2026-07-05T08:55:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Stkm1LBiFQYl1jWovvBhwhDhzfdHF1h/0zgJgeAKTjmq9tQOUzPmu+AKHzMjBGACJWg6OsxhCIy5unjSTGpxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:56:18.367298Z"},"content_sha256":"9ef55868cb86c93f4192d874f2aa2ef3f26bc0f18f6615064fb9f92672c247dc","schema_version":"1.0","event_id":"sha256:9ef55868cb86c93f4192d874f2aa2ef3f26bc0f18f6615064fb9f92672c247dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:3JAIREDAN2IFVIJ6KI2LDWD2SF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flexibility of Two-Dimensional Euler Flows with Integrable Vorticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anuj Kumar, Elia Bru\\`e, Maria Colombo","submitted_at":"2024-08-15T05:08:48Z","abstract_excerpt":"We propose a new convex integration scheme in fluid mechanics, and we provide an application to the two-dimensional Euler equations. We prove the flexibility and nonuniqueness of $L^\\infty L^2$ weak solutions with vorticity in $L^\\infty L^p$ for some $p>1$, surpassing for the first time the critical scaling of the standard convex integration technique.\n  To achieve this, we introduce several new ideas, including:\n  (i) A new family of building blocks built from the Lamb-Chaplygin dipole.\n  (ii) A new method to cancel the error based on time averages and non-periodic, spatially-anisotropic pert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07934","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/2408.07934/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":"2026-07-05T08:55:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dAZSG+JaEZyf6/rMaG8tZYKB08eNdAodKVWqcpmHaZvXylCyFEAmHtW+oIMnisonRo0yqPZBOW8CZ5Q06lyoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:56:18.367784Z"},"content_sha256":"20a456df94c3a8a515b32016103332190c0f912a834830f770e400fbb8861195","schema_version":"1.0","event_id":"sha256:20a456df94c3a8a515b32016103332190c0f912a834830f770e400fbb8861195"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3JAIREDAN2IFVIJ6KI2LDWD2SF/bundle.json","state_url":"https://pith.science/pith/3JAIREDAN2IFVIJ6KI2LDWD2SF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3JAIREDAN2IFVIJ6KI2LDWD2SF/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":"2026-08-08T19:56:18Z","links":{"resolver":"https://pith.science/pith/3JAIREDAN2IFVIJ6KI2LDWD2SF","bundle":"https://pith.science/pith/3JAIREDAN2IFVIJ6KI2LDWD2SF/bundle.json","state":"https://pith.science/pith/3JAIREDAN2IFVIJ6KI2LDWD2SF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3JAIREDAN2IFVIJ6KI2LDWD2SF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:3JAIREDAN2IFVIJ6KI2LDWD2SF","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":"3936fc290dd3a112fe73087d91aa228b4da80bb80cbebb8d052999b3c9f11dfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-15T05:08:48Z","title_canon_sha256":"9af51dedf26f09e96cff45b577efd35ca5d904929292b689ddfd1c6acd9a0c18"},"schema_version":"1.0","source":{"id":"2408.07934","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.07934","created_at":"2026-07-05T08:55:42Z"},{"alias_kind":"arxiv_version","alias_value":"2408.07934v1","created_at":"2026-07-05T08:55:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.07934","created_at":"2026-07-05T08:55:42Z"},{"alias_kind":"pith_short_12","alias_value":"3JAIREDAN2IF","created_at":"2026-07-05T08:55:42Z"},{"alias_kind":"pith_short_16","alias_value":"3JAIREDAN2IFVIJ6","created_at":"2026-07-05T08:55:42Z"},{"alias_kind":"pith_short_8","alias_value":"3JAIREDA","created_at":"2026-07-05T08:55:42Z"}],"graph_snapshots":[{"event_id":"sha256:20a456df94c3a8a515b32016103332190c0f912a834830f770e400fbb8861195","target":"graph","created_at":"2026-07-05T08:55:42Z","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/2408.07934/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a new convex integration scheme in fluid mechanics, and we provide an application to the two-dimensional Euler equations. We prove the flexibility and nonuniqueness of $L^\\infty L^2$ weak solutions with vorticity in $L^\\infty L^p$ for some $p>1$, surpassing for the first time the critical scaling of the standard convex integration technique.\n  To achieve this, we introduce several new ideas, including:\n  (i) A new family of building blocks built from the Lamb-Chaplygin dipole.\n  (ii) A new method to cancel the error based on time averages and non-periodic, spatially-anisotropic pert","authors_text":"Anuj Kumar, Elia Bru\\`e, Maria Colombo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-15T05:08:48Z","title":"Flexibility of Two-Dimensional Euler Flows with Integrable Vorticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07934","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":"sha256:9ef55868cb86c93f4192d874f2aa2ef3f26bc0f18f6615064fb9f92672c247dc","target":"record","created_at":"2026-07-05T08:55:42Z","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":"3936fc290dd3a112fe73087d91aa228b4da80bb80cbebb8d052999b3c9f11dfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-15T05:08:48Z","title_canon_sha256":"9af51dedf26f09e96cff45b577efd35ca5d904929292b689ddfd1c6acd9a0c18"},"schema_version":"1.0","source":{"id":"2408.07934","kind":"arxiv","version":1}},"canonical_sha256":"da408890606e905aa13e5234b1d87a917bec5041dd35fbf873cdd2f6d239a466","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da408890606e905aa13e5234b1d87a917bec5041dd35fbf873cdd2f6d239a466","first_computed_at":"2026-07-05T08:55:42.209634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:55:42.209634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ThU0+13EvWN/7wzD2xDx8pvvs84PDe3CPiw9KNM/kUZTa+5+c8LNB43HHIFYecwqZRlXLv5TXY+tXxYoMspcDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:55:42.210114Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.07934","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ef55868cb86c93f4192d874f2aa2ef3f26bc0f18f6615064fb9f92672c247dc","sha256:20a456df94c3a8a515b32016103332190c0f912a834830f770e400fbb8861195"],"state_sha256":"e577fe9ae0479a113ffb66626e4244cc5e178b0620eea568ef9cc5137fbef889"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HjoXcegfKRcgH6yKVrEq5bJ0QZZUeXKxF77/qJ1M1LCmgvsaOdNOt3W30nCKSnty9BvvhczsHN+CGHWcaDCFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T19:56:18.372206Z","bundle_sha256":"c643ad55edbc8a8d40faa8ff806ba70022a5e4b63c9be8110dc1772e7e2bab8b"}}