{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RANJS7A5WJFOLO2W4722ZJV64Q","short_pith_number":"pith:RANJS7A5","canonical_record":{"source":{"id":"1906.05252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-12T17:22:36Z","cross_cats_sorted":[],"title_canon_sha256":"78f6a3ec9f84b46d6f51b2be7d9e7995ea38a42a57bc6b382e84038608c06734","abstract_canon_sha256":"25d1e80a84a47bcf4afe3707d97f3d82d3ae7bc870b7e64e66829b06f25ad97d"},"schema_version":"1.0"},"canonical_sha256":"881a997c1db24ae5bb56e7f5aca6bee40f0d77164ff2c806afeae658a8b73238","source":{"kind":"arxiv","id":"1906.05252","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.05252","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"arxiv_version","alias_value":"1906.05252v1","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.05252","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"pith_short_12","alias_value":"RANJS7A5WJFO","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RANJS7A5WJFOLO2W","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RANJS7A5","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RANJS7A5WJFOLO2W4722ZJV64Q","target":"record","payload":{"canonical_record":{"source":{"id":"1906.05252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-12T17:22:36Z","cross_cats_sorted":[],"title_canon_sha256":"78f6a3ec9f84b46d6f51b2be7d9e7995ea38a42a57bc6b382e84038608c06734","abstract_canon_sha256":"25d1e80a84a47bcf4afe3707d97f3d82d3ae7bc870b7e64e66829b06f25ad97d"},"schema_version":"1.0"},"canonical_sha256":"881a997c1db24ae5bb56e7f5aca6bee40f0d77164ff2c806afeae658a8b73238","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:29.059413Z","signature_b64":"pbghaS9LOMChCNdqiBTW49Sh1mZPmzO5aVfbIMnKufWTUO/OyLZm8kdfNv7JqbVeQCUHwBdSIZeYkak4E48ZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"881a997c1db24ae5bb56e7f5aca6bee40f0d77164ff2c806afeae658a8b73238","last_reissued_at":"2026-05-17T23:43:29.058685Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:29.058685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.05252","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":"2026-05-17T23:43:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RcW9FpcDFFRN4UpuKmJ/rMXXXsP1dXG2VXPRsXCEcVuDs/xOGOH905eEvGwiE0QC7JLICTtqLtMce0zJBuQPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:56:09.740194Z"},"content_sha256":"ffa8e47560a2e3694b2d1fd9edeb7cdee945090af85e66fecfc1462c620fc940","schema_version":"1.0","event_id":"sha256:ffa8e47560a2e3694b2d1fd9edeb7cdee945090af85e66fecfc1462c620fc940"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RANJS7A5WJFOLO2W4722ZJV64Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A sufficient condition for uniqueness of weak solutions of the incompressible Euler system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Animesh Jana, Shyam Sundar Ghoshal","submitted_at":"2019-06-12T17:22:36Z","abstract_excerpt":"We give a new sufficient criteria to prove the uniqueness of the incompressible Euler equation in dimension $N\\geq2$. In their celebrated works by V. Scheffer [18], A. Shnirelman [19], C. De Lellis and L. Sz\\'ekelyhidi Jr. [7] they have obtained the nonuniqeness of weak solutions of incompressible Euler equation. Here we obtain uniqueness criteria for the same equation under some mild regularity condition on weak solutions. Our proof is simple and can be employed to other equations like inhomogeneous incompressible Euler and Euler-Boussinesq equations. One of the key ingredients in our proof i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05252","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":""},"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":"2026-05-17T23:43:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lYZ1V6kySc/ge/JOPCv1mQpi6M478E0/9q0Al8hJpivZifLottwec0YRhBM+bc2IWfPzO+qxiJZMQU2Yq8vpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:56:09.740916Z"},"content_sha256":"0ece11b43f3e78f4806021c175dc4348e992f9fba72261195bde0527ec1bbdbf","schema_version":"1.0","event_id":"sha256:0ece11b43f3e78f4806021c175dc4348e992f9fba72261195bde0527ec1bbdbf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RANJS7A5WJFOLO2W4722ZJV64Q/bundle.json","state_url":"https://pith.science/pith/RANJS7A5WJFOLO2W4722ZJV64Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RANJS7A5WJFOLO2W4722ZJV64Q/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":"2026-05-26T19:56:09Z","links":{"resolver":"https://pith.science/pith/RANJS7A5WJFOLO2W4722ZJV64Q","bundle":"https://pith.science/pith/RANJS7A5WJFOLO2W4722ZJV64Q/bundle.json","state":"https://pith.science/pith/RANJS7A5WJFOLO2W4722ZJV64Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RANJS7A5WJFOLO2W4722ZJV64Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RANJS7A5WJFOLO2W4722ZJV64Q","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":"25d1e80a84a47bcf4afe3707d97f3d82d3ae7bc870b7e64e66829b06f25ad97d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-12T17:22:36Z","title_canon_sha256":"78f6a3ec9f84b46d6f51b2be7d9e7995ea38a42a57bc6b382e84038608c06734"},"schema_version":"1.0","source":{"id":"1906.05252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.05252","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"arxiv_version","alias_value":"1906.05252v1","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.05252","created_at":"2026-05-17T23:43:29Z"},{"alias_kind":"pith_short_12","alias_value":"RANJS7A5WJFO","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RANJS7A5WJFOLO2W","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RANJS7A5","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:0ece11b43f3e78f4806021c175dc4348e992f9fba72261195bde0527ec1bbdbf","target":"graph","created_at":"2026-05-17T23:43:29Z","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":"We give a new sufficient criteria to prove the uniqueness of the incompressible Euler equation in dimension $N\\geq2$. In their celebrated works by V. Scheffer [18], A. Shnirelman [19], C. De Lellis and L. Sz\\'ekelyhidi Jr. [7] they have obtained the nonuniqeness of weak solutions of incompressible Euler equation. Here we obtain uniqueness criteria for the same equation under some mild regularity condition on weak solutions. Our proof is simple and can be employed to other equations like inhomogeneous incompressible Euler and Euler-Boussinesq equations. One of the key ingredients in our proof i","authors_text":"Animesh Jana, Shyam Sundar Ghoshal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-12T17:22:36Z","title":"A sufficient condition for uniqueness of weak solutions of the incompressible Euler system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05252","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:ffa8e47560a2e3694b2d1fd9edeb7cdee945090af85e66fecfc1462c620fc940","target":"record","created_at":"2026-05-17T23:43:29Z","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":"25d1e80a84a47bcf4afe3707d97f3d82d3ae7bc870b7e64e66829b06f25ad97d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-12T17:22:36Z","title_canon_sha256":"78f6a3ec9f84b46d6f51b2be7d9e7995ea38a42a57bc6b382e84038608c06734"},"schema_version":"1.0","source":{"id":"1906.05252","kind":"arxiv","version":1}},"canonical_sha256":"881a997c1db24ae5bb56e7f5aca6bee40f0d77164ff2c806afeae658a8b73238","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"881a997c1db24ae5bb56e7f5aca6bee40f0d77164ff2c806afeae658a8b73238","first_computed_at":"2026-05-17T23:43:29.058685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:29.058685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pbghaS9LOMChCNdqiBTW49Sh1mZPmzO5aVfbIMnKufWTUO/OyLZm8kdfNv7JqbVeQCUHwBdSIZeYkak4E48ZAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:29.059413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.05252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffa8e47560a2e3694b2d1fd9edeb7cdee945090af85e66fecfc1462c620fc940","sha256:0ece11b43f3e78f4806021c175dc4348e992f9fba72261195bde0527ec1bbdbf"],"state_sha256":"188b5b45ed5a053c65c6a6f46d5a1d86b9571fd68eb6c97e4f491a1e3047221c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/U9CckjG9ffQY4pMcsyCLmgAxrazYI3IScrCjSH3kgrox+3XVQ2wwJqzA3jRninx7iezmdCIRWTjQx4fEGnTCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:56:09.744630Z","bundle_sha256":"bda4c42caa7d7c5d32c59eaca872b0baf793cfd0abb09d7b935a2ac8d19cdefa"}}