{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:P7PDSLWJAHNSOJDG32RTMOW7MW","short_pith_number":"pith:P7PDSLWJ","canonical_record":{"source":{"id":"2401.12796","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-01-23T14:30:11Z","cross_cats_sorted":[],"title_canon_sha256":"b93c3f47967833cf84cd1db810d0e8a201ac78bf8e98c81bf0bf0f22ecbe3683","abstract_canon_sha256":"5fe1a82151e7274ee08ad372b955ca19f07a6e422a027796759b1952cdc74eaa"},"schema_version":"1.0"},"canonical_sha256":"7fde392ec901db272466dea3363adf65a9554fbbe0c1b4eebc1ced52c28adf33","source":{"kind":"arxiv","id":"2401.12796","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.12796","created_at":"2026-07-05T09:30:06Z"},{"alias_kind":"arxiv_version","alias_value":"2401.12796v3","created_at":"2026-07-05T09:30:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.12796","created_at":"2026-07-05T09:30:06Z"},{"alias_kind":"pith_short_12","alias_value":"P7PDSLWJAHNS","created_at":"2026-07-05T09:30:06Z"},{"alias_kind":"pith_short_16","alias_value":"P7PDSLWJAHNSOJDG","created_at":"2026-07-05T09:30:06Z"},{"alias_kind":"pith_short_8","alias_value":"P7PDSLWJ","created_at":"2026-07-05T09:30:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:P7PDSLWJAHNSOJDG32RTMOW7MW","target":"record","payload":{"canonical_record":{"source":{"id":"2401.12796","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-01-23T14:30:11Z","cross_cats_sorted":[],"title_canon_sha256":"b93c3f47967833cf84cd1db810d0e8a201ac78bf8e98c81bf0bf0f22ecbe3683","abstract_canon_sha256":"5fe1a82151e7274ee08ad372b955ca19f07a6e422a027796759b1952cdc74eaa"},"schema_version":"1.0"},"canonical_sha256":"7fde392ec901db272466dea3363adf65a9554fbbe0c1b4eebc1ced52c28adf33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:30:06.590533Z","signature_b64":"3SfQ3gk6RcBngiH2HOgGXD1jKDes6VGO94KiVrT/r986OVVOWq2q6H++zf9+GSBVOX3azpjOSBa62gmssg69Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fde392ec901db272466dea3363adf65a9554fbbe0c1b4eebc1ced52c28adf33","last_reissued_at":"2026-07-05T09:30:06.590065Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:30:06.590065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.12796","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:30:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a6WMlXnzP3Q2X7qOyuhA0yFYEqiU66caoyP9ycWDV44GEfigaOIqAV4PexVLIsU2QQtvIwKz8+V8CxHX8ySsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-24T04:46:07.669204Z"},"content_sha256":"7a14522e7563593298aa9cc1572e6dc1eb5713803072e3bb66c445ee68b768b3","schema_version":"1.0","event_id":"sha256:7a14522e7563593298aa9cc1572e6dc1eb5713803072e3bb66c445ee68b768b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:P7PDSLWJAHNSOJDG32RTMOW7MW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strichartz estimates and low regularity solutions of 3D relativistic Euler equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huali Zhang","submitted_at":"2024-01-23T14:30:11Z","abstract_excerpt":"We study the low regularity well-posedness for Cauchy problem of 3D relativistic Euler equations. Firstly, we introduce a new decomposition for relativistic velocity and derive new transport equations for vorticity, which both play a crucial role in energy and Strichartz estimates. According to Smith-Tataru's approach, we then establish a Strichartz estimate of linear wave equations endowed with the acoustic metric. This leads us to prove a complete local well-posedness result if the initial logarithmic enthalpy, velocity, and modified vorticity $(h_0, \\bu_0, \\bw_0) \\in H^s \\times H^s \\times H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.12796","kind":"arxiv","version":3},"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/2401.12796/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":"2026-07-05T09:30:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oFPSI/y8mliv+NmIrz4PP8fFj129CW5Cy2hex6oyyMYvR9seApQx3/z8ceCK5M8FI9msyH20wtmbaFyYsnaWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-24T04:46:07.669581Z"},"content_sha256":"1799a2f44294154dd311c65d2673539a9b4886735af3667bed1b6173b67d30f9","schema_version":"1.0","event_id":"sha256:1799a2f44294154dd311c65d2673539a9b4886735af3667bed1b6173b67d30f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7PDSLWJAHNSOJDG32RTMOW7MW/bundle.json","state_url":"https://pith.science/pith/P7PDSLWJAHNSOJDG32RTMOW7MW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7PDSLWJAHNSOJDG32RTMOW7MW/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":"2026-07-24T04:46:07Z","links":{"resolver":"https://pith.science/pith/P7PDSLWJAHNSOJDG32RTMOW7MW","bundle":"https://pith.science/pith/P7PDSLWJAHNSOJDG32RTMOW7MW/bundle.json","state":"https://pith.science/pith/P7PDSLWJAHNSOJDG32RTMOW7MW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7PDSLWJAHNSOJDG32RTMOW7MW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:P7PDSLWJAHNSOJDG32RTMOW7MW","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":"5fe1a82151e7274ee08ad372b955ca19f07a6e422a027796759b1952cdc74eaa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-01-23T14:30:11Z","title_canon_sha256":"b93c3f47967833cf84cd1db810d0e8a201ac78bf8e98c81bf0bf0f22ecbe3683"},"schema_version":"1.0","source":{"id":"2401.12796","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.12796","created_at":"2026-07-05T09:30:06Z"},{"alias_kind":"arxiv_version","alias_value":"2401.12796v3","created_at":"2026-07-05T09:30:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.12796","created_at":"2026-07-05T09:30:06Z"},{"alias_kind":"pith_short_12","alias_value":"P7PDSLWJAHNS","created_at":"2026-07-05T09:30:06Z"},{"alias_kind":"pith_short_16","alias_value":"P7PDSLWJAHNSOJDG","created_at":"2026-07-05T09:30:06Z"},{"alias_kind":"pith_short_8","alias_value":"P7PDSLWJ","created_at":"2026-07-05T09:30:06Z"}],"graph_snapshots":[{"event_id":"sha256:1799a2f44294154dd311c65d2673539a9b4886735af3667bed1b6173b67d30f9","target":"graph","created_at":"2026-07-05T09:30:06Z","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/2401.12796/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the low regularity well-posedness for Cauchy problem of 3D relativistic Euler equations. Firstly, we introduce a new decomposition for relativistic velocity and derive new transport equations for vorticity, which both play a crucial role in energy and Strichartz estimates. According to Smith-Tataru's approach, we then establish a Strichartz estimate of linear wave equations endowed with the acoustic metric. This leads us to prove a complete local well-posedness result if the initial logarithmic enthalpy, velocity, and modified vorticity $(h_0, \\bu_0, \\bw_0) \\in H^s \\times H^s \\times H","authors_text":"Huali Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-01-23T14:30:11Z","title":"Strichartz estimates and low regularity solutions of 3D relativistic Euler equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.12796","kind":"arxiv","version":3},"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":"sha256:7a14522e7563593298aa9cc1572e6dc1eb5713803072e3bb66c445ee68b768b3","target":"record","created_at":"2026-07-05T09:30:06Z","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":"5fe1a82151e7274ee08ad372b955ca19f07a6e422a027796759b1952cdc74eaa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-01-23T14:30:11Z","title_canon_sha256":"b93c3f47967833cf84cd1db810d0e8a201ac78bf8e98c81bf0bf0f22ecbe3683"},"schema_version":"1.0","source":{"id":"2401.12796","kind":"arxiv","version":3}},"canonical_sha256":"7fde392ec901db272466dea3363adf65a9554fbbe0c1b4eebc1ced52c28adf33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fde392ec901db272466dea3363adf65a9554fbbe0c1b4eebc1ced52c28adf33","first_computed_at":"2026-07-05T09:30:06.590065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:30:06.590065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3SfQ3gk6RcBngiH2HOgGXD1jKDes6VGO94KiVrT/r986OVVOWq2q6H++zf9+GSBVOX3azpjOSBa62gmssg69Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:30:06.590533Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.12796","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a14522e7563593298aa9cc1572e6dc1eb5713803072e3bb66c445ee68b768b3","sha256:1799a2f44294154dd311c65d2673539a9b4886735af3667bed1b6173b67d30f9"],"state_sha256":"ddb8c33f40cd626612681b483a2c8f9ef5f2fc01e668026cc2eb23c12230dc7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YfJ/3xvUn1ShpyT7b4CgKzbf/f4rHgFe6dIqL51ikEgX3bNm8PJBg0AoKgoEIYER0syjeac26bOZuPv4W27rAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-24T04:46:07.672049Z","bundle_sha256":"fb269d79ec8540db11e153bbfbd097dbaa1300a992dbe9aa645ce78f1999f736"}}