{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:4VTTDURP3U76L7OWTPGG6FFI2M","short_pith_number":"pith:4VTTDURP","schema_version":"1.0","canonical_sha256":"e56731d22fdd3fe5fdd69bcc6f14a8d3267c9bf328fd9625a40c08e5b3c8c5c6","source":{"kind":"arxiv","id":"2204.03344","version":1},"attestation_state":"computed","paper":{"title":"Infinitely many non-conservative solutions for the three-dimensional Euler equations with arbitrary initial data in $C^{1/3-\\epsilon}$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Calvin Khor, Changxing Miao, Weikui Ye","submitted_at":"2022-04-07T10:30:03Z","abstract_excerpt":"Let $0<\\beta<\\bar\\beta<1/3$. We construct infinitely many distributional solutions in $C^{\\beta}_{x,t}$ to the three-dimensional Euler equations that do not conserve the energy, for a given initial data in $C^{\\bar\\beta}$. We also show that there is some limited control on the increase in the energy for $t>1$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2204.03344","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2022-04-07T10:30:03Z","cross_cats_sorted":[],"title_canon_sha256":"f2bf9355fe4321ee992c876773cf38d05b8dcaffe0a24c8bec74e198e0e984b3","abstract_canon_sha256":"eed40efdf4ff381edc45741cb431a4edc7dae6fc2628b5b89dc280beb2e02f3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:12:22.197484Z","signature_b64":"DZ7AZJi6J0urFynXYTZJfuTSW/Srl2iEXIEYabncgZdypgC8PLsrpMoM0NmQm9M0pqor82FlHTrpIujF1KcQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e56731d22fdd3fe5fdd69bcc6f14a8d3267c9bf328fd9625a40c08e5b3c8c5c6","last_reissued_at":"2026-07-05T04:12:22.197062Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:12:22.197062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely many non-conservative solutions for the three-dimensional Euler equations with arbitrary initial data in $C^{1/3-\\epsilon}$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Calvin Khor, Changxing Miao, Weikui Ye","submitted_at":"2022-04-07T10:30:03Z","abstract_excerpt":"Let $0<\\beta<\\bar\\beta<1/3$. We construct infinitely many distributional solutions in $C^{\\beta}_{x,t}$ to the three-dimensional Euler equations that do not conserve the energy, for a given initial data in $C^{\\bar\\beta}$. We also show that there is some limited control on the increase in the energy for $t>1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.03344","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/2204.03344/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2204.03344","created_at":"2026-07-05T04:12:22.197120+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.03344v1","created_at":"2026-07-05T04:12:22.197120+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.03344","created_at":"2026-07-05T04:12:22.197120+00:00"},{"alias_kind":"pith_short_12","alias_value":"4VTTDURP3U76","created_at":"2026-07-05T04:12:22.197120+00:00"},{"alias_kind":"pith_short_16","alias_value":"4VTTDURP3U76L7OW","created_at":"2026-07-05T04:12:22.197120+00:00"},{"alias_kind":"pith_short_8","alias_value":"4VTTDURP","created_at":"2026-07-05T04:12:22.197120+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.12192","citing_title":"A Generalized Framework for $L^r$ Convex Integration and its Application to Geophysical Models","ref_index":91,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4VTTDURP3U76L7OWTPGG6FFI2M","json":"https://pith.science/pith/4VTTDURP3U76L7OWTPGG6FFI2M.json","graph_json":"https://pith.science/api/pith-number/4VTTDURP3U76L7OWTPGG6FFI2M/graph.json","events_json":"https://pith.science/api/pith-number/4VTTDURP3U76L7OWTPGG6FFI2M/events.json","paper":"https://pith.science/paper/4VTTDURP"},"agent_actions":{"view_html":"https://pith.science/pith/4VTTDURP3U76L7OWTPGG6FFI2M","download_json":"https://pith.science/pith/4VTTDURP3U76L7OWTPGG6FFI2M.json","view_paper":"https://pith.science/paper/4VTTDURP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.03344&json=true","fetch_graph":"https://pith.science/api/pith-number/4VTTDURP3U76L7OWTPGG6FFI2M/graph.json","fetch_events":"https://pith.science/api/pith-number/4VTTDURP3U76L7OWTPGG6FFI2M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4VTTDURP3U76L7OWTPGG6FFI2M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4VTTDURP3U76L7OWTPGG6FFI2M/action/storage_attestation","attest_author":"https://pith.science/pith/4VTTDURP3U76L7OWTPGG6FFI2M/action/author_attestation","sign_citation":"https://pith.science/pith/4VTTDURP3U76L7OWTPGG6FFI2M/action/citation_signature","submit_replication":"https://pith.science/pith/4VTTDURP3U76L7OWTPGG6FFI2M/action/replication_record"}},"created_at":"2026-07-05T04:12:22.197120+00:00","updated_at":"2026-07-05T04:12:22.197120+00:00"}