{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:2PJ3CDUSEQVXFTRBZL5Z2JFCVY","short_pith_number":"pith:2PJ3CDUS","schema_version":"1.0","canonical_sha256":"d3d3b10e92242b72ce21cafb9d24a2ae29452357d2caa7655450630f775b5a15","source":{"kind":"arxiv","id":"2104.11872","version":2},"attestation_state":"computed","paper":{"title":"Weak solutions of the three-dimensional hypoviscous elastodynamics with finite kinetic energy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Liu, Ke Chen","submitted_at":"2021-04-24T03:24:04Z","abstract_excerpt":"We construct weak solutions to the 3D hypoviscous incompressible elastodynamics with finite kinetic energy which was unknown in literatures. Our result holds for fractional hypoviscosity $(-\\Delta)^\\theta$, where $0\\leq\\theta<1$. The proof {consists of a convex integration scheme with new building blocks of 2D intermittency and suitable temporal correctors, which are motivated by} the inherent geometric structure of the viscoelastic equations."},"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":"2104.11872","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-04-24T03:24:04Z","cross_cats_sorted":[],"title_canon_sha256":"69a6aa6050d1bb973b46979a42e8d77fd521ecfbeb0fae17c4f75f194325cbd3","abstract_canon_sha256":"1776e88b41df823032e75f625d0f4d4e08fdc117e7440a4ba11a37cc56ffbb46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:51:37.811540Z","signature_b64":"vJM9gKTX3eB91mJYzluBpwyi6f2oVHvM7FQBy2VJhFUT2rzTan3k6cc2qv0dSup37L3WxYDxBkFJJvZIEC9DCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3d3b10e92242b72ce21cafb9d24a2ae29452357d2caa7655450630f775b5a15","last_reissued_at":"2026-07-05T04:51:37.811142Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:51:37.811142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak solutions of the three-dimensional hypoviscous elastodynamics with finite kinetic energy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jie Liu, Ke Chen","submitted_at":"2021-04-24T03:24:04Z","abstract_excerpt":"We construct weak solutions to the 3D hypoviscous incompressible elastodynamics with finite kinetic energy which was unknown in literatures. Our result holds for fractional hypoviscosity $(-\\Delta)^\\theta$, where $0\\leq\\theta<1$. The proof {consists of a convex integration scheme with new building blocks of 2D intermittency and suitable temporal correctors, which are motivated by} the inherent geometric structure of the viscoelastic equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.11872","kind":"arxiv","version":2},"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/2104.11872/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":"2104.11872","created_at":"2026-07-05T04:51:37.811199+00:00"},{"alias_kind":"arxiv_version","alias_value":"2104.11872v2","created_at":"2026-07-05T04:51:37.811199+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.11872","created_at":"2026-07-05T04:51:37.811199+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PJ3CDUSEQVX","created_at":"2026-07-05T04:51:37.811199+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PJ3CDUSEQVXFTRB","created_at":"2026-07-05T04:51:37.811199+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PJ3CDUS","created_at":"2026-07-05T04:51:37.811199+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2PJ3CDUSEQVXFTRBZL5Z2JFCVY","json":"https://pith.science/pith/2PJ3CDUSEQVXFTRBZL5Z2JFCVY.json","graph_json":"https://pith.science/api/pith-number/2PJ3CDUSEQVXFTRBZL5Z2JFCVY/graph.json","events_json":"https://pith.science/api/pith-number/2PJ3CDUSEQVXFTRBZL5Z2JFCVY/events.json","paper":"https://pith.science/paper/2PJ3CDUS"},"agent_actions":{"view_html":"https://pith.science/pith/2PJ3CDUSEQVXFTRBZL5Z2JFCVY","download_json":"https://pith.science/pith/2PJ3CDUSEQVXFTRBZL5Z2JFCVY.json","view_paper":"https://pith.science/paper/2PJ3CDUS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2104.11872&json=true","fetch_graph":"https://pith.science/api/pith-number/2PJ3CDUSEQVXFTRBZL5Z2JFCVY/graph.json","fetch_events":"https://pith.science/api/pith-number/2PJ3CDUSEQVXFTRBZL5Z2JFCVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PJ3CDUSEQVXFTRBZL5Z2JFCVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PJ3CDUSEQVXFTRBZL5Z2JFCVY/action/storage_attestation","attest_author":"https://pith.science/pith/2PJ3CDUSEQVXFTRBZL5Z2JFCVY/action/author_attestation","sign_citation":"https://pith.science/pith/2PJ3CDUSEQVXFTRBZL5Z2JFCVY/action/citation_signature","submit_replication":"https://pith.science/pith/2PJ3CDUSEQVXFTRBZL5Z2JFCVY/action/replication_record"}},"created_at":"2026-07-05T04:51:37.811199+00:00","updated_at":"2026-07-05T04:51:37.811199+00:00"}