{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NLJB4U7WKCBL65UOXQ2QLJDQWK","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":"a1247eed77656d715fa20c800f26b45c807ef2af57014120c4b14e1a383109d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-14T09:11:38Z","title_canon_sha256":"17bd075292e4ef33d6ae832e58f8d0be21c3273f2a328e77fc49c4c6e6444ed7"},"schema_version":"1.0","source":{"id":"1604.04083","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04083","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04083v2","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04083","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"NLJB4U7WKCBL","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NLJB4U7WKCBL65UO","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NLJB4U7W","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:6dcf8e3756ab540cc98450aba44eb84b154f08e94a2525aa1afd796ca7bf98b1","target":"graph","created_at":"2026-05-18T01:16:59Z","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":"After reformulate the incompressible Euler-$\\alpha$ equations in 3D smooth domain with Drichlet data, we obtain the unique classical solutions to Euler-$\\alpha$ equations exist in uniform time interval independent of $\\alpha$. We also show the solution of the Euler-$\\alpha$ converge to the corresponding solution of Euler equation in $L^2$ in space, uniformly in time. In the sequel, it follows that the $H^s$ $(s>\\frac{n}{2}+1)$ solutions of Euler-$\\alpha$ equations exist in any fixed sub-interval of the maximum existent interval for the Euler equations provided that initial is regular enough an","authors_text":"Aibin Zang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-14T09:11:38Z","title":"The uniform time of existence of the smooth solution for 3D Euler-$\\alpha$ equations with Dirichlet boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04083","kind":"arxiv","version":2},"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":"sha256:774c9e1c8bcafc6aba6414352027d9122d2ccac969fae703e2e377e6ba0c35ab","target":"record","created_at":"2026-05-18T01:16:59Z","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":"a1247eed77656d715fa20c800f26b45c807ef2af57014120c4b14e1a383109d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-14T09:11:38Z","title_canon_sha256":"17bd075292e4ef33d6ae832e58f8d0be21c3273f2a328e77fc49c4c6e6444ed7"},"schema_version":"1.0","source":{"id":"1604.04083","kind":"arxiv","version":2}},"canonical_sha256":"6ad21e53f65082bf768ebc3505a470b2860f74fe01644fa33d2b382dc7cf9dde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ad21e53f65082bf768ebc3505a470b2860f74fe01644fa33d2b382dc7cf9dde","first_computed_at":"2026-05-18T01:16:59.139515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:59.139515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sOD9Ex+rk0IlC0YCmcqbS+AKky32CqG5dM+KkbI7IOilVWQVCiP7RQ5IuuunkiuK5SygUAaSLZVEX4PDzEhhBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:59.140189Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04083","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:774c9e1c8bcafc6aba6414352027d9122d2ccac969fae703e2e377e6ba0c35ab","sha256:6dcf8e3756ab540cc98450aba44eb84b154f08e94a2525aa1afd796ca7bf98b1"],"state_sha256":"f0ceefc3a293dbe4607bc4ab06d33565f2dde7059fb6d76e9d9e87adbc190e3f"}