{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:W3QCUVPDGT6SZNWNX3QNDFXOMH","short_pith_number":"pith:W3QCUVPD","canonical_record":{"source":{"id":"1407.0453","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-02T04:03:45Z","cross_cats_sorted":[],"title_canon_sha256":"027134e5145056fc2a3e505a2236082e3a7d52a6d8f75a8c43b76710295bfaa5","abstract_canon_sha256":"2705b910c165abf6034ca0836eab642d5924b7205c1669fb0d7a77195c99019d"},"schema_version":"1.0"},"canonical_sha256":"b6e02a55e334fd2cb6cdbee0d196ee61deade7c37d34a39118a7d2952be22e49","source":{"kind":"arxiv","id":"1407.0453","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0453","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0453v4","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0453","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"pith_short_12","alias_value":"W3QCUVPDGT6S","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W3QCUVPDGT6SZNWN","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W3QCUVPD","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:W3QCUVPDGT6SZNWNX3QNDFXOMH","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0453","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-02T04:03:45Z","cross_cats_sorted":[],"title_canon_sha256":"027134e5145056fc2a3e505a2236082e3a7d52a6d8f75a8c43b76710295bfaa5","abstract_canon_sha256":"2705b910c165abf6034ca0836eab642d5924b7205c1669fb0d7a77195c99019d"},"schema_version":"1.0"},"canonical_sha256":"b6e02a55e334fd2cb6cdbee0d196ee61deade7c37d34a39118a7d2952be22e49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:41.296983Z","signature_b64":"6L5GFzEZLXgcXEXW+rDdP0qL57xlPYFd1VPg03KB6eh1mKSQ7OTH2cmWwqZa5+JxN3+sEyMMwiDwvbh8t/tUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6e02a55e334fd2cb6cdbee0d196ee61deade7c37d34a39118a7d2952be22e49","last_reissued_at":"2026-05-18T00:58:41.296283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:41.296283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0453","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sqQaWIVZpisLvE3oxqJu5RfMdyHtxZAxq37YVukvI8B85A7zSVJnRnsl7rO/dvc/zfykoBNFvSR9i0ALv7ZZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:30:16.710688Z"},"content_sha256":"e64b534acb3f901ab391e6e89df994d4f318faef5588724ff7610988dd57b89d","schema_version":"1.0","event_id":"sha256:e64b534acb3f901ab391e6e89df994d4f318faef5588724ff7610988dd57b89d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:W3QCUVPDGT6SZNWNX3QNDFXOMH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global existence for the 2D incompressible isotropic elastodynamics for small initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xuecheng Wang","submitted_at":"2014-07-02T04:03:45Z","abstract_excerpt":"We establish the global existence and the asymptotic behavior for the 2D incompressible isotropic elastodynamics for sufficiently small, smooth initial data in the Eulerian coordinates formulation.The main tools used to derive the main results are, on the one hand, a modified energy method to derive the energy estimate and on the other hand, a Fourier transform method with a suitable choice of $Z-$ norm to derive the sharp $L^\\infty-$ estimate. We mention that the global existence of the same system but in the Lagrangian coordinates formulation was recently obtained by Lei. Our goal is to impr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0453","kind":"arxiv","version":4},"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":"2026-05-18T00:58:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z/FC88wDV3YnPPmEoszEEAiZr8kzLgT74TfKn8tj3rqP4Pn7YiheCkXxD6LjBdoi4bAwO0J4wmw+6p/AKSXVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:30:16.711224Z"},"content_sha256":"32cf89c1faf181f12857ea6ecbb509352f774bd7c3d90e660000e18ed15ed29d","schema_version":"1.0","event_id":"sha256:32cf89c1faf181f12857ea6ecbb509352f774bd7c3d90e660000e18ed15ed29d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W3QCUVPDGT6SZNWNX3QNDFXOMH/bundle.json","state_url":"https://pith.science/pith/W3QCUVPDGT6SZNWNX3QNDFXOMH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W3QCUVPDGT6SZNWNX3QNDFXOMH/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":"2026-06-02T13:30:16Z","links":{"resolver":"https://pith.science/pith/W3QCUVPDGT6SZNWNX3QNDFXOMH","bundle":"https://pith.science/pith/W3QCUVPDGT6SZNWNX3QNDFXOMH/bundle.json","state":"https://pith.science/pith/W3QCUVPDGT6SZNWNX3QNDFXOMH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W3QCUVPDGT6SZNWNX3QNDFXOMH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:W3QCUVPDGT6SZNWNX3QNDFXOMH","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":"2705b910c165abf6034ca0836eab642d5924b7205c1669fb0d7a77195c99019d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-02T04:03:45Z","title_canon_sha256":"027134e5145056fc2a3e505a2236082e3a7d52a6d8f75a8c43b76710295bfaa5"},"schema_version":"1.0","source":{"id":"1407.0453","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0453","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0453v4","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0453","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"pith_short_12","alias_value":"W3QCUVPDGT6S","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W3QCUVPDGT6SZNWN","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W3QCUVPD","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:32cf89c1faf181f12857ea6ecbb509352f774bd7c3d90e660000e18ed15ed29d","target":"graph","created_at":"2026-05-18T00:58:41Z","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 establish the global existence and the asymptotic behavior for the 2D incompressible isotropic elastodynamics for sufficiently small, smooth initial data in the Eulerian coordinates formulation.The main tools used to derive the main results are, on the one hand, a modified energy method to derive the energy estimate and on the other hand, a Fourier transform method with a suitable choice of $Z-$ norm to derive the sharp $L^\\infty-$ estimate. We mention that the global existence of the same system but in the Lagrangian coordinates formulation was recently obtained by Lei. Our goal is to impr","authors_text":"Xuecheng Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-02T04:03:45Z","title":"Global existence for the 2D incompressible isotropic elastodynamics for small initial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0453","kind":"arxiv","version":4},"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:e64b534acb3f901ab391e6e89df994d4f318faef5588724ff7610988dd57b89d","target":"record","created_at":"2026-05-18T00:58:41Z","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":"2705b910c165abf6034ca0836eab642d5924b7205c1669fb0d7a77195c99019d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-02T04:03:45Z","title_canon_sha256":"027134e5145056fc2a3e505a2236082e3a7d52a6d8f75a8c43b76710295bfaa5"},"schema_version":"1.0","source":{"id":"1407.0453","kind":"arxiv","version":4}},"canonical_sha256":"b6e02a55e334fd2cb6cdbee0d196ee61deade7c37d34a39118a7d2952be22e49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6e02a55e334fd2cb6cdbee0d196ee61deade7c37d34a39118a7d2952be22e49","first_computed_at":"2026-05-18T00:58:41.296283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:41.296283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6L5GFzEZLXgcXEXW+rDdP0qL57xlPYFd1VPg03KB6eh1mKSQ7OTH2cmWwqZa5+JxN3+sEyMMwiDwvbh8t/tUDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:41.296983Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0453","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e64b534acb3f901ab391e6e89df994d4f318faef5588724ff7610988dd57b89d","sha256:32cf89c1faf181f12857ea6ecbb509352f774bd7c3d90e660000e18ed15ed29d"],"state_sha256":"69bab35c94e1f8b06d6c83a8f3f1e023e76683e6aa70ce1a613c0ad08ad855b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hLM86CSvNSz14mqT0Y4VippZ96tP7HxCFpmZbgJ7Y/WH0cnZV4tYrvbktNYQW9nefYwRQ9ytJ21wgXwSPnnKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:30:16.715415Z","bundle_sha256":"d4fbf70226994d2e00efeeed28b46a32f0391549b55d586f547af1f303363c92"}}