{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:IFOUEWEXNA5LXEOFQWHAVYVFJO","short_pith_number":"pith:IFOUEWEX","schema_version":"1.0","canonical_sha256":"415d425897683abb91c5858e0ae2a54bb65d3e7eb98c33da75a53c3e1207f4d5","source":{"kind":"arxiv","id":"1212.6391","version":1},"attestation_state":"computed","paper":{"title":"Almost Global Existence for 2-D Incompressible Isotropic Elastodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Thomas C. Sideris, Yi Zhou, Zhen Lei","submitted_at":"2012-12-27T16:27:31Z","abstract_excerpt":"We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval $[0,{T}/{\\epsilon}]$, for initial data of the form $\\epsilon U_0$, where $T$ depends only on some Sobolev norm of $U_0$. We show that for such data there exists a unique solution on a time interval $[0, \\exp{T}/{\\epsilon}]$, provided that $\\epsilon$ is sufficiently small. This is achieved by careful consideration of the structure of the nonlinearity. The incompressible elasticity equation is inherently linearly degenerate in the isotropic case; in oth"},"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":"1212.6391","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-27T16:27:31Z","cross_cats_sorted":[],"title_canon_sha256":"e37350f5f549c83dcbc4daea853a373a8ccd37d47ab19fb836bfe0562f2e3919","abstract_canon_sha256":"f1b50ab33f1007accf4be499e18752f6ea8e4f86cdc2c1fc95a7c47cb11f0aee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:39.860855Z","signature_b64":"SXTN2jByrHeZteEaTek4lBNM0BUnpr3VEDOqWcH8RP7smdWN3zNxkacO0P4VJSXOiGmEq4PBTqBYuktRUhKQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"415d425897683abb91c5858e0ae2a54bb65d3e7eb98c33da75a53c3e1207f4d5","last_reissued_at":"2026-05-18T03:37:39.860283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:39.860283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost Global Existence for 2-D Incompressible Isotropic Elastodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Thomas C. Sideris, Yi Zhou, Zhen Lei","submitted_at":"2012-12-27T16:27:31Z","abstract_excerpt":"We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval $[0,{T}/{\\epsilon}]$, for initial data of the form $\\epsilon U_0$, where $T$ depends only on some Sobolev norm of $U_0$. We show that for such data there exists a unique solution on a time interval $[0, \\exp{T}/{\\epsilon}]$, provided that $\\epsilon$ is sufficiently small. This is achieved by careful consideration of the structure of the nonlinearity. The incompressible elasticity equation is inherently linearly degenerate in the isotropic case; in oth"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6391","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":""},"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":"1212.6391","created_at":"2026-05-18T03:37:39.860382+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.6391v1","created_at":"2026-05-18T03:37:39.860382+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6391","created_at":"2026-05-18T03:37:39.860382+00:00"},{"alias_kind":"pith_short_12","alias_value":"IFOUEWEXNA5L","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"IFOUEWEXNA5LXEOF","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"IFOUEWEX","created_at":"2026-05-18T12:27:09.501522+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/IFOUEWEXNA5LXEOFQWHAVYVFJO","json":"https://pith.science/pith/IFOUEWEXNA5LXEOFQWHAVYVFJO.json","graph_json":"https://pith.science/api/pith-number/IFOUEWEXNA5LXEOFQWHAVYVFJO/graph.json","events_json":"https://pith.science/api/pith-number/IFOUEWEXNA5LXEOFQWHAVYVFJO/events.json","paper":"https://pith.science/paper/IFOUEWEX"},"agent_actions":{"view_html":"https://pith.science/pith/IFOUEWEXNA5LXEOFQWHAVYVFJO","download_json":"https://pith.science/pith/IFOUEWEXNA5LXEOFQWHAVYVFJO.json","view_paper":"https://pith.science/paper/IFOUEWEX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.6391&json=true","fetch_graph":"https://pith.science/api/pith-number/IFOUEWEXNA5LXEOFQWHAVYVFJO/graph.json","fetch_events":"https://pith.science/api/pith-number/IFOUEWEXNA5LXEOFQWHAVYVFJO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IFOUEWEXNA5LXEOFQWHAVYVFJO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IFOUEWEXNA5LXEOFQWHAVYVFJO/action/storage_attestation","attest_author":"https://pith.science/pith/IFOUEWEXNA5LXEOFQWHAVYVFJO/action/author_attestation","sign_citation":"https://pith.science/pith/IFOUEWEXNA5LXEOFQWHAVYVFJO/action/citation_signature","submit_replication":"https://pith.science/pith/IFOUEWEXNA5LXEOFQWHAVYVFJO/action/replication_record"}},"created_at":"2026-05-18T03:37:39.860382+00:00","updated_at":"2026-05-18T03:37:39.860382+00:00"}