{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NSZL5JD5TYKW55ST5UUVQVJ3UG","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":"e0fddd918994bda6f75481b602e72f69f9e9549f3fab01af3b7c11fb9c57eec3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-04T11:20:10Z","title_canon_sha256":"5901c045e64b723db5ce3f4aedb346e3f806aaf26628bad0caf9bde6bc6a9325"},"schema_version":"1.0","source":{"id":"1512.01373","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01373","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01373v2","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01373","created_at":"2026-05-18T01:23:48Z"},{"alias_kind":"pith_short_12","alias_value":"NSZL5JD5TYKW","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NSZL5JD5TYKW55ST","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NSZL5JD5","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:64a89c7f71e89e94ad3f8d0204bd652d2396e0b4c8c56c53a0d2603663366043","target":"graph","created_at":"2026-05-18T01:23:48Z","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":"In this manuscript we first give the explicit variational structure of the nonlinear elastic waves for isotropic, homogeneous, hyperelastic materials in 2-D. Based on this variational structure, we suggest a null condition which is a kind of structural condition on the nonlinearity in order to stop the formation of finite time singularities of local smooth solutions. In the radial symmetric case, inspired by Alinhac's work [3] on 2-D quasilinear wave equations, we show that such null condition can ensure the globalexistence of smooth solutions with small initial data.","authors_text":"Dongbing Zha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-04T11:20:10Z","title":"Remarks on Nonlinear Elastic Waves in the Radial Symmetry in 2-D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01373","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:aa1f13ceed6d938a47dc14ccd7509a9a4fbb0ce6603dc29e8a6b07e30f68e589","target":"record","created_at":"2026-05-18T01:23:48Z","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":"e0fddd918994bda6f75481b602e72f69f9e9549f3fab01af3b7c11fb9c57eec3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-04T11:20:10Z","title_canon_sha256":"5901c045e64b723db5ce3f4aedb346e3f806aaf26628bad0caf9bde6bc6a9325"},"schema_version":"1.0","source":{"id":"1512.01373","kind":"arxiv","version":2}},"canonical_sha256":"6cb2bea47d9e156ef653ed2958553ba19a5116e224946cbfb6da7e648f393384","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cb2bea47d9e156ef653ed2958553ba19a5116e224946cbfb6da7e648f393384","first_computed_at":"2026-05-18T01:23:48.117237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:48.117237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6n+uPpXmbGwPwVITbPBJcPm1t3biAYHazGO8YCgEdGu7X7GpREFUQbqQ21iE93GfAK+6TGudjFxsZFKX3azVDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:48.117897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01373","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa1f13ceed6d938a47dc14ccd7509a9a4fbb0ce6603dc29e8a6b07e30f68e589","sha256:64a89c7f71e89e94ad3f8d0204bd652d2396e0b4c8c56c53a0d2603663366043"],"state_sha256":"c4b9d3b3b88aa8839eb49f45853fb690fa0dc6a4e113a20ab88ec8c182a157d7"}