{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EF3IWBFXSLGXIMV5XWJMZRX6AW","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":"c8092fcd9b1519a53a93b1bcad5cd915fe554ef0cfd47b787e2a0e0b058f085f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-02T13:47:48Z","title_canon_sha256":"0c45516a30ec6b3069b8fe900c2bc625694f9a19915927e5f5c644e8fe3adf7d"},"schema_version":"1.0","source":{"id":"1409.0707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0707","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0707v1","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0707","created_at":"2026-05-18T02:43:46Z"},{"alias_kind":"pith_short_12","alias_value":"EF3IWBFXSLGX","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EF3IWBFXSLGXIMV5","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EF3IWBFX","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:f13f882dd82c34dd4ed5ae8ad6ad1602b67d1ce310952c056e00c9d87d322c65","target":"graph","created_at":"2026-05-18T02:43:46Z","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 [19-20], we have established the existence and singularity structures of low regularity solutions to the semilinear generalized Tricomi equations in the degenerate hyperbolic regions and to the higher order degenerate hyperbolic equations, respectively. In the present paper, we shall be concerned with the low regularity solution problem for the semilinear mixed type equation $\\p_t^2u-t^{2l-1}\\Delta u= f(t,x,u)$ with an initial data $u(0,x)=\\varphi(x)\\in H^{s}(\\Bbb R^n)$ ($0\\le s<\\f{n}{2}$), where $(t,x)\\in\\Bbb R \\times\\Bbb R^n$, $n\\ge 2$, $l\\in\\Bbb N$, $f(t,x,u)$ is $C^1$ smooth in its argu","authors_text":"Huicheng Yin, Ingo Witt, Zhuoping Ruan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-02T13:47:48Z","title":"On the existence of low regularity solutions to semilinear generalized Tricomi equations in mixed type domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0707","kind":"arxiv","version":1},"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":"sha256:9c7727c43780557683af8adfb063412b2384db791485bcdf5aa776197cc3aef0","target":"record","created_at":"2026-05-18T02:43:46Z","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":"c8092fcd9b1519a53a93b1bcad5cd915fe554ef0cfd47b787e2a0e0b058f085f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-09-02T13:47:48Z","title_canon_sha256":"0c45516a30ec6b3069b8fe900c2bc625694f9a19915927e5f5c644e8fe3adf7d"},"schema_version":"1.0","source":{"id":"1409.0707","kind":"arxiv","version":1}},"canonical_sha256":"21768b04b792cd7432bdbd92ccc6fe05a9d662438abd286db7a61883f167f7b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21768b04b792cd7432bdbd92ccc6fe05a9d662438abd286db7a61883f167f7b5","first_computed_at":"2026-05-18T02:43:46.315536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:46.315536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r8TswGJd/dlgkqmUGctUUiyYkVxlEnFxrevHvGAxdSdsV5VTsmiRDkTgq4p5PLbOt5cDUQUvnp+g+V6pwZDNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:46.315993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c7727c43780557683af8adfb063412b2384db791485bcdf5aa776197cc3aef0","sha256:f13f882dd82c34dd4ed5ae8ad6ad1602b67d1ce310952c056e00c9d87d322c65"],"state_sha256":"6ade73ba2a67240cc2c6cde8b26e09611cb4edb9331e1859098207be4af32c35"}