{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LIEXCEKLQ4W4O43IZAN4X4S3TT","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":"915b115679f8ff07368dfbd73c85fdcd9a45a64aaca412293f54bd1b836985b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-02T00:47:57Z","title_canon_sha256":"0a43dcd942629f03aa265e7d7f88285fea104193c7181172e9db5a8d44b593ce"},"schema_version":"1.0","source":{"id":"1211.0334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0334","created_at":"2026-05-18T03:41:41Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0334v1","created_at":"2026-05-18T03:41:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0334","created_at":"2026-05-18T03:41:41Z"},{"alias_kind":"pith_short_12","alias_value":"LIEXCEKLQ4W4","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LIEXCEKLQ4W4O43I","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LIEXCEKL","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:376995e15f8a92503e8bfed939809313b33c0befe52d84b3dd906dc192f9cdf5","target":"graph","created_at":"2026-05-18T03:41:41Z","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":"In this paper, we are concerned with the local existence and singularity structure of low regularity solutions to the semilinear generalized Tricomi equation $\\p_t^2u-t^m\\Delta u=f(t,x,u)$ with typical discontinuous initial data $(u(0,x), \\p_tu(0,x))=(0, \\vp(x))$; here $m\\in\\Bbb N$, $x=(x_1, ..., x_n)$, $n\\ge 2$, and $f(t,x,u)$ is $C^{\\infty}$ smooth in its arguments. When the initial data $\\vp(x)$ is a homogeneous function of degree zero or a piecewise smooth function singular along the hyperplane ${t=x_1=0}$, it is shown that the local solution $u(t,x)\\in L^{\\infty}([0,T]\\times\\Bbb R^n)$ exi","authors_text":"Huicheng Yin (Nanjing University), Ingo Witt (University of G\\\"ottingen), Zhuoping Ruan (Nanjing University)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-02T00:47:57Z","title":"On the existence and cusp singularity of solutions to semilinear generalized Tricomi equations with discontinuous initial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0334","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":"sha256:5c72ec31ef1270cdebb3bcd716eaf1b5ca254be0898902decf51bfc68808cef6","target":"record","created_at":"2026-05-18T03:41:41Z","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":"915b115679f8ff07368dfbd73c85fdcd9a45a64aaca412293f54bd1b836985b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-11-02T00:47:57Z","title_canon_sha256":"0a43dcd942629f03aa265e7d7f88285fea104193c7181172e9db5a8d44b593ce"},"schema_version":"1.0","source":{"id":"1211.0334","kind":"arxiv","version":1}},"canonical_sha256":"5a0971114b872dc77368c81bcbf25b9cfcff768eef00ad2993aa51ea68724005","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a0971114b872dc77368c81bcbf25b9cfcff768eef00ad2993aa51ea68724005","first_computed_at":"2026-05-18T03:41:41.514254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:41.514254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O0V5UvCpPH8wvosj2Y83LrgdcNM549TYFoTjHJW+dVOxUPZ0IFAlGOHG/Wgx/Vcl1KXR8NhBvWOQUN1ByM2zBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:41.515112Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c72ec31ef1270cdebb3bcd716eaf1b5ca254be0898902decf51bfc68808cef6","sha256:376995e15f8a92503e8bfed939809313b33c0befe52d84b3dd906dc192f9cdf5"],"state_sha256":"19267f091f0859996ffded443b78a5c139b601b7be30cb4be32936df4b316661"}