{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LDFTENXYABUYB7F7DSCZBQ7ESI","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":"62fea4a5c1fb87b8dc347adb3ba2b9f48a14f4f1d2caae54ec2ccc5e71b4a733","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-30T16:57:30Z","title_canon_sha256":"a4f64067bcb9dcbe5cc2a1eb3af4697593f9762890935b3a296e28facd80c894"},"schema_version":"1.0","source":{"id":"1804.00560","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.00560","created_at":"2026-05-18T00:19:36Z"},{"alias_kind":"arxiv_version","alias_value":"1804.00560v1","created_at":"2026-05-18T00:19:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00560","created_at":"2026-05-18T00:19:36Z"},{"alias_kind":"pith_short_12","alias_value":"LDFTENXYABUY","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LDFTENXYABUYB7F7","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LDFTENXY","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:a68fd1e0dc419b07c667c4a5f498ee038c57f574bd3d3e9b7dd345d91577da4a","target":"graph","created_at":"2026-05-18T00:19:36Z","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 consider the following semi-linear complex heat equation \\begin{eqnarray*} \\partial_t u = \\Delta u + u^p, u \\in \\mathbb{C} \\end{eqnarray*} in $\\mathbb{R}^n,$ with an arbitrary power $p,$ $ p > 1$. In particular, $p$ can be non integer and even irrational. We construct for this equation a complex solution $u = u_1 + i u_2$, which blows up in finite time $T$ and only at one blowup point $a.$ Moreover, we also describe the asymptotics of the solution by the following final profiles: \\begin{eqnarray*} u(x,T) &\\sim & \\left[ \\frac{(p-1)^2 |x-a|^2}{ 8 p |\\ln|x-a||}\\right]^{-\\frac{1}","authors_text":"Giao Ky Duong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-30T16:57:30Z","title":"A blowup solution of a complex semi-linear heat equation with an irrational power"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00560","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":"sha256:774dd4b59116a59b3e12818e39570f522ce7be8ffc1e1f1af223e71619712222","target":"record","created_at":"2026-05-18T00:19:36Z","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":"62fea4a5c1fb87b8dc347adb3ba2b9f48a14f4f1d2caae54ec2ccc5e71b4a733","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-30T16:57:30Z","title_canon_sha256":"a4f64067bcb9dcbe5cc2a1eb3af4697593f9762890935b3a296e28facd80c894"},"schema_version":"1.0","source":{"id":"1804.00560","kind":"arxiv","version":1}},"canonical_sha256":"58cb3236f8006980fcbf1c8590c3e49201800b6774ccf5716168aeb8c17cf0c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58cb3236f8006980fcbf1c8590c3e49201800b6774ccf5716168aeb8c17cf0c6","first_computed_at":"2026-05-18T00:19:36.647221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:36.647221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RLspCRnzKGcmZccIMkuFWLOTBGGRvOe/mHqSe9KVSocnOaI3ccLBYmC5jk9snsg6yUxJpvacd1sFUwh2N7OHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:36.647914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.00560","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:774dd4b59116a59b3e12818e39570f522ce7be8ffc1e1f1af223e71619712222","sha256:a68fd1e0dc419b07c667c4a5f498ee038c57f574bd3d3e9b7dd345d91577da4a"],"state_sha256":"43425827bda97fbae60f26eaff48ca8dcffd0afe8a72be366e1f0343133d0f13"}