{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:F7MC4CLF4534LWOP4ASS6UVYBM","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":"a1a98127ac0584b2f165dff359c88130479a3b6d0e1ba36778fb973147600774","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-09T16:47:18Z","title_canon_sha256":"c894132e8649a49392c02fa41e4f0771a6451899888410cd1a600eed831ab7f2"},"schema_version":"1.0","source":{"id":"1312.2509","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2509","created_at":"2026-05-18T03:05:10Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2509v1","created_at":"2026-05-18T03:05:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2509","created_at":"2026-05-18T03:05:10Z"},{"alias_kind":"pith_short_12","alias_value":"F7MC4CLF4534","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"F7MC4CLF4534LWOP","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"F7MC4CLF","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:df4042cef5eaf19047e54670f2973d24c029d50d9812e54dafa7b5691536c535","target":"graph","created_at":"2026-05-18T03:05:10Z","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":"Let $\\Omega$ be a bounded domain in ${\\mathbb R}^N$ and $T>0$. We study the problem \\begin{equation} (P)\\left\\{ \\begin{array}{lll} u_t - \\Delta u \\pm g(u) &= \\mu \\quad &\\text{in } Q_T:=\\Omega \\times (0,T) \\\\ \\phantom{------,} u&=0 &\\text{on } \\partial \\Omega \\times (0,T)\\\\ \\phantom{----,} u(.,0) &=\\omega &\\text{in } \\Omega. \\end{array} \\right. \\end{equation} where $\\mu$ and $\\omega$ are bounded Radon measures in $Q_T$ and $\\Omega$ respectively and $g(u) \\sim e^{a |u|^q} $ with $a>0$ and $q \\geq 1$. We provide a sufficient condition in terms of fractional maximal potentials of $\\mu$ and $\\omega","authors_text":"Phuoc-Tai Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-09T16:47:18Z","title":"Parabolic equations with exponential nonlinearity and measure data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2509","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:aee50be38fab1767a2d765fed3bef1d150a6c731659630bbbf3579b6ec9c91e2","target":"record","created_at":"2026-05-18T03:05:10Z","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":"a1a98127ac0584b2f165dff359c88130479a3b6d0e1ba36778fb973147600774","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-09T16:47:18Z","title_canon_sha256":"c894132e8649a49392c02fa41e4f0771a6451899888410cd1a600eed831ab7f2"},"schema_version":"1.0","source":{"id":"1312.2509","kind":"arxiv","version":1}},"canonical_sha256":"2fd82e0965e777c5d9cfe0252f52b80b2530560366aa2a2c028f071dbfd18547","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fd82e0965e777c5d9cfe0252f52b80b2530560366aa2a2c028f071dbfd18547","first_computed_at":"2026-05-18T03:05:10.130710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:10.130710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2O5+4O9XdUOuAIAWr5a2gcneBqXR4WAGxopoacVUnN2dsQPKyJyPunVxr6y6b8Usvqea64NDFH1rXVoPmxCqDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:10.131257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2509","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aee50be38fab1767a2d765fed3bef1d150a6c731659630bbbf3579b6ec9c91e2","sha256:df4042cef5eaf19047e54670f2973d24c029d50d9812e54dafa7b5691536c535"],"state_sha256":"a08b756aa6c2e5e8425db4820bb601391ea9c1659906aa04b044720eabe21d27"}