{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3EEOUVGMD5NSDGM2IB4BVE265Y","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":"bd729023926d16a452813e397c4ed1c74296a8ea46ce9577e05d399526b1512d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-10T19:18:06Z","title_canon_sha256":"f374fa7bc9c75862fdb61038aa47c2a130436dc4e724b8c8dba6c540f4bcfd06"},"schema_version":"1.0","source":{"id":"1411.2545","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2545","created_at":"2026-05-18T02:37:44Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2545v2","created_at":"2026-05-18T02:37:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2545","created_at":"2026-05-18T02:37:44Z"},{"alias_kind":"pith_short_12","alias_value":"3EEOUVGMD5NS","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3EEOUVGMD5NSDGM2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3EEOUVGM","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:02f4d5302d538f751d2dee2934bead73e2970ea8c38b2aabc3d8745f6271953d","target":"graph","created_at":"2026-05-18T02:37:44Z","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 deal with local estimates for parabolic problems in $\\mathbb{R}^N$ with absorbing first order terms, whose model is $\\{ {l} u_t- \\Delta u +u |\\nabla u|^q = f(t,x) \\quad &{in}\\, (0,T) \\times \\mathbb{R}^N\\,, \\\\[1.5 ex] u(0,x)= u_0 (x) &box{in}\\, \\mathbb{R}^N.$ where $T>0$, $N\\geq 2$, $1<q\\leq 2$, $f(t,x)\\in L^1( 0,T; L^1_{\\rm loc} (\\mathbb{R}^N))$ and $u_0\\in L^1_{\\rm loc} (\\mathbb{R}^N)$.","authors_text":"Francesco Petitta, Tommaso Leonori","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-10T19:18:06Z","title":"Local estimates for parabolic equations with nonlinear gradient terms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2545","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":"sha256:72f9c1a27133da943413c9a4e36fd9728ae0b2678d78dfec9c1ea60e2b534949","target":"record","created_at":"2026-05-18T02:37:44Z","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":"bd729023926d16a452813e397c4ed1c74296a8ea46ce9577e05d399526b1512d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-10T19:18:06Z","title_canon_sha256":"f374fa7bc9c75862fdb61038aa47c2a130436dc4e724b8c8dba6c540f4bcfd06"},"schema_version":"1.0","source":{"id":"1411.2545","kind":"arxiv","version":2}},"canonical_sha256":"d908ea54cc1f5b21999a40781a935eee3d7a0ca198988453cdcf087743ed9335","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d908ea54cc1f5b21999a40781a935eee3d7a0ca198988453cdcf087743ed9335","first_computed_at":"2026-05-18T02:37:44.116443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:44.116443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Dm+L4V8jNZvxevJWZSWFG/+PcSxdGQF2PkbIR88cACDOfaO80Y7a4dxekvFZy/GtnsLHrG2oy5zlg7qiDyyCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:44.117001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2545","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72f9c1a27133da943413c9a4e36fd9728ae0b2678d78dfec9c1ea60e2b534949","sha256:02f4d5302d538f751d2dee2934bead73e2970ea8c38b2aabc3d8745f6271953d"],"state_sha256":"810fc0e7cf5115aece2509bdaba4bbf440bc645ee561b0190f8a346df78f8bd5"}