{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EBZEN7BFVKVMX4JS6VBANOX7YP","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":"d195dd317cdad30b2152ac6bbb459290ede084b964d2f3ede17a0d35b880b4c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-06T06:17:48Z","title_canon_sha256":"3d6890c1a12230c2bdb705d50a3f7e5a50f644f57822294eaca308b80e393833"},"schema_version":"1.0","source":{"id":"1806.02022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02022","created_at":"2026-05-18T00:14:02Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02022v1","created_at":"2026-05-18T00:14:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02022","created_at":"2026-05-18T00:14:02Z"},{"alias_kind":"pith_short_12","alias_value":"EBZEN7BFVKVM","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EBZEN7BFVKVMX4JS","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EBZEN7BF","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:472f3a46889c691301d894380a5ce64515efe7614202bbee15941b1b4c9c12f3","target":"graph","created_at":"2026-05-18T00:14:02Z","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":"We consider the large time behaviour of solutions to the porous medium equation with a Fisher-KPP type reaction term and nonnegative, compactly supported initial function in $L^\\infty(\\mathbb{R}^N)\\setminus\\{0\\}$: \\begin{equation} \\label{eq:abstract} \\tag{$\\star$}u_t=\\Delta u^m+u-u^2\\quad\\text{in }Q:=\\mathbb{R}^N\\times\\mathbb{R}_+,\\qquad u(\\cdot,0)=u_0\\quad\\text{in }\\mathbb{R}^N, \\end{equation} with $m>1$. It is well known that the spatial support of the solution $u(\\cdot, t)$ to this problem remains bounded for all time $t>0$. In spatial dimension one it is known that there is a minimal speed","authors_text":"Fernando Quiros, Maolin Zhou, Yihong Du","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-06T06:17:48Z","title":"Logarithmic corrections in Fisher-KPP type Porous Medium Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02022","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":"sha256:99ffb6806c1c2a05dbc49459fadd95747a3d770e808c6bd1614f92d0b630d71f","target":"record","created_at":"2026-05-18T00:14:02Z","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":"d195dd317cdad30b2152ac6bbb459290ede084b964d2f3ede17a0d35b880b4c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-06T06:17:48Z","title_canon_sha256":"3d6890c1a12230c2bdb705d50a3f7e5a50f644f57822294eaca308b80e393833"},"schema_version":"1.0","source":{"id":"1806.02022","kind":"arxiv","version":1}},"canonical_sha256":"207246fc25aaaacbf132f54206baffc3e5b89102fd26397865da98b2c5102dfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"207246fc25aaaacbf132f54206baffc3e5b89102fd26397865da98b2c5102dfd","first_computed_at":"2026-05-18T00:14:02.976240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:02.976240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q3ckALGOsUaqoRRmal/WN6AiFVnszWxBDOM22Ajr1H2ApiRGkLpa9UHfaCkHwdKBsd0TWDWH11tu8BZLMi2CCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:02.976907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99ffb6806c1c2a05dbc49459fadd95747a3d770e808c6bd1614f92d0b630d71f","sha256:472f3a46889c691301d894380a5ce64515efe7614202bbee15941b1b4c9c12f3"],"state_sha256":"2dd6355e3a92b166343cd907e16653125d00d2fc78de0d24d7cc9bca438305f3"}