{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XKXI6D3CLBEFHV4IQU2XJGOCPM","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":"c12fa0644c150cecfd149d71cd8eb68521907c7206b41673957c399c54585dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-30T13:49:55Z","title_canon_sha256":"09c2bc467e03707225669fd6e06c1da7d887f6a854d8609fe03bed3db2ed9a78"},"schema_version":"1.0","source":{"id":"1009.6131","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.6131","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"arxiv_version","alias_value":"1009.6131v2","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.6131","created_at":"2026-05-18T04:15:59Z"},{"alias_kind":"pith_short_12","alias_value":"XKXI6D3CLBEF","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XKXI6D3CLBEFHV4I","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XKXI6D3C","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:512742f35683c5922b9607f3d7305ac7afe4d25bb850b2361490a6d234f4e8bd","target":"graph","created_at":"2026-05-18T04:15:59Z","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 domain in $\\mathbb R^N$, where $N \\ge 2$ and $\\partial\\Omega$ is not necessarily bounded. We consider nonlinear diffusion equations of the form $\\partial_t u= \\Delta \\phi(u)$. Let $u=u(x,t)$ be the solution of either the initial-boundary value problem over $\\Omega$, where the initial value equals zero and the boundary value equals 1, or the Cauchy problem where the initial data is the characteristic function of the set $\\mathbb R^N\\setminus \\Omega$.\n  We consider an open ball $B$ in $\\Omega$ whose closure intersects $\\partial\\Omega$ only at one point, and we derive asymptotic","authors_text":"Rolando Magnanini, Shigeru Sakaguchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-30T13:49:55Z","title":"Interaction between nonlinear diffusion and geometry of domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6131","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":"sha256:710c0074d8ba3ca4f15ea230b0e41088a361cad0613881ab207d0f4179516c91","target":"record","created_at":"2026-05-18T04:15:59Z","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":"c12fa0644c150cecfd149d71cd8eb68521907c7206b41673957c399c54585dae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-30T13:49:55Z","title_canon_sha256":"09c2bc467e03707225669fd6e06c1da7d887f6a854d8609fe03bed3db2ed9a78"},"schema_version":"1.0","source":{"id":"1009.6131","kind":"arxiv","version":2}},"canonical_sha256":"baae8f0f62584853d78885357499c27b21982e534441eb035939260726caa1b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baae8f0f62584853d78885357499c27b21982e534441eb035939260726caa1b7","first_computed_at":"2026-05-18T04:15:59.498243Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:59.498243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8hgJRjHO53zDau9pcy08gSL9rapOWisawuKETm38fyZ3xRNWKlu2qtZVrRdsoBQ3O7rE11G5pYzunj0fxPzHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:59.498793Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.6131","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:710c0074d8ba3ca4f15ea230b0e41088a361cad0613881ab207d0f4179516c91","sha256:512742f35683c5922b9607f3d7305ac7afe4d25bb850b2361490a6d234f4e8bd"],"state_sha256":"474ed51eb4e740a13e4556f4072e11e0873842de477a32baffffe6de5d9c0a8e"}