{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:XKXI6D3CLBEFHV4IQU2XJGOCPM","short_pith_number":"pith:XKXI6D3C","schema_version":"1.0","canonical_sha256":"baae8f0f62584853d78885357499c27b21982e534441eb035939260726caa1b7","source":{"kind":"arxiv","id":"1009.6131","version":2},"attestation_state":"computed","paper":{"title":"Interaction between nonlinear diffusion and geometry of domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rolando Magnanini, Shigeru Sakaguchi","submitted_at":"2010-09-30T13:49:55Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.6131","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-30T13:49:55Z","cross_cats_sorted":[],"title_canon_sha256":"09c2bc467e03707225669fd6e06c1da7d887f6a854d8609fe03bed3db2ed9a78","abstract_canon_sha256":"c12fa0644c150cecfd149d71cd8eb68521907c7206b41673957c399c54585dae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:59.498793Z","signature_b64":"8hgJRjHO53zDau9pcy08gSL9rapOWisawuKETm38fyZ3xRNWKlu2qtZVrRdsoBQ3O7rE11G5pYzunj0fxPzHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baae8f0f62584853d78885357499c27b21982e534441eb035939260726caa1b7","last_reissued_at":"2026-05-18T04:15:59.498243Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:59.498243Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interaction between nonlinear diffusion and geometry of domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rolando Magnanini, Shigeru Sakaguchi","submitted_at":"2010-09-30T13:49:55Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6131","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.6131","created_at":"2026-05-18T04:15:59.498337+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.6131v2","created_at":"2026-05-18T04:15:59.498337+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.6131","created_at":"2026-05-18T04:15:59.498337+00:00"},{"alias_kind":"pith_short_12","alias_value":"XKXI6D3CLBEF","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"XKXI6D3CLBEFHV4I","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"XKXI6D3C","created_at":"2026-05-18T12:26:17.028572+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XKXI6D3CLBEFHV4IQU2XJGOCPM","json":"https://pith.science/pith/XKXI6D3CLBEFHV4IQU2XJGOCPM.json","graph_json":"https://pith.science/api/pith-number/XKXI6D3CLBEFHV4IQU2XJGOCPM/graph.json","events_json":"https://pith.science/api/pith-number/XKXI6D3CLBEFHV4IQU2XJGOCPM/events.json","paper":"https://pith.science/paper/XKXI6D3C"},"agent_actions":{"view_html":"https://pith.science/pith/XKXI6D3CLBEFHV4IQU2XJGOCPM","download_json":"https://pith.science/pith/XKXI6D3CLBEFHV4IQU2XJGOCPM.json","view_paper":"https://pith.science/paper/XKXI6D3C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.6131&json=true","fetch_graph":"https://pith.science/api/pith-number/XKXI6D3CLBEFHV4IQU2XJGOCPM/graph.json","fetch_events":"https://pith.science/api/pith-number/XKXI6D3CLBEFHV4IQU2XJGOCPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XKXI6D3CLBEFHV4IQU2XJGOCPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XKXI6D3CLBEFHV4IQU2XJGOCPM/action/storage_attestation","attest_author":"https://pith.science/pith/XKXI6D3CLBEFHV4IQU2XJGOCPM/action/author_attestation","sign_citation":"https://pith.science/pith/XKXI6D3CLBEFHV4IQU2XJGOCPM/action/citation_signature","submit_replication":"https://pith.science/pith/XKXI6D3CLBEFHV4IQU2XJGOCPM/action/replication_record"}},"created_at":"2026-05-18T04:15:59.498337+00:00","updated_at":"2026-05-18T04:15:59.498337+00:00"}