{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5PLPH5L2MC2UDUA6CGS4R5NACA","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":"1052ce16b8df8fe5bb01a1b427a3d371ab615be851cce28d2fe727e6eb07d2e1","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-02-25T06:19:25Z","title_canon_sha256":"b7d4bf979d4fbe23b184f44b8607f4d35bbeed2117213ebe8cfd5f9ffd51b0f8"},"schema_version":"1.0","source":{"id":"0902.4290","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.4290","created_at":"2026-05-18T02:14:39Z"},{"alias_kind":"arxiv_version","alias_value":"0902.4290v1","created_at":"2026-05-18T02:14:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.4290","created_at":"2026-05-18T02:14:39Z"},{"alias_kind":"pith_short_12","alias_value":"5PLPH5L2MC2U","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5PLPH5L2MC2UDUA6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5PLPH5L2","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:fb63fd0c1ae22998a85e9d0f102c9f0acd734a6a43a7a7350cdb766cce4a0c16","target":"graph","created_at":"2026-05-18T02:14:39Z","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 study global dynamics of the Poisson-Nernst-Planck (PNP) system for flows of two types of ions through a narrow tubular-like membrane channel. As the radius of the cross-section of the three-dimensional tubular-like membrane channel approaches zero, a one-dimensional limiting PNP system is derived. This one-dimensional limiting system differs from previous studied one-dimensional PNP systems in that it encodes the defining geometry of the three-dimensional membrane channel. To justify this limiting process, we show that the global attractors of the three-dimensional PNP systems are upper se","authors_text":"Bixiang Wang, Weishi Liu","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-02-25T06:19:25Z","title":"Poisson-Nernst-Planck Systems for Narrow Tubular-like Membrane Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4290","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":"sha256:8245637a9d49162242b22650d38319b42b51c36d763d315097c79a602bcdf1a3","target":"record","created_at":"2026-05-18T02:14:39Z","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":"1052ce16b8df8fe5bb01a1b427a3d371ab615be851cce28d2fe727e6eb07d2e1","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-02-25T06:19:25Z","title_canon_sha256":"b7d4bf979d4fbe23b184f44b8607f4d35bbeed2117213ebe8cfd5f9ffd51b0f8"},"schema_version":"1.0","source":{"id":"0902.4290","kind":"arxiv","version":1}},"canonical_sha256":"ebd6f3f57a60b541d01e11a5c8f5a01030b2c6dc1121113dd6eceb6582bf6f4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebd6f3f57a60b541d01e11a5c8f5a01030b2c6dc1121113dd6eceb6582bf6f4d","first_computed_at":"2026-05-18T02:14:39.205725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:39.205725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"luok56wtIp+JboSwr/S+cpNqgaNk5ZLXjbYW7ztB1YfcMDp2j9teUacdKfIIM0J723Rm0wnAJQWufJZTNHQxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:39.206290Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.4290","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8245637a9d49162242b22650d38319b42b51c36d763d315097c79a602bcdf1a3","sha256:fb63fd0c1ae22998a85e9d0f102c9f0acd734a6a43a7a7350cdb766cce4a0c16"],"state_sha256":"3e9285cca990d194f0387938b0dd62b7e08b244023343cdd71dc60315a239f23"}