{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2IVHHFEXPQRMNBYQLIN7TMDZV3","short_pith_number":"pith:2IVHHFEX","canonical_record":{"source":{"id":"1806.08228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2018-06-19T19:18:17Z","cross_cats_sorted":[],"title_canon_sha256":"5f3a9dc9d20ddd0efb9d0fe82f7280d66c520b6a5746894c9f3c65e3cd8efa28","abstract_canon_sha256":"6e31b63c121e6ad86879f935a1b31842f398f9b65fa0af2012cf5469ad626193"},"schema_version":"1.0"},"canonical_sha256":"d22a7394977c22c687105a1bf9b079aee7e23e3a32800f00ca86d325dde66be1","source":{"kind":"arxiv","id":"1806.08228","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08228","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08228v1","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08228","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"2IVHHFEXPQRM","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2IVHHFEXPQRMNBYQ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2IVHHFEX","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2IVHHFEXPQRMNBYQLIN7TMDZV3","target":"record","payload":{"canonical_record":{"source":{"id":"1806.08228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2018-06-19T19:18:17Z","cross_cats_sorted":[],"title_canon_sha256":"5f3a9dc9d20ddd0efb9d0fe82f7280d66c520b6a5746894c9f3c65e3cd8efa28","abstract_canon_sha256":"6e31b63c121e6ad86879f935a1b31842f398f9b65fa0af2012cf5469ad626193"},"schema_version":"1.0"},"canonical_sha256":"d22a7394977c22c687105a1bf9b079aee7e23e3a32800f00ca86d325dde66be1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:41.676182Z","signature_b64":"bPM76AXAhUfBb5B0+OG0LeKUhjWmhfzglY0k+p+5TqlP2jNPxMvzmhETTDALp4hpn2rgW6HvpSjqpFss6GCTCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d22a7394977c22c687105a1bf9b079aee7e23e3a32800f00ca86d325dde66be1","last_reissued_at":"2026-05-18T00:12:41.675655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:41.675655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.08228","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cHc5g7feMm7KIDAeClerSGfky4331BKH/yG1+Jp+rllVIMavTSUaQ4rnfLmQ8/G8BiOrnIbnuBGCGOWZ3yXBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T16:44:52.210652Z"},"content_sha256":"3c2a4eac3bdc8cfc90800df81193e322f3c24b259fe9618003ae445469735187","schema_version":"1.0","event_id":"sha256:3c2a4eac3bdc8cfc90800df81193e322f3c24b259fe9618003ae445469735187"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2IVHHFEXPQRMNBYQLIN7TMDZV3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Electro-Neutral Models for dynamic Poisson-Nernst-Planck System: 2D Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.bio-ph","authors_text":"Huaxiong Huang, Xiulei Cao, Zilong Song","submitted_at":"2018-06-19T19:18:17Z","abstract_excerpt":"The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modelling and computational challenges. In a previous paper, we derived simplified electro-neutral (EN) models in one dimensional space where the thin boundary layers are replaced by effective boundary conditions. In this paper, we extend our analysis to the two dimensional case where the EN model enjoys even greater advantages. First of all, it is much cheaper to solve the EN models numerically. Secondl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08228","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vvXZMZmMM9+hc3lbug6t25pBsnDFh+0GiAAZOiQeyqH0+fOamP3fSiYr9EWvPQvnIGiNQDyeKskSjs8QANRhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T16:44:52.211005Z"},"content_sha256":"b0d11b3423be1fcd9e0da5f2e5cc010adc5c85ff6042ee355e898ea0a0517336","schema_version":"1.0","event_id":"sha256:b0d11b3423be1fcd9e0da5f2e5cc010adc5c85ff6042ee355e898ea0a0517336"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2IVHHFEXPQRMNBYQLIN7TMDZV3/bundle.json","state_url":"https://pith.science/pith/2IVHHFEXPQRMNBYQLIN7TMDZV3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2IVHHFEXPQRMNBYQLIN7TMDZV3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T16:44:52Z","links":{"resolver":"https://pith.science/pith/2IVHHFEXPQRMNBYQLIN7TMDZV3","bundle":"https://pith.science/pith/2IVHHFEXPQRMNBYQLIN7TMDZV3/bundle.json","state":"https://pith.science/pith/2IVHHFEXPQRMNBYQLIN7TMDZV3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2IVHHFEXPQRMNBYQLIN7TMDZV3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2IVHHFEXPQRMNBYQLIN7TMDZV3","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":"6e31b63c121e6ad86879f935a1b31842f398f9b65fa0af2012cf5469ad626193","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2018-06-19T19:18:17Z","title_canon_sha256":"5f3a9dc9d20ddd0efb9d0fe82f7280d66c520b6a5746894c9f3c65e3cd8efa28"},"schema_version":"1.0","source":{"id":"1806.08228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.08228","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"arxiv_version","alias_value":"1806.08228v1","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.08228","created_at":"2026-05-18T00:12:41Z"},{"alias_kind":"pith_short_12","alias_value":"2IVHHFEXPQRM","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2IVHHFEXPQRMNBYQ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2IVHHFEX","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:b0d11b3423be1fcd9e0da5f2e5cc010adc5c85ff6042ee355e898ea0a0517336","target":"graph","created_at":"2026-05-18T00:12:41Z","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":"The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modelling and computational challenges. In a previous paper, we derived simplified electro-neutral (EN) models in one dimensional space where the thin boundary layers are replaced by effective boundary conditions. In this paper, we extend our analysis to the two dimensional case where the EN model enjoys even greater advantages. First of all, it is much cheaper to solve the EN models numerically. Secondl","authors_text":"Huaxiong Huang, Xiulei Cao, Zilong Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2018-06-19T19:18:17Z","title":"Electro-Neutral Models for dynamic Poisson-Nernst-Planck System: 2D Case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08228","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":"sha256:3c2a4eac3bdc8cfc90800df81193e322f3c24b259fe9618003ae445469735187","target":"record","created_at":"2026-05-18T00:12:41Z","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":"6e31b63c121e6ad86879f935a1b31842f398f9b65fa0af2012cf5469ad626193","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2018-06-19T19:18:17Z","title_canon_sha256":"5f3a9dc9d20ddd0efb9d0fe82f7280d66c520b6a5746894c9f3c65e3cd8efa28"},"schema_version":"1.0","source":{"id":"1806.08228","kind":"arxiv","version":1}},"canonical_sha256":"d22a7394977c22c687105a1bf9b079aee7e23e3a32800f00ca86d325dde66be1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d22a7394977c22c687105a1bf9b079aee7e23e3a32800f00ca86d325dde66be1","first_computed_at":"2026-05-18T00:12:41.675655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:41.675655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bPM76AXAhUfBb5B0+OG0LeKUhjWmhfzglY0k+p+5TqlP2jNPxMvzmhETTDALp4hpn2rgW6HvpSjqpFss6GCTCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:41.676182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.08228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c2a4eac3bdc8cfc90800df81193e322f3c24b259fe9618003ae445469735187","sha256:b0d11b3423be1fcd9e0da5f2e5cc010adc5c85ff6042ee355e898ea0a0517336"],"state_sha256":"f6336bdcd729c7a8d2c04d22639b53682fe5f650b7b5da559411be4c6e039399"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fzrHqU7LAR6+kIupHBwPphkk3pAbjlitfGUftckdmiVKaLo0+fR78ObgyNxnvgX4PXjOi0kljPfWd9M/nU2iBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T16:44:52.212949Z","bundle_sha256":"a75bc7f35f049c5267a745503a0f4f1757a859b57897f021b467404e973b75ab"}}