{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:V6Z6QONGRIMGNQWYZ3YTTODSMD","short_pith_number":"pith:V6Z6QONG","canonical_record":{"source":{"id":"1805.03332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-09T00:53:07Z","cross_cats_sorted":[],"title_canon_sha256":"7f6609d662d7341382d970d3726ad8c6247210bf21ce7a41988b289bfe2c2316","abstract_canon_sha256":"ed5abc7a47c7db424e825645cbfc082fd69c95fb1b02be8efbfbb3b1e2fe49cc"},"schema_version":"1.0"},"canonical_sha256":"afb3e839a68a1866c2d8cef139b87260e825bee53f9b11c5d20d7bc1ff9dec88","source":{"kind":"arxiv","id":"1805.03332","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03332","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03332v1","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03332","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"V6Z6QONGRIMG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"V6Z6QONGRIMGNQWY","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"V6Z6QONG","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:V6Z6QONGRIMGNQWYZ3YTTODSMD","target":"record","payload":{"canonical_record":{"source":{"id":"1805.03332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-09T00:53:07Z","cross_cats_sorted":[],"title_canon_sha256":"7f6609d662d7341382d970d3726ad8c6247210bf21ce7a41988b289bfe2c2316","abstract_canon_sha256":"ed5abc7a47c7db424e825645cbfc082fd69c95fb1b02be8efbfbb3b1e2fe49cc"},"schema_version":"1.0"},"canonical_sha256":"afb3e839a68a1866c2d8cef139b87260e825bee53f9b11c5d20d7bc1ff9dec88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:20.480772Z","signature_b64":"la2SE4n9Rf8nhgziZpkE1iIN1smOxh59vM4VWLsVCeAue0ZsXrBYz+MSODRFPrKMKqNYPQEG7NcfGlG4+ZD/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afb3e839a68a1866c2d8cef139b87260e825bee53f9b11c5d20d7bc1ff9dec88","last_reissued_at":"2026-05-18T00:16:20.480188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:20.480188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.03332","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":"2026-05-18T00:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xHs1TOPEk7eSM7VxrxWW5msKtzCzGtyFY81Mn/peBAGSp1UON2VhKw1me7VQQhFREutYTWl5F6MdzXjasEHiBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:00:49.746979Z"},"content_sha256":"ea2c50650b67ff63435f434d07d5bf190594526e104af312ef3c387b22c4ff59","schema_version":"1.0","event_id":"sha256:ea2c50650b67ff63435f434d07d5bf190594526e104af312ef3c387b22c4ff59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:V6Z6QONGRIMGNQWYZ3YTTODSMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite domain effects in steady-state solutions of Poisson-Nernst-Planck equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Doron Elad, Nir Gavish","submitted_at":"2018-05-09T00:53:07Z","abstract_excerpt":"Steady-state solutions of the Poisson-Nernst-Planck model are studied in the asymptotic limit of large, but finite domains. By using asymptotic matching for integrals, we derive an approximate solution for the steady-state equation with exponentially small error with respect to the domain size. The approximation is used to quantify the extent of finite domain effects over the full parameter space. Surprisingly, already for small applied voltages (several thermal voltages), we found that finite domain effects are significant even for large domains (on the scale of hundreds of Debye lengths). Na"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03332","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":"2026-05-18T00:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lBB1tgqz150z2nyu5Iq/0ogUK/1ZG5l9A3C8hasiVVTsUZ92jQtbA1Ei03lvvLlbpSgaK6zRaNXwea5FJfkhDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:00:49.747353Z"},"content_sha256":"4d3502c44cf0c586cde8e44cf59e2b6bb2c2c621163e538bf9a0529269435947","schema_version":"1.0","event_id":"sha256:4d3502c44cf0c586cde8e44cf59e2b6bb2c2c621163e538bf9a0529269435947"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6Z6QONGRIMGNQWYZ3YTTODSMD/bundle.json","state_url":"https://pith.science/pith/V6Z6QONGRIMGNQWYZ3YTTODSMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6Z6QONGRIMGNQWYZ3YTTODSMD/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":"2026-06-02T20:00:49Z","links":{"resolver":"https://pith.science/pith/V6Z6QONGRIMGNQWYZ3YTTODSMD","bundle":"https://pith.science/pith/V6Z6QONGRIMGNQWYZ3YTTODSMD/bundle.json","state":"https://pith.science/pith/V6Z6QONGRIMGNQWYZ3YTTODSMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6Z6QONGRIMGNQWYZ3YTTODSMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V6Z6QONGRIMGNQWYZ3YTTODSMD","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":"ed5abc7a47c7db424e825645cbfc082fd69c95fb1b02be8efbfbb3b1e2fe49cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-09T00:53:07Z","title_canon_sha256":"7f6609d662d7341382d970d3726ad8c6247210bf21ce7a41988b289bfe2c2316"},"schema_version":"1.0","source":{"id":"1805.03332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03332","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03332v1","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03332","created_at":"2026-05-18T00:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"V6Z6QONGRIMG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"V6Z6QONGRIMGNQWY","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"V6Z6QONG","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:4d3502c44cf0c586cde8e44cf59e2b6bb2c2c621163e538bf9a0529269435947","target":"graph","created_at":"2026-05-18T00:16:20Z","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":"Steady-state solutions of the Poisson-Nernst-Planck model are studied in the asymptotic limit of large, but finite domains. By using asymptotic matching for integrals, we derive an approximate solution for the steady-state equation with exponentially small error with respect to the domain size. The approximation is used to quantify the extent of finite domain effects over the full parameter space. Surprisingly, already for small applied voltages (several thermal voltages), we found that finite domain effects are significant even for large domains (on the scale of hundreds of Debye lengths). Na","authors_text":"Doron Elad, Nir Gavish","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-09T00:53:07Z","title":"Finite domain effects in steady-state solutions of Poisson-Nernst-Planck equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03332","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:ea2c50650b67ff63435f434d07d5bf190594526e104af312ef3c387b22c4ff59","target":"record","created_at":"2026-05-18T00:16:20Z","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":"ed5abc7a47c7db424e825645cbfc082fd69c95fb1b02be8efbfbb3b1e2fe49cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-09T00:53:07Z","title_canon_sha256":"7f6609d662d7341382d970d3726ad8c6247210bf21ce7a41988b289bfe2c2316"},"schema_version":"1.0","source":{"id":"1805.03332","kind":"arxiv","version":1}},"canonical_sha256":"afb3e839a68a1866c2d8cef139b87260e825bee53f9b11c5d20d7bc1ff9dec88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afb3e839a68a1866c2d8cef139b87260e825bee53f9b11c5d20d7bc1ff9dec88","first_computed_at":"2026-05-18T00:16:20.480188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:20.480188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"la2SE4n9Rf8nhgziZpkE1iIN1smOxh59vM4VWLsVCeAue0ZsXrBYz+MSODRFPrKMKqNYPQEG7NcfGlG4+ZD/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:20.480772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.03332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea2c50650b67ff63435f434d07d5bf190594526e104af312ef3c387b22c4ff59","sha256:4d3502c44cf0c586cde8e44cf59e2b6bb2c2c621163e538bf9a0529269435947"],"state_sha256":"41f183e5d88ff2aa756ad13ebc83c7e2095f195e1a1511fb19285d01cf087b11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8lI9A2MxfGMnT5astb5ITmIBih4IhxuePJid8eLgd+h2OvLiHX3UQJr2NyRPlcM62sIvP1GjLzr8VhhP+Uf3Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:00:49.749428Z","bundle_sha256":"2081490d36cd866e45006984d216b8d2e87e5707c91a78a373ea60bfa49dea37"}}