{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BND4ZXSP6BOPJ6N32VUKLJK6VB","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":"b790e0f63f0298eed733e0fec3b38eb32871dcdc1bebbf2a854b57aac7a7a11e","cross_cats_sorted":["physics.bio-ph","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2018-04-20T17:36:04Z","title_canon_sha256":"ec18869720b513581b2a673b4eacca2cc04b77365cd9ba6438f85e9bdd0108f5"},"schema_version":"1.0","source":{"id":"1804.07743","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07743","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07743v2","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07743","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"pith_short_12","alias_value":"BND4ZXSP6BOP","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BND4ZXSP6BOPJ6N3","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BND4ZXSP","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:7bb30f9890deca9f412f4ef5f2343fba7830d19b4f6e91b0f3d4871da2cb506c","target":"graph","created_at":"2026-05-17T23:56:25Z","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":"Smoluchowski-type models for diffusion-influenced reactions (A+B -> C) can be formulated within two frameworks: the probabilistic-based approach for a pair A, B of reacting particles and the concentration-based approach for systems in contact with a bath that generates a concentration gradient of B particles that interact with A. Although these two approaches are mathematically similar, it is not straightforward to establish a precise mathematical relationship between them. Determining this relationship is essential to derive particle-based numerical methods that are quantitatively consistent ","authors_text":"Frank No\\'e, Hong Qian, Mauricio J. Del Razo","cross_cats":["physics.bio-ph","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2018-04-20T17:36:04Z","title":"Grand canonical diffusion-influenced reactions: a stochastic theory with applications to multiscale reaction-diffusion simulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07743","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":"sha256:059ad4d7eb8685e8d22739afe5e6f662acb64490dc45c18d9c1ac457e0f31efa","target":"record","created_at":"2026-05-17T23:56:25Z","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":"b790e0f63f0298eed733e0fec3b38eb32871dcdc1bebbf2a854b57aac7a7a11e","cross_cats_sorted":["physics.bio-ph","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2018-04-20T17:36:04Z","title_canon_sha256":"ec18869720b513581b2a673b4eacca2cc04b77365cd9ba6438f85e9bdd0108f5"},"schema_version":"1.0","source":{"id":"1804.07743","kind":"arxiv","version":2}},"canonical_sha256":"0b47ccde4ff05cf4f9bbd568a5a55ea85958262179c494c68355a18abf7e8dbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b47ccde4ff05cf4f9bbd568a5a55ea85958262179c494c68355a18abf7e8dbf","first_computed_at":"2026-05-17T23:56:25.068086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:25.068086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zQ79hmiiqckRp0JzuHizFnbv1zrzmmjzM/+4KmdzLhHPMUoE9EjY7yXMaY/JkNtEDu4UHRC5ZtgxlmThJ+FYDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:25.068484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07743","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:059ad4d7eb8685e8d22739afe5e6f662acb64490dc45c18d9c1ac457e0f31efa","sha256:7bb30f9890deca9f412f4ef5f2343fba7830d19b4f6e91b0f3d4871da2cb506c"],"state_sha256":"72cfd83538e519a326ec40c629ccb4f7a876fbd79a73b998a033611eeadf486b"}