{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ESJ2IT5ITZATX7AADA2ANHDP5K","short_pith_number":"pith:ESJ2IT5I","canonical_record":{"source":{"id":"1603.03346","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2016-03-10T17:42:04Z","cross_cats_sorted":[],"title_canon_sha256":"901faabee6e51e3dadcd22fe785372c06df7d92731ae44351950ebfa7eb8f2ed","abstract_canon_sha256":"a15ecd9bb775539130509c9ab66da5f985686f3e8b998b94d4a9f5674d39d9fb"},"schema_version":"1.0"},"canonical_sha256":"2493a44fa89e413bfc001834069c6feabd494e102347becca6cf3dbbe6a2563d","source":{"kind":"arxiv","id":"1603.03346","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03346","created_at":"2026-05-18T01:13:54Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03346v3","created_at":"2026-05-18T01:13:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03346","created_at":"2026-05-18T01:13:54Z"},{"alias_kind":"pith_short_12","alias_value":"ESJ2IT5ITZAT","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"ESJ2IT5ITZATX7AA","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"ESJ2IT5I","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ESJ2IT5ITZATX7AADA2ANHDP5K","target":"record","payload":{"canonical_record":{"source":{"id":"1603.03346","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2016-03-10T17:42:04Z","cross_cats_sorted":[],"title_canon_sha256":"901faabee6e51e3dadcd22fe785372c06df7d92731ae44351950ebfa7eb8f2ed","abstract_canon_sha256":"a15ecd9bb775539130509c9ab66da5f985686f3e8b998b94d4a9f5674d39d9fb"},"schema_version":"1.0"},"canonical_sha256":"2493a44fa89e413bfc001834069c6feabd494e102347becca6cf3dbbe6a2563d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:54.448774Z","signature_b64":"+FHFv1FDxOS8QIaDvayy5QUFbDXpp8gigOeUz3u5Xm0PNoYQ3x0o7NHIvVPJX4v3UN5Us82qT0U6IEFipuE2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2493a44fa89e413bfc001834069c6feabd494e102347becca6cf3dbbe6a2563d","last_reissued_at":"2026-05-18T01:13:54.448257Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:54.448257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.03346","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UDy3OGCvn/ak6bT1xTzdEppBu4Cxdb2j65p2vCu4su5tXf/AV7/nrmVtTcxFRXtpjzgoLcUDWYCkcP1Fcs50CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:59:01.331356Z"},"content_sha256":"97f4874e373156b6fcffb52915b6c867694afe3020503bcbb284cca127bb5abd","schema_version":"1.0","event_id":"sha256:97f4874e373156b6fcffb52915b6c867694afe3020503bcbb284cca127bb5abd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ESJ2IT5ITZATX7AADA2ANHDP5K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.QM","authors_text":"Christian A. Yates, Matthew J. Simpson, Paul R. Taylor, Ruth E. Baker","submitted_at":"2016-03-10T17:42:04Z","abstract_excerpt":"Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use stochastic models to accurately capture the behaviour of a system, especially when the number of diffusing particles is low. The stochastic models we consider in this paper are `compartment-based': the domain is discretized into compartments, and particles can jump between these compartments. Volume-excluding effects (crowding) can be incorporated by blocking movemen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03346","kind":"arxiv","version":3},"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":"2026-05-18T01:13:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bAxDs/DYwK/NmqE3c6aXGh+SOapNWYd+Q/fOXveo6Po9Fl7x+obWRiP4yx9XKyNYNNRtOFCm2KKTBDKkODpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:59:01.331868Z"},"content_sha256":"88c47b7b79ad08bedb4c2ab5d8516322d8476d880362fc0246a07898fe7aea67","schema_version":"1.0","event_id":"sha256:88c47b7b79ad08bedb4c2ab5d8516322d8476d880362fc0246a07898fe7aea67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ESJ2IT5ITZATX7AADA2ANHDP5K/bundle.json","state_url":"https://pith.science/pith/ESJ2IT5ITZATX7AADA2ANHDP5K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ESJ2IT5ITZATX7AADA2ANHDP5K/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":"2026-05-26T14:59:01Z","links":{"resolver":"https://pith.science/pith/ESJ2IT5ITZATX7AADA2ANHDP5K","bundle":"https://pith.science/pith/ESJ2IT5ITZATX7AADA2ANHDP5K/bundle.json","state":"https://pith.science/pith/ESJ2IT5ITZATX7AADA2ANHDP5K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ESJ2IT5ITZATX7AADA2ANHDP5K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ESJ2IT5ITZATX7AADA2ANHDP5K","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":"a15ecd9bb775539130509c9ab66da5f985686f3e8b998b94d4a9f5674d39d9fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2016-03-10T17:42:04Z","title_canon_sha256":"901faabee6e51e3dadcd22fe785372c06df7d92731ae44351950ebfa7eb8f2ed"},"schema_version":"1.0","source":{"id":"1603.03346","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03346","created_at":"2026-05-18T01:13:54Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03346v3","created_at":"2026-05-18T01:13:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03346","created_at":"2026-05-18T01:13:54Z"},{"alias_kind":"pith_short_12","alias_value":"ESJ2IT5ITZAT","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"ESJ2IT5ITZATX7AA","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"ESJ2IT5I","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:88c47b7b79ad08bedb4c2ab5d8516322d8476d880362fc0246a07898fe7aea67","target":"graph","created_at":"2026-05-18T01:13:54Z","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":"Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use stochastic models to accurately capture the behaviour of a system, especially when the number of diffusing particles is low. The stochastic models we consider in this paper are `compartment-based': the domain is discretized into compartments, and particles can jump between these compartments. Volume-excluding effects (crowding) can be incorporated by blocking movemen","authors_text":"Christian A. Yates, Matthew J. Simpson, Paul R. Taylor, Ruth E. Baker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2016-03-10T17:42:04Z","title":"Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03346","kind":"arxiv","version":3},"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":"sha256:97f4874e373156b6fcffb52915b6c867694afe3020503bcbb284cca127bb5abd","target":"record","created_at":"2026-05-18T01:13:54Z","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":"a15ecd9bb775539130509c9ab66da5f985686f3e8b998b94d4a9f5674d39d9fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2016-03-10T17:42:04Z","title_canon_sha256":"901faabee6e51e3dadcd22fe785372c06df7d92731ae44351950ebfa7eb8f2ed"},"schema_version":"1.0","source":{"id":"1603.03346","kind":"arxiv","version":3}},"canonical_sha256":"2493a44fa89e413bfc001834069c6feabd494e102347becca6cf3dbbe6a2563d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2493a44fa89e413bfc001834069c6feabd494e102347becca6cf3dbbe6a2563d","first_computed_at":"2026-05-18T01:13:54.448257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:54.448257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+FHFv1FDxOS8QIaDvayy5QUFbDXpp8gigOeUz3u5Xm0PNoYQ3x0o7NHIvVPJX4v3UN5Us82qT0U6IEFipuE2Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:54.448774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03346","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97f4874e373156b6fcffb52915b6c867694afe3020503bcbb284cca127bb5abd","sha256:88c47b7b79ad08bedb4c2ab5d8516322d8476d880362fc0246a07898fe7aea67"],"state_sha256":"ac71a203cac429d2398fdae68d9b4d03f78a7afb853b7258491380ae120403ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A1xhlkMs0sgARsGliUwIPo63YOwVGhOXzc85ybvSrAIwo7PN0N9x8KlTTHnbt67tNCxZ5B6eXbarGpxjE5r/Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:59:01.334913Z","bundle_sha256":"97d8d28d21517374111b387c67e774559654750f1511c48d1171d61a253312c8"}}