{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HBVFAG34EU2B7AD76HPZXBJ3OU","short_pith_number":"pith:HBVFAG34","schema_version":"1.0","canonical_sha256":"386a501b7c25341f807ff1df9b853b7533334c5f57960c74d6de8de8fd7b565f","source":{"kind":"arxiv","id":"1709.10244","version":1},"attestation_state":"computed","paper":{"title":"Distribution of randomly diffusing particles in inhomogeneous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.bio-ph","authors_text":"Christoph A. Haselwandter, Osman Kahraman, Yiwei Li","submitted_at":"2017-09-29T05:52:14Z","abstract_excerpt":"Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct particle hopping rates. Starting from the master equations (MEs) governing diffusion in inhomogeneous media we derive here, for arbitrary spatial dimensions, the deterministic lattice equations (DLEs) specifying the average particle number at each lattice site for randomly diffusing particles in inhomogeneous media. We consider the case of free diffusion with no st"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1709.10244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2017-09-29T05:52:14Z","cross_cats_sorted":[],"title_canon_sha256":"7c4906d20a4deb5671273e4a985fb5ddf58dc16d67ee8a40636b57954fffc915","abstract_canon_sha256":"5223674fbbaf0af122e337fbccbb6455799621354492d9fc6a3ba5e95cc8f365"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:03.794091Z","signature_b64":"4AfOJMDitFFQFwoQGJIGboDI+4CYEv8sj0WBMFMmxKlbaILmB96Roofllbei7tdpQM9vgPCfqB0LiK6P7veQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"386a501b7c25341f807ff1df9b853b7533334c5f57960c74d6de8de8fd7b565f","last_reissued_at":"2026-05-18T00:34:03.793389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:03.793389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distribution of randomly diffusing particles in inhomogeneous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.bio-ph","authors_text":"Christoph A. Haselwandter, Osman Kahraman, Yiwei Li","submitted_at":"2017-09-29T05:52:14Z","abstract_excerpt":"Diffusion can be conceptualized, at microscopic scales, as the random hopping of particles between neighboring lattice sites. In the case of diffusion in inhomogeneous media, distinct spatial domains in the system may yield distinct particle hopping rates. Starting from the master equations (MEs) governing diffusion in inhomogeneous media we derive here, for arbitrary spatial dimensions, the deterministic lattice equations (DLEs) specifying the average particle number at each lattice site for randomly diffusing particles in inhomogeneous media. We consider the case of free diffusion with no st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10244","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.10244","created_at":"2026-05-18T00:34:03.793513+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.10244v1","created_at":"2026-05-18T00:34:03.793513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10244","created_at":"2026-05-18T00:34:03.793513+00:00"},{"alias_kind":"pith_short_12","alias_value":"HBVFAG34EU2B","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HBVFAG34EU2B7AD7","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HBVFAG34","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HBVFAG34EU2B7AD76HPZXBJ3OU","json":"https://pith.science/pith/HBVFAG34EU2B7AD76HPZXBJ3OU.json","graph_json":"https://pith.science/api/pith-number/HBVFAG34EU2B7AD76HPZXBJ3OU/graph.json","events_json":"https://pith.science/api/pith-number/HBVFAG34EU2B7AD76HPZXBJ3OU/events.json","paper":"https://pith.science/paper/HBVFAG34"},"agent_actions":{"view_html":"https://pith.science/pith/HBVFAG34EU2B7AD76HPZXBJ3OU","download_json":"https://pith.science/pith/HBVFAG34EU2B7AD76HPZXBJ3OU.json","view_paper":"https://pith.science/paper/HBVFAG34","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.10244&json=true","fetch_graph":"https://pith.science/api/pith-number/HBVFAG34EU2B7AD76HPZXBJ3OU/graph.json","fetch_events":"https://pith.science/api/pith-number/HBVFAG34EU2B7AD76HPZXBJ3OU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HBVFAG34EU2B7AD76HPZXBJ3OU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HBVFAG34EU2B7AD76HPZXBJ3OU/action/storage_attestation","attest_author":"https://pith.science/pith/HBVFAG34EU2B7AD76HPZXBJ3OU/action/author_attestation","sign_citation":"https://pith.science/pith/HBVFAG34EU2B7AD76HPZXBJ3OU/action/citation_signature","submit_replication":"https://pith.science/pith/HBVFAG34EU2B7AD76HPZXBJ3OU/action/replication_record"}},"created_at":"2026-05-18T00:34:03.793513+00:00","updated_at":"2026-05-18T00:34:03.793513+00:00"}