{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WIV432ZGB23CV3SUGIDNYBRW2E","short_pith_number":"pith:WIV432ZG","canonical_record":{"source":{"id":"1710.02699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-10-07T15:45:46Z","cross_cats_sorted":[],"title_canon_sha256":"5ff5e87a881f288e0118dc3d6ed678f90af7af1a21b2c61ca5529d247c16cb03","abstract_canon_sha256":"5a3cd1b17d51fe14ec718b501ba9e55bd464fd655ad0b0a3655d55d76ce95e32"},"schema_version":"1.0"},"canonical_sha256":"b22bcdeb260eb62aee543206dc0636d132bfe8b52128a686d6ae1b01305f6ce1","source":{"kind":"arxiv","id":"1710.02699","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02699","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02699v2","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02699","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"WIV432ZGB23C","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WIV432ZGB23CV3SU","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WIV432ZG","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WIV432ZGB23CV3SUGIDNYBRW2E","target":"record","payload":{"canonical_record":{"source":{"id":"1710.02699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-10-07T15:45:46Z","cross_cats_sorted":[],"title_canon_sha256":"5ff5e87a881f288e0118dc3d6ed678f90af7af1a21b2c61ca5529d247c16cb03","abstract_canon_sha256":"5a3cd1b17d51fe14ec718b501ba9e55bd464fd655ad0b0a3655d55d76ce95e32"},"schema_version":"1.0"},"canonical_sha256":"b22bcdeb260eb62aee543206dc0636d132bfe8b52128a686d6ae1b01305f6ce1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:00.093511Z","signature_b64":"9t0+5qvPQfMcjvD+hpTxBSkKDJwAAOKk6oV+41Ekxxwo731fvTBpWdT26TO1wbrY6ETqUUoPmlfFXlEQU1e3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b22bcdeb260eb62aee543206dc0636d132bfe8b52128a686d6ae1b01305f6ce1","last_reissued_at":"2026-05-17T23:45:00.092976Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:00.092976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.02699","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nO69ra+69fQyEp6OveXDbncxrf3Oojx17uvk174Th7LMZ5gn/cgxP/aLxPND2NS+TyQwPqkuOq06nLT/fDO5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:56:10.958596Z"},"content_sha256":"0eefd3dcf06ab44b753ffa747b14cdca36f8809e291ad008d71e27ba3f6e03c1","schema_version":"1.0","event_id":"sha256:0eefd3dcf06ab44b753ffa747b14cdca36f8809e291ad008d71e27ba3f6e03c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WIV432ZGB23CV3SUGIDNYBRW2E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dispersion in two dimensional channels - the Fick-Jacobs approximation revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"D.S. Dean, M. Mangeat, T. Gu\\'erin","submitted_at":"2017-10-07T15:45:46Z","abstract_excerpt":"We examine the dispersion of Brownian particles in a symmetric two dimensional channel, this classical problem has been widely studied in the literature using the so called Fick-Jacobs' approximation and its various improvements. Most studies rely on the reduction to an effective one dimensional diffusion equation, here we drive an explicit formula for the diffusion constant which avoids this reduction. Using this formula the effective diffusion constant can be evaluated numerically without resorting to Brownian simulations. In addition a perturbation theory can be developed in $\\varepsilon = "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02699","kind":"arxiv","version":2},"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":"2026-05-17T23:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hlqdv+QDIoMSMyr3dHfFQM/4nMrtzkTZOBrrVUZC1f6HO37RG8pULHnLHUBH8DaDv8ynBueMKtAGOF+x/mkNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:56:10.958936Z"},"content_sha256":"0307a099f25b3175990cf04debcaec3f588aefdd2c8587362aed489b0a8f63b2","schema_version":"1.0","event_id":"sha256:0307a099f25b3175990cf04debcaec3f588aefdd2c8587362aed489b0a8f63b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WIV432ZGB23CV3SUGIDNYBRW2E/bundle.json","state_url":"https://pith.science/pith/WIV432ZGB23CV3SUGIDNYBRW2E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WIV432ZGB23CV3SUGIDNYBRW2E/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":"2026-06-23T22:56:10Z","links":{"resolver":"https://pith.science/pith/WIV432ZGB23CV3SUGIDNYBRW2E","bundle":"https://pith.science/pith/WIV432ZGB23CV3SUGIDNYBRW2E/bundle.json","state":"https://pith.science/pith/WIV432ZGB23CV3SUGIDNYBRW2E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WIV432ZGB23CV3SUGIDNYBRW2E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WIV432ZGB23CV3SUGIDNYBRW2E","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":"5a3cd1b17d51fe14ec718b501ba9e55bd464fd655ad0b0a3655d55d76ce95e32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-10-07T15:45:46Z","title_canon_sha256":"5ff5e87a881f288e0118dc3d6ed678f90af7af1a21b2c61ca5529d247c16cb03"},"schema_version":"1.0","source":{"id":"1710.02699","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02699","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02699v2","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02699","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"WIV432ZGB23C","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WIV432ZGB23CV3SU","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WIV432ZG","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:0307a099f25b3175990cf04debcaec3f588aefdd2c8587362aed489b0a8f63b2","target":"graph","created_at":"2026-05-17T23:45:00Z","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":"We examine the dispersion of Brownian particles in a symmetric two dimensional channel, this classical problem has been widely studied in the literature using the so called Fick-Jacobs' approximation and its various improvements. Most studies rely on the reduction to an effective one dimensional diffusion equation, here we drive an explicit formula for the diffusion constant which avoids this reduction. Using this formula the effective diffusion constant can be evaluated numerically without resorting to Brownian simulations. In addition a perturbation theory can be developed in $\\varepsilon = ","authors_text":"D.S. Dean, M. Mangeat, T. Gu\\'erin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-10-07T15:45:46Z","title":"Dispersion in two dimensional channels - the Fick-Jacobs approximation revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02699","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":"sha256:0eefd3dcf06ab44b753ffa747b14cdca36f8809e291ad008d71e27ba3f6e03c1","target":"record","created_at":"2026-05-17T23:45:00Z","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":"5a3cd1b17d51fe14ec718b501ba9e55bd464fd655ad0b0a3655d55d76ce95e32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-10-07T15:45:46Z","title_canon_sha256":"5ff5e87a881f288e0118dc3d6ed678f90af7af1a21b2c61ca5529d247c16cb03"},"schema_version":"1.0","source":{"id":"1710.02699","kind":"arxiv","version":2}},"canonical_sha256":"b22bcdeb260eb62aee543206dc0636d132bfe8b52128a686d6ae1b01305f6ce1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b22bcdeb260eb62aee543206dc0636d132bfe8b52128a686d6ae1b01305f6ce1","first_computed_at":"2026-05-17T23:45:00.092976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:00.092976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9t0+5qvPQfMcjvD+hpTxBSkKDJwAAOKk6oV+41Ekxxwo731fvTBpWdT26TO1wbrY6ETqUUoPmlfFXlEQU1e3BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:00.093511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.02699","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0eefd3dcf06ab44b753ffa747b14cdca36f8809e291ad008d71e27ba3f6e03c1","sha256:0307a099f25b3175990cf04debcaec3f588aefdd2c8587362aed489b0a8f63b2"],"state_sha256":"4941f396dfe1477a6c2a6b84bf7b6b71dbd21e5f293c50fb6b9d90e68b95d81b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cmGsmVdUxd130o7RIlLNLGpMsvTuqLUaMN0Ri68p7r977+dsK86tnemDcN+g8vVjG5Z9wmyWh7daF2twX8gsCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T22:56:10.960991Z","bundle_sha256":"e051972141cf492d41f57d02cd335693de13ebb21e8846bf96cb25885085ba63"}}