{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:MXFUUANWL3EG76OGYDXRVBJ5WT","short_pith_number":"pith:MXFUUANW","schema_version":"1.0","canonical_sha256":"65cb4a01b65ec86ff9c6c0ef1a853db4eacbbbf489f83187d0cbd3095a3fc212","source":{"kind":"arxiv","id":"1208.5423","version":1},"attestation_state":"computed","paper":{"title":"Slow flow in channels with porous walls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Kaare H. Jensen","submitted_at":"2012-08-27T15:39:10Z","abstract_excerpt":"We consider the slow flow of a viscous incompressible liquid in a channel of constant but arbitrary cross section shape, driven by non-uniform suction or injection through the porous channel walls. A similarity transformation reduces the Navier-Stokes equations to a set of coupled equations for the velocity potential in two dimensions. When the channel aspect ratio and Reynolds number are both small, the problem reduces to solving the biharmonic equation with constant forcing in two dimensions. With the relevant boundary conditions, determining the velocity field in a porous channels is thus e"},"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":"1208.5423","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-08-27T15:39:10Z","cross_cats_sorted":[],"title_canon_sha256":"81ab0f0278f39de124e89e3f9da0a5a073ddf9c56ac880e2e1e0fe342f3eb45b","abstract_canon_sha256":"1e140a86358ff00af6af22e0f8eb5a97f12fc91e957b65dee6ac1a0db92f7f3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:59.496051Z","signature_b64":"EDHBL+LdS2Hm9e7QGSosy+kbJAExkRgKPc1c7nW491CYgaewRzjp9qRj27HCu0NJD926xXmHyuF2m6sBrEBgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65cb4a01b65ec86ff9c6c0ef1a853db4eacbbbf489f83187d0cbd3095a3fc212","last_reissued_at":"2026-05-18T03:46:59.495476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:59.495476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Slow flow in channels with porous walls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Kaare H. Jensen","submitted_at":"2012-08-27T15:39:10Z","abstract_excerpt":"We consider the slow flow of a viscous incompressible liquid in a channel of constant but arbitrary cross section shape, driven by non-uniform suction or injection through the porous channel walls. A similarity transformation reduces the Navier-Stokes equations to a set of coupled equations for the velocity potential in two dimensions. When the channel aspect ratio and Reynolds number are both small, the problem reduces to solving the biharmonic equation with constant forcing in two dimensions. With the relevant boundary conditions, determining the velocity field in a porous channels is thus e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5423","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":"1208.5423","created_at":"2026-05-18T03:46:59.495571+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.5423v1","created_at":"2026-05-18T03:46:59.495571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5423","created_at":"2026-05-18T03:46:59.495571+00:00"},{"alias_kind":"pith_short_12","alias_value":"MXFUUANWL3EG","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MXFUUANWL3EG76OG","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MXFUUANW","created_at":"2026-05-18T12:27:14.488303+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/MXFUUANWL3EG76OGYDXRVBJ5WT","json":"https://pith.science/pith/MXFUUANWL3EG76OGYDXRVBJ5WT.json","graph_json":"https://pith.science/api/pith-number/MXFUUANWL3EG76OGYDXRVBJ5WT/graph.json","events_json":"https://pith.science/api/pith-number/MXFUUANWL3EG76OGYDXRVBJ5WT/events.json","paper":"https://pith.science/paper/MXFUUANW"},"agent_actions":{"view_html":"https://pith.science/pith/MXFUUANWL3EG76OGYDXRVBJ5WT","download_json":"https://pith.science/pith/MXFUUANWL3EG76OGYDXRVBJ5WT.json","view_paper":"https://pith.science/paper/MXFUUANW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.5423&json=true","fetch_graph":"https://pith.science/api/pith-number/MXFUUANWL3EG76OGYDXRVBJ5WT/graph.json","fetch_events":"https://pith.science/api/pith-number/MXFUUANWL3EG76OGYDXRVBJ5WT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MXFUUANWL3EG76OGYDXRVBJ5WT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MXFUUANWL3EG76OGYDXRVBJ5WT/action/storage_attestation","attest_author":"https://pith.science/pith/MXFUUANWL3EG76OGYDXRVBJ5WT/action/author_attestation","sign_citation":"https://pith.science/pith/MXFUUANWL3EG76OGYDXRVBJ5WT/action/citation_signature","submit_replication":"https://pith.science/pith/MXFUUANWL3EG76OGYDXRVBJ5WT/action/replication_record"}},"created_at":"2026-05-18T03:46:59.495571+00:00","updated_at":"2026-05-18T03:46:59.495571+00:00"}