{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ZOXYXTB2GZGHIXMJ4SADBFU2MM","short_pith_number":"pith:ZOXYXTB2","schema_version":"1.0","canonical_sha256":"cbaf8bcc3a364c745d89e48030969a632abdda9a0a4bc1cb22b88f43f138980d","source":{"kind":"arxiv","id":"2506.07331","version":1},"attestation_state":"computed","paper":{"title":"On the stationary Navier-Stokes equations in distorted pipes under energy-stable outflow boundary conditions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Falocchi, Ana Leonor Silvestre, Gianmarco Sperone","submitted_at":"2025-06-09T00:12:09Z","abstract_excerpt":"The steady motion of a viscous incompressible fluid in distorted pipes, of finite length, is modeled through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by an arbitrary member of the Lions-Magenes class with positive influx, and the fluid motion is subject to a directional do-nothing boundary condition on the outlet, together with the standard no-slip assumption on the remaining walls of the domain. Existence of a weak solution to such Navier-Stokes system is proved without any restriction on the data (that is, inlet velocity and external force) by means of "},"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":"2506.07331","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-09T00:12:09Z","cross_cats_sorted":[],"title_canon_sha256":"4512e9790a453b3136b484a9f4d8763acc5dd716d06789995e4e9709f8701cf2","abstract_canon_sha256":"8a3aa44ac744738445a5ada1288dea8b17beebf6ac03d8ec567d78910fa7cb74"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:25.183482Z","signature_b64":"cZBdavEly1/RDaulYUZJjh3EzDVFsRZGQdDHDeyX761LvSjUA7Y1+8MoG++5Q4WWG8n9MeFt7vdZhSI4QjDPAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbaf8bcc3a364c745d89e48030969a632abdda9a0a4bc1cb22b88f43f138980d","last_reissued_at":"2026-07-05T11:18:25.182979Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:25.182979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the stationary Navier-Stokes equations in distorted pipes under energy-stable outflow boundary conditions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Falocchi, Ana Leonor Silvestre, Gianmarco Sperone","submitted_at":"2025-06-09T00:12:09Z","abstract_excerpt":"The steady motion of a viscous incompressible fluid in distorted pipes, of finite length, is modeled through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by an arbitrary member of the Lions-Magenes class with positive influx, and the fluid motion is subject to a directional do-nothing boundary condition on the outlet, together with the standard no-slip assumption on the remaining walls of the domain. Existence of a weak solution to such Navier-Stokes system is proved without any restriction on the data (that is, inlet velocity and external force) by means of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07331","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.07331/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.07331","created_at":"2026-07-05T11:18:25.183040+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.07331v1","created_at":"2026-07-05T11:18:25.183040+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07331","created_at":"2026-07-05T11:18:25.183040+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZOXYXTB2GZGH","created_at":"2026-07-05T11:18:25.183040+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZOXYXTB2GZGHIXMJ","created_at":"2026-07-05T11:18:25.183040+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZOXYXTB2","created_at":"2026-07-05T11:18:25.183040+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/ZOXYXTB2GZGHIXMJ4SADBFU2MM","json":"https://pith.science/pith/ZOXYXTB2GZGHIXMJ4SADBFU2MM.json","graph_json":"https://pith.science/api/pith-number/ZOXYXTB2GZGHIXMJ4SADBFU2MM/graph.json","events_json":"https://pith.science/api/pith-number/ZOXYXTB2GZGHIXMJ4SADBFU2MM/events.json","paper":"https://pith.science/paper/ZOXYXTB2"},"agent_actions":{"view_html":"https://pith.science/pith/ZOXYXTB2GZGHIXMJ4SADBFU2MM","download_json":"https://pith.science/pith/ZOXYXTB2GZGHIXMJ4SADBFU2MM.json","view_paper":"https://pith.science/paper/ZOXYXTB2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.07331&json=true","fetch_graph":"https://pith.science/api/pith-number/ZOXYXTB2GZGHIXMJ4SADBFU2MM/graph.json","fetch_events":"https://pith.science/api/pith-number/ZOXYXTB2GZGHIXMJ4SADBFU2MM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZOXYXTB2GZGHIXMJ4SADBFU2MM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZOXYXTB2GZGHIXMJ4SADBFU2MM/action/storage_attestation","attest_author":"https://pith.science/pith/ZOXYXTB2GZGHIXMJ4SADBFU2MM/action/author_attestation","sign_citation":"https://pith.science/pith/ZOXYXTB2GZGHIXMJ4SADBFU2MM/action/citation_signature","submit_replication":"https://pith.science/pith/ZOXYXTB2GZGHIXMJ4SADBFU2MM/action/replication_record"}},"created_at":"2026-07-05T11:18:25.183040+00:00","updated_at":"2026-07-05T11:18:25.183040+00:00"}