{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:HYTP2Q2YNXNEVK6BYZKEC3IL7P","short_pith_number":"pith:HYTP2Q2Y","schema_version":"1.0","canonical_sha256":"3e26fd43586dda4aabc1c654416d0bfbe06b30aa5ccbab586ae2a9f6c58deb69","source":{"kind":"arxiv","id":"2505.14642","version":1},"attestation_state":"computed","paper":{"title":"The steady Navier-Stokes equations in a system of unbounded channels with sources and sinks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filippo Gazzola, Gianmarco Sperone, Mikhail V. Korobkov, Xiao Ren","submitted_at":"2025-05-20T17:29:21Z","abstract_excerpt":"The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous works, the domain is not assumed to be simply-connected and the fluxes are not assumed to be small. In this very general setting, we prove the existence of a solution with a uniformly bounded Dirichlet integral in every compact subset. This is a generalization of the classical Ladyzhenskaya-Solonnikov result obtained under the additional assumption of zero bou"},"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":"2505.14642","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-20T17:29:21Z","cross_cats_sorted":[],"title_canon_sha256":"c934ee467e7bb6d9c3de0ac4befb7df3cf51228e7449d6d7cc8ab2de1f5aa93e","abstract_canon_sha256":"adeac7594fb0d38bb13e6b2be18401c6db950f32eaa04e2daa7c8425bed75e0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:06:16.951257Z","signature_b64":"qu/2YBg5P2Ay/RMEpGHg/DYKJSghMYAKdiz87T55N4Iy3U8mFFDJ9huzWswNsnGHQwyV7N6SBaY8u3rqEm/EBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e26fd43586dda4aabc1c654416d0bfbe06b30aa5ccbab586ae2a9f6c58deb69","last_reissued_at":"2026-07-05T11:06:16.950706Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:06:16.950706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The steady Navier-Stokes equations in a system of unbounded channels with sources and sinks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filippo Gazzola, Gianmarco Sperone, Mikhail V. Korobkov, Xiao Ren","submitted_at":"2025-05-20T17:29:21Z","abstract_excerpt":"The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous works, the domain is not assumed to be simply-connected and the fluxes are not assumed to be small. In this very general setting, we prove the existence of a solution with a uniformly bounded Dirichlet integral in every compact subset. This is a generalization of the classical Ladyzhenskaya-Solonnikov result obtained under the additional assumption of zero bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14642","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/2505.14642/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":"2505.14642","created_at":"2026-07-05T11:06:16.950767+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.14642v1","created_at":"2026-07-05T11:06:16.950767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.14642","created_at":"2026-07-05T11:06:16.950767+00:00"},{"alias_kind":"pith_short_12","alias_value":"HYTP2Q2YNXNE","created_at":"2026-07-05T11:06:16.950767+00:00"},{"alias_kind":"pith_short_16","alias_value":"HYTP2Q2YNXNEVK6B","created_at":"2026-07-05T11:06:16.950767+00:00"},{"alias_kind":"pith_short_8","alias_value":"HYTP2Q2Y","created_at":"2026-07-05T11:06:16.950767+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.07331","citing_title":"On the stationary Navier-Stokes equations in distorted pipes under energy-stable outflow boundary conditions","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HYTP2Q2YNXNEVK6BYZKEC3IL7P","json":"https://pith.science/pith/HYTP2Q2YNXNEVK6BYZKEC3IL7P.json","graph_json":"https://pith.science/api/pith-number/HYTP2Q2YNXNEVK6BYZKEC3IL7P/graph.json","events_json":"https://pith.science/api/pith-number/HYTP2Q2YNXNEVK6BYZKEC3IL7P/events.json","paper":"https://pith.science/paper/HYTP2Q2Y"},"agent_actions":{"view_html":"https://pith.science/pith/HYTP2Q2YNXNEVK6BYZKEC3IL7P","download_json":"https://pith.science/pith/HYTP2Q2YNXNEVK6BYZKEC3IL7P.json","view_paper":"https://pith.science/paper/HYTP2Q2Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.14642&json=true","fetch_graph":"https://pith.science/api/pith-number/HYTP2Q2YNXNEVK6BYZKEC3IL7P/graph.json","fetch_events":"https://pith.science/api/pith-number/HYTP2Q2YNXNEVK6BYZKEC3IL7P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HYTP2Q2YNXNEVK6BYZKEC3IL7P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HYTP2Q2YNXNEVK6BYZKEC3IL7P/action/storage_attestation","attest_author":"https://pith.science/pith/HYTP2Q2YNXNEVK6BYZKEC3IL7P/action/author_attestation","sign_citation":"https://pith.science/pith/HYTP2Q2YNXNEVK6BYZKEC3IL7P/action/citation_signature","submit_replication":"https://pith.science/pith/HYTP2Q2YNXNEVK6BYZKEC3IL7P/action/replication_record"}},"created_at":"2026-07-05T11:06:16.950767+00:00","updated_at":"2026-07-05T11:06:16.950767+00:00"}