{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:L7IRLSRNXDG5SRQN2C2BEOSALE","short_pith_number":"pith:L7IRLSRN","schema_version":"1.0","canonical_sha256":"5fd115ca2db8cdd9460dd0b4123a405928ca0e78c7f7c17d27e6b2c07564cadb","source":{"kind":"arxiv","id":"2606.07501","version":1},"attestation_state":"computed","paper":{"title":"On the non-uniqueness of solutions of the axi-symmetric swirl-free Navier-Stokes equations, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandru D. Ionescu, Hao Jia, Stan Palasek","submitted_at":"2026-06-05T17:53:56Z","abstract_excerpt":"In this paper we construct numerically a new class of unstable self-similar solutions of the incompressible Navier-Stokes equations in $\\mathbb{R}^3$. Our solutions are axially symmetric and homogeneous of degree $-1$ at $\\infty$, and are unstable in the sense that the linearization around these solutions contains unstable modes. Solutions of this type have been discovered numerically by Guillod and \\v{S}ver\\'ak and Hou, Wang, and Yang, and have applications to proving non-uniqueness results.\n  The main novelty in this paper is that we discover the existence of such solutions in the space of a"},"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":"2606.07501","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-05T17:53:56Z","cross_cats_sorted":[],"title_canon_sha256":"a5ebd6a3387a1f1d3ed2e0f978971fef9e70c72403c4a7482ecf88e1e1af901e","abstract_canon_sha256":"b9a3434e013ee35a39234686eb2041f9ce27b9f2724b47da0bdaedb99dc9004b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:05:31.302505Z","signature_b64":"kuH8XWLzv+CQwBb+47yl5pHxvO3sAgw0qBBvPolsoxEq47jnEFa7H07AbXGV07qU4FsGnQAS7yl4B5JCp3OVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fd115ca2db8cdd9460dd0b4123a405928ca0e78c7f7c17d27e6b2c07564cadb","last_reissued_at":"2026-06-08T01:05:31.301578Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:05:31.301578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the non-uniqueness of solutions of the axi-symmetric swirl-free Navier-Stokes equations, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandru D. Ionescu, Hao Jia, Stan Palasek","submitted_at":"2026-06-05T17:53:56Z","abstract_excerpt":"In this paper we construct numerically a new class of unstable self-similar solutions of the incompressible Navier-Stokes equations in $\\mathbb{R}^3$. Our solutions are axially symmetric and homogeneous of degree $-1$ at $\\infty$, and are unstable in the sense that the linearization around these solutions contains unstable modes. Solutions of this type have been discovered numerically by Guillod and \\v{S}ver\\'ak and Hou, Wang, and Yang, and have applications to proving non-uniqueness results.\n  The main novelty in this paper is that we discover the existence of such solutions in the space of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07501","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/2606.07501/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":"2606.07501","created_at":"2026-06-08T01:05:31.301783+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.07501v1","created_at":"2026-06-08T01:05:31.301783+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07501","created_at":"2026-06-08T01:05:31.301783+00:00"},{"alias_kind":"pith_short_12","alias_value":"L7IRLSRNXDG5","created_at":"2026-06-08T01:05:31.301783+00:00"},{"alias_kind":"pith_short_16","alias_value":"L7IRLSRNXDG5SRQN","created_at":"2026-06-08T01:05:31.301783+00:00"},{"alias_kind":"pith_short_8","alias_value":"L7IRLSRN","created_at":"2026-06-08T01:05:31.301783+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/L7IRLSRNXDG5SRQN2C2BEOSALE","json":"https://pith.science/pith/L7IRLSRNXDG5SRQN2C2BEOSALE.json","graph_json":"https://pith.science/api/pith-number/L7IRLSRNXDG5SRQN2C2BEOSALE/graph.json","events_json":"https://pith.science/api/pith-number/L7IRLSRNXDG5SRQN2C2BEOSALE/events.json","paper":"https://pith.science/paper/L7IRLSRN"},"agent_actions":{"view_html":"https://pith.science/pith/L7IRLSRNXDG5SRQN2C2BEOSALE","download_json":"https://pith.science/pith/L7IRLSRNXDG5SRQN2C2BEOSALE.json","view_paper":"https://pith.science/paper/L7IRLSRN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.07501&json=true","fetch_graph":"https://pith.science/api/pith-number/L7IRLSRNXDG5SRQN2C2BEOSALE/graph.json","fetch_events":"https://pith.science/api/pith-number/L7IRLSRNXDG5SRQN2C2BEOSALE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L7IRLSRNXDG5SRQN2C2BEOSALE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L7IRLSRNXDG5SRQN2C2BEOSALE/action/storage_attestation","attest_author":"https://pith.science/pith/L7IRLSRNXDG5SRQN2C2BEOSALE/action/author_attestation","sign_citation":"https://pith.science/pith/L7IRLSRNXDG5SRQN2C2BEOSALE/action/citation_signature","submit_replication":"https://pith.science/pith/L7IRLSRNXDG5SRQN2C2BEOSALE/action/replication_record"}},"created_at":"2026-06-08T01:05:31.301783+00:00","updated_at":"2026-06-08T01:05:31.301783+00:00"}