{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:SIHMZAIYD3I7HETM5CX3EUJFZJ","short_pith_number":"pith:SIHMZAIY","schema_version":"1.0","canonical_sha256":"920ecc81181ed1f3926ce8afb25125ca559794890b48715fead8599051b0889a","source":{"kind":"arxiv","id":"2001.04257","version":2},"attestation_state":"computed","paper":{"title":"Solutions to the $\\sigma_k$-Loewner-Nirenberg problem on annuli are locally Lipschitz and not differentiable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Luc Nguyen, Yanyan Li","submitted_at":"2020-01-13T14:13:00Z","abstract_excerpt":"We show for $k \\geq 2$ that the locally Lipschitz viscosity solution to the $\\sigma_k$-Loewner-Nirenberg problem on a given annulus $\\{a < |x| < b\\}$ is $C^{1,\\frac{1}{k}}_{\\rm loc}$ in each of $\\{a < |x| \\leq \\sqrt{ab}\\}$ and $\\{\\sqrt{ab} \\leq |x| < b\\}$ and has a jump in radial derivative across $|x| = \\sqrt{ab}$. Furthermore, the solution is not $C^{1,\\gamma}_{\\rm loc}$ for any $\\gamma > \\frac{1}{k}$. Optimal regularity for solutions to the $\\sigma_k$-Yamabe problem on annuli with finite constant boundary values is also established."},"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":"2001.04257","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-01-13T14:13:00Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"f998d1ff5495728e7a610da2fa65af1ca3dd1edfa27ba6edf40a86f60c71f86d","abstract_canon_sha256":"a114fa0b5b5c409f4667539428ab8a7e4649d9d4cc7b433ac5e4b8292d7f0005"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:59:43.086759Z","signature_b64":"pZQhsN4o4hlUZV4s0ihSjxij/8ZXG4V6My+RTv085MACFbRQ2QnE3i5f5m7qu9a2Rfs93KEQw9ZvoRxmR+fhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"920ecc81181ed1f3926ce8afb25125ca559794890b48715fead8599051b0889a","last_reissued_at":"2026-07-05T00:59:43.086326Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:59:43.086326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solutions to the $\\sigma_k$-Loewner-Nirenberg problem on annuli are locally Lipschitz and not differentiable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Luc Nguyen, Yanyan Li","submitted_at":"2020-01-13T14:13:00Z","abstract_excerpt":"We show for $k \\geq 2$ that the locally Lipschitz viscosity solution to the $\\sigma_k$-Loewner-Nirenberg problem on a given annulus $\\{a < |x| < b\\}$ is $C^{1,\\frac{1}{k}}_{\\rm loc}$ in each of $\\{a < |x| \\leq \\sqrt{ab}\\}$ and $\\{\\sqrt{ab} \\leq |x| < b\\}$ and has a jump in radial derivative across $|x| = \\sqrt{ab}$. Furthermore, the solution is not $C^{1,\\gamma}_{\\rm loc}$ for any $\\gamma > \\frac{1}{k}$. Optimal regularity for solutions to the $\\sigma_k$-Yamabe problem on annuli with finite constant boundary values is also established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.04257","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.04257/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":"2001.04257","created_at":"2026-07-05T00:59:43.086384+00:00"},{"alias_kind":"arxiv_version","alias_value":"2001.04257v2","created_at":"2026-07-05T00:59:43.086384+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.04257","created_at":"2026-07-05T00:59:43.086384+00:00"},{"alias_kind":"pith_short_12","alias_value":"SIHMZAIYD3I7","created_at":"2026-07-05T00:59:43.086384+00:00"},{"alias_kind":"pith_short_16","alias_value":"SIHMZAIYD3I7HETM","created_at":"2026-07-05T00:59:43.086384+00:00"},{"alias_kind":"pith_short_8","alias_value":"SIHMZAIY","created_at":"2026-07-05T00:59:43.086384+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/SIHMZAIYD3I7HETM5CX3EUJFZJ","json":"https://pith.science/pith/SIHMZAIYD3I7HETM5CX3EUJFZJ.json","graph_json":"https://pith.science/api/pith-number/SIHMZAIYD3I7HETM5CX3EUJFZJ/graph.json","events_json":"https://pith.science/api/pith-number/SIHMZAIYD3I7HETM5CX3EUJFZJ/events.json","paper":"https://pith.science/paper/SIHMZAIY"},"agent_actions":{"view_html":"https://pith.science/pith/SIHMZAIYD3I7HETM5CX3EUJFZJ","download_json":"https://pith.science/pith/SIHMZAIYD3I7HETM5CX3EUJFZJ.json","view_paper":"https://pith.science/paper/SIHMZAIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2001.04257&json=true","fetch_graph":"https://pith.science/api/pith-number/SIHMZAIYD3I7HETM5CX3EUJFZJ/graph.json","fetch_events":"https://pith.science/api/pith-number/SIHMZAIYD3I7HETM5CX3EUJFZJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SIHMZAIYD3I7HETM5CX3EUJFZJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SIHMZAIYD3I7HETM5CX3EUJFZJ/action/storage_attestation","attest_author":"https://pith.science/pith/SIHMZAIYD3I7HETM5CX3EUJFZJ/action/author_attestation","sign_citation":"https://pith.science/pith/SIHMZAIYD3I7HETM5CX3EUJFZJ/action/citation_signature","submit_replication":"https://pith.science/pith/SIHMZAIYD3I7HETM5CX3EUJFZJ/action/replication_record"}},"created_at":"2026-07-05T00:59:43.086384+00:00","updated_at":"2026-07-05T00:59:43.086384+00:00"}