{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:FS64PWICI2EDIQHH3BWFMKBJVE","short_pith_number":"pith:FS64PWIC","schema_version":"1.0","canonical_sha256":"2cbdc7d90246883440e7d86c562829a9003cc8965208eaf0cf3318f6bcc81341","source":{"kind":"arxiv","id":"2210.09110","version":2},"attestation_state":"computed","paper":{"title":"Symmetry of positive solutions for Lane-Emden systems involving the Logarithmic Laplacian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Ruzhansky, Rong Zhang, Vishvesh Kumar","submitted_at":"2022-10-17T14:00:56Z","abstract_excerpt":"We study the Lane-Emden system involving the logarithmic Laplacian: $$ \\begin{cases} \\ \\mathcal{L}_{\\Delta}u(x)=v^{p}(x) ,& x\\in\\mathbb{R}^{n},\\\\ \\ \\mathcal{L}_{\\Delta}v(x)=u^{q}(x) ,& x\\in\\mathbb{R}^{n}, \\end{cases} $$ where $p,q>1$ and $\\mathcal{L}_{\\Delta}$ denotes the Logarithmic Laplacian arising as a formal derivative $\\partial_s|_{s=0}(-\\Delta)^s$ of fractional Laplacians at $s=0.$ By using a direct method of moving planes for the logarithmic Laplacian, we obtain the symmetry and monotonicity of the positive solutions to the Lane-Emden system. We also establish some key ingredients need"},"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":"2210.09110","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-10-17T14:00:56Z","cross_cats_sorted":[],"title_canon_sha256":"22261a3c0942258c2802d77f0f1a4eeed59f7a5aed37db17ea2766eaf29c4728","abstract_canon_sha256":"a1bed77faf20188dbf9687d9ca37ae6e9bd9a91c07664c03afc208e643b36caf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:34:03.093668Z","signature_b64":"PPzTBmJsH2FqFWQ6qsluZsa8KUfUzQ39xLfy1XlDFoMGOhz+k5tgL+R/UqZCnX/MgobOHzb4EKMXKuqjJ3Z1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cbdc7d90246883440e7d86c562829a9003cc8965208eaf0cf3318f6bcc81341","last_reissued_at":"2026-07-05T05:34:03.093203Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:34:03.093203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetry of positive solutions for Lane-Emden systems involving the Logarithmic Laplacian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Ruzhansky, Rong Zhang, Vishvesh Kumar","submitted_at":"2022-10-17T14:00:56Z","abstract_excerpt":"We study the Lane-Emden system involving the logarithmic Laplacian: $$ \\begin{cases} \\ \\mathcal{L}_{\\Delta}u(x)=v^{p}(x) ,& x\\in\\mathbb{R}^{n},\\\\ \\ \\mathcal{L}_{\\Delta}v(x)=u^{q}(x) ,& x\\in\\mathbb{R}^{n}, \\end{cases} $$ where $p,q>1$ and $\\mathcal{L}_{\\Delta}$ denotes the Logarithmic Laplacian arising as a formal derivative $\\partial_s|_{s=0}(-\\Delta)^s$ of fractional Laplacians at $s=0.$ By using a direct method of moving planes for the logarithmic Laplacian, we obtain the symmetry and monotonicity of the positive solutions to the Lane-Emden system. We also establish some key ingredients need"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.09110","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/2210.09110/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":"2210.09110","created_at":"2026-07-05T05:34:03.093259+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.09110v2","created_at":"2026-07-05T05:34:03.093259+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.09110","created_at":"2026-07-05T05:34:03.093259+00:00"},{"alias_kind":"pith_short_12","alias_value":"FS64PWICI2ED","created_at":"2026-07-05T05:34:03.093259+00:00"},{"alias_kind":"pith_short_16","alias_value":"FS64PWICI2EDIQHH","created_at":"2026-07-05T05:34:03.093259+00:00"},{"alias_kind":"pith_short_8","alias_value":"FS64PWIC","created_at":"2026-07-05T05:34:03.093259+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/FS64PWICI2EDIQHH3BWFMKBJVE","json":"https://pith.science/pith/FS64PWICI2EDIQHH3BWFMKBJVE.json","graph_json":"https://pith.science/api/pith-number/FS64PWICI2EDIQHH3BWFMKBJVE/graph.json","events_json":"https://pith.science/api/pith-number/FS64PWICI2EDIQHH3BWFMKBJVE/events.json","paper":"https://pith.science/paper/FS64PWIC"},"agent_actions":{"view_html":"https://pith.science/pith/FS64PWICI2EDIQHH3BWFMKBJVE","download_json":"https://pith.science/pith/FS64PWICI2EDIQHH3BWFMKBJVE.json","view_paper":"https://pith.science/paper/FS64PWIC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.09110&json=true","fetch_graph":"https://pith.science/api/pith-number/FS64PWICI2EDIQHH3BWFMKBJVE/graph.json","fetch_events":"https://pith.science/api/pith-number/FS64PWICI2EDIQHH3BWFMKBJVE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FS64PWICI2EDIQHH3BWFMKBJVE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FS64PWICI2EDIQHH3BWFMKBJVE/action/storage_attestation","attest_author":"https://pith.science/pith/FS64PWICI2EDIQHH3BWFMKBJVE/action/author_attestation","sign_citation":"https://pith.science/pith/FS64PWICI2EDIQHH3BWFMKBJVE/action/citation_signature","submit_replication":"https://pith.science/pith/FS64PWICI2EDIQHH3BWFMKBJVE/action/replication_record"}},"created_at":"2026-07-05T05:34:03.093259+00:00","updated_at":"2026-07-05T05:34:03.093259+00:00"}