{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:A4EMHDMKRMOWKP3J6XYL5SYSAJ","short_pith_number":"pith:A4EMHDMK","schema_version":"1.0","canonical_sha256":"0708c38d8a8b1d653f69f5f0becb120271ae8ce375f08d0944124cf9f92eb9e2","source":{"kind":"arxiv","id":"1604.08258","version":2},"attestation_state":"computed","paper":{"title":"A Pohozaev Identity for the Fractional H$\\acute{e}$non System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fengquan Li, Pei Ma, Yan Li","submitted_at":"2016-04-27T22:02:40Z","abstract_excerpt":"In this paper, we study the Pohozaev identity associated with a H$\\acute{e}$non-Lane-Emden system involving the fractional Laplacian:\n  \\begin{equation}\n  \\left\\{\\begin{array}{ll}\n  (-\\triangle)^su=|x|^av^p,&x\\in\\Omega,\n  (-\\triangle)^sv=|x|^bu^q,&x\\in\\Omega, u=v=0,&x\\in R^n\\backslash\\Omega,\n  \\end{array}\n  \\right.\n  \\end{equation} in a star-shaped and bounded domain $\\Omega$ for $s\\in(0,1)$. As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases."},"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":"1604.08258","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-27T22:02:40Z","cross_cats_sorted":[],"title_canon_sha256":"1eeb1e2623b9fdb6e45db85c415a03d29bac90b45c2c4e222cdaaeb3a3b769b8","abstract_canon_sha256":"3c31648c973bc16562507aa3d5bb341915c7c8fb1b4e5d07f6dddfb3c458558a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:18.739404Z","signature_b64":"PLh5vY3E5cF9ONYcg3Phtd9fgvwroigIPKd8eY9jgzlK0WAZlHECRBW2xLNYl1omm6llCtpnyJjw+0iYty63Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0708c38d8a8b1d653f69f5f0becb120271ae8ce375f08d0944124cf9f92eb9e2","last_reissued_at":"2026-05-18T00:38:18.738529Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:18.738529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Pohozaev Identity for the Fractional H$\\acute{e}$non System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fengquan Li, Pei Ma, Yan Li","submitted_at":"2016-04-27T22:02:40Z","abstract_excerpt":"In this paper, we study the Pohozaev identity associated with a H$\\acute{e}$non-Lane-Emden system involving the fractional Laplacian:\n  \\begin{equation}\n  \\left\\{\\begin{array}{ll}\n  (-\\triangle)^su=|x|^av^p,&x\\in\\Omega,\n  (-\\triangle)^sv=|x|^bu^q,&x\\in\\Omega, u=v=0,&x\\in R^n\\backslash\\Omega,\n  \\end{array}\n  \\right.\n  \\end{equation} in a star-shaped and bounded domain $\\Omega$ for $s\\in(0,1)$. As an application of our identity, we deduce the nonexistence of positive solutions in the critical and supercritical cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08258","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":""},"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":"1604.08258","created_at":"2026-05-18T00:38:18.738654+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.08258v2","created_at":"2026-05-18T00:38:18.738654+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08258","created_at":"2026-05-18T00:38:18.738654+00:00"},{"alias_kind":"pith_short_12","alias_value":"A4EMHDMKRMOW","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"A4EMHDMKRMOWKP3J","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"A4EMHDMK","created_at":"2026-05-18T12:30:04.600751+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/A4EMHDMKRMOWKP3J6XYL5SYSAJ","json":"https://pith.science/pith/A4EMHDMKRMOWKP3J6XYL5SYSAJ.json","graph_json":"https://pith.science/api/pith-number/A4EMHDMKRMOWKP3J6XYL5SYSAJ/graph.json","events_json":"https://pith.science/api/pith-number/A4EMHDMKRMOWKP3J6XYL5SYSAJ/events.json","paper":"https://pith.science/paper/A4EMHDMK"},"agent_actions":{"view_html":"https://pith.science/pith/A4EMHDMKRMOWKP3J6XYL5SYSAJ","download_json":"https://pith.science/pith/A4EMHDMKRMOWKP3J6XYL5SYSAJ.json","view_paper":"https://pith.science/paper/A4EMHDMK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.08258&json=true","fetch_graph":"https://pith.science/api/pith-number/A4EMHDMKRMOWKP3J6XYL5SYSAJ/graph.json","fetch_events":"https://pith.science/api/pith-number/A4EMHDMKRMOWKP3J6XYL5SYSAJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A4EMHDMKRMOWKP3J6XYL5SYSAJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A4EMHDMKRMOWKP3J6XYL5SYSAJ/action/storage_attestation","attest_author":"https://pith.science/pith/A4EMHDMKRMOWKP3J6XYL5SYSAJ/action/author_attestation","sign_citation":"https://pith.science/pith/A4EMHDMKRMOWKP3J6XYL5SYSAJ/action/citation_signature","submit_replication":"https://pith.science/pith/A4EMHDMKRMOWKP3J6XYL5SYSAJ/action/replication_record"}},"created_at":"2026-05-18T00:38:18.738654+00:00","updated_at":"2026-05-18T00:38:18.738654+00:00"}