{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:S7MWN52R35TXX6DKJWVESZRUTT","short_pith_number":"pith:S7MWN52R","schema_version":"1.0","canonical_sha256":"97d966f751df677bf86a4daa4966349cebb8c65832de24ce4b33bf69c7fc79bc","source":{"kind":"arxiv","id":"1308.0073","version":1},"attestation_state":"computed","paper":{"title":"Liouville theorems for the polyharmonic Henon-Lane-Emden system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mostafa Fazly","submitted_at":"2013-08-01T00:54:08Z","abstract_excerpt":"We study Liouville theorems for the following polyharmonic H\\'{e}non-Lane-Emden system \\begin{eqnarray*}\n  \\left\\{\\begin{array}{lcl} (-\\Delta)^m u&=& |x|^{a}v^p \\ \\ \\text{in}\\ \\ \\mathbb{R}^n,\\\\ (-\\Delta)^m v&=& |x|^{b}u^q \\ \\ \\text{in}\\ \\ \\mathbb{R}^n, \\end{array}\\right.\n  \\end{eqnarray*} when $m,p,q \\ge 1,$ $pq\\neq1$, $a,b\\ge0$. The main conjecture states that $(u,v)=(0,0)$ is the unique nonnegative solution of this system whenever $(p,q)$ is {\\it under} the critical Sobolev hyperbola, i.e. $ \\frac{n+a}{p+1}+\\frac{n+b}{q+1}>{n-2m}$. We show that this is indeed the case in dimension $n=2m+1$ f"},"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":"1308.0073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-01T00:54:08Z","cross_cats_sorted":[],"title_canon_sha256":"d486efa5c2205de58d3b896c0b58ae6e9fed0dad793f701f681041d013ac6b13","abstract_canon_sha256":"e69d01aa7be4add1ee18f1097f6ece9b3f53bfa8e23fd4ecfbe753bec1348c69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:00.681275Z","signature_b64":"mCGbzMFsx3zbp6iiuu1nhkYbfJmMFbiEnaz3OhxzKsFLVWzfVkUN5M8nMoDxzeHGBlvAtuhtL1lJnVMrt5rnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97d966f751df677bf86a4daa4966349cebb8c65832de24ce4b33bf69c7fc79bc","last_reissued_at":"2026-05-18T03:17:00.680728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:00.680728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Liouville theorems for the polyharmonic Henon-Lane-Emden system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mostafa Fazly","submitted_at":"2013-08-01T00:54:08Z","abstract_excerpt":"We study Liouville theorems for the following polyharmonic H\\'{e}non-Lane-Emden system \\begin{eqnarray*}\n  \\left\\{\\begin{array}{lcl} (-\\Delta)^m u&=& |x|^{a}v^p \\ \\ \\text{in}\\ \\ \\mathbb{R}^n,\\\\ (-\\Delta)^m v&=& |x|^{b}u^q \\ \\ \\text{in}\\ \\ \\mathbb{R}^n, \\end{array}\\right.\n  \\end{eqnarray*} when $m,p,q \\ge 1,$ $pq\\neq1$, $a,b\\ge0$. The main conjecture states that $(u,v)=(0,0)$ is the unique nonnegative solution of this system whenever $(p,q)$ is {\\it under} the critical Sobolev hyperbola, i.e. $ \\frac{n+a}{p+1}+\\frac{n+b}{q+1}>{n-2m}$. We show that this is indeed the case in dimension $n=2m+1$ f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0073","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":""},"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":"1308.0073","created_at":"2026-05-18T03:17:00.680816+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.0073v1","created_at":"2026-05-18T03:17:00.680816+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0073","created_at":"2026-05-18T03:17:00.680816+00:00"},{"alias_kind":"pith_short_12","alias_value":"S7MWN52R35TX","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"S7MWN52R35TXX6DK","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"S7MWN52R","created_at":"2026-05-18T12:27:59.945178+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/S7MWN52R35TXX6DKJWVESZRUTT","json":"https://pith.science/pith/S7MWN52R35TXX6DKJWVESZRUTT.json","graph_json":"https://pith.science/api/pith-number/S7MWN52R35TXX6DKJWVESZRUTT/graph.json","events_json":"https://pith.science/api/pith-number/S7MWN52R35TXX6DKJWVESZRUTT/events.json","paper":"https://pith.science/paper/S7MWN52R"},"agent_actions":{"view_html":"https://pith.science/pith/S7MWN52R35TXX6DKJWVESZRUTT","download_json":"https://pith.science/pith/S7MWN52R35TXX6DKJWVESZRUTT.json","view_paper":"https://pith.science/paper/S7MWN52R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.0073&json=true","fetch_graph":"https://pith.science/api/pith-number/S7MWN52R35TXX6DKJWVESZRUTT/graph.json","fetch_events":"https://pith.science/api/pith-number/S7MWN52R35TXX6DKJWVESZRUTT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S7MWN52R35TXX6DKJWVESZRUTT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S7MWN52R35TXX6DKJWVESZRUTT/action/storage_attestation","attest_author":"https://pith.science/pith/S7MWN52R35TXX6DKJWVESZRUTT/action/author_attestation","sign_citation":"https://pith.science/pith/S7MWN52R35TXX6DKJWVESZRUTT/action/citation_signature","submit_replication":"https://pith.science/pith/S7MWN52R35TXX6DKJWVESZRUTT/action/replication_record"}},"created_at":"2026-05-18T03:17:00.680816+00:00","updated_at":"2026-05-18T03:17:00.680816+00:00"}