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Namely, we will show that for any $\\alpha>0$ there exists a constant $C_{\\alpha}>0$ such that \\[ \\int_{\\mathbb{B}^{4}}(e^{32\\pi^{2} u^{2}}-1-32\\pi^{2} u^{2})dV=16\\int_{\\mathbb{B}^{4}}\\frac{e^{32\\pi^{2} u^{2}}-1-32\\pi^{2} u^{2}}{(1-|x|^{2})^{4}}dx\\leq C_{\\alpha}. \\] for any $u\\in C^{\\infty}_{0}(\\mathbb{B}^{4})$ with \\[ \\int_{\\mathbb{B}^{4}}\\left(-\\Delta_{\\mathbb{H}}-\\frac{9}{4}\\right)(-\\Delta_{\\mathbb{H}}+\\alpha)u\\cdot udV\\leq1. \\]\n  As applications, we obtain a sharpened Adams inequality on hype"},"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":"1703.08149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-23T17:27:40Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"ac183367a23fcb9363b91a8296829ea05c29028dfbf0836a6db89b7c6d532e3e","abstract_canon_sha256":"e1b91cf6f371f4de74ea1c6456c1b39e0a28b3919c4ef4b18b7727c92e4f0d8a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:03.749734Z","signature_b64":"cNlNSbZSnKKyRHEmXeWWbJ36qhAWQfHpaca+wdt7HzgbG7M3AD6n+ZwqqEBI5VBhG/aRVOrxG9ftKE1ut/9sBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e56fa3ec2ed7428e7d6ce4748f5c96cc09757ce1ce2080f7edee669b081a0f3","last_reissued_at":"2026-05-18T00:48:03.749088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:03.749088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp Hardy-Adams inequalities for bi-Laplacian on hyperbolic space of dimension four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Guozhen Lu, Qiaohua Yang","submitted_at":"2017-03-23T17:27:40Z","abstract_excerpt":"We establish sharp Hardy-Adams inequalities on hyperbolic space $\\mathbb{B}^{4}$ of dimension four. Namely, we will show that for any $\\alpha>0$ there exists a constant $C_{\\alpha}>0$ such that \\[ \\int_{\\mathbb{B}^{4}}(e^{32\\pi^{2} u^{2}}-1-32\\pi^{2} u^{2})dV=16\\int_{\\mathbb{B}^{4}}\\frac{e^{32\\pi^{2} u^{2}}-1-32\\pi^{2} u^{2}}{(1-|x|^{2})^{4}}dx\\leq C_{\\alpha}. \\] for any $u\\in C^{\\infty}_{0}(\\mathbb{B}^{4})$ with \\[ \\int_{\\mathbb{B}^{4}}\\left(-\\Delta_{\\mathbb{H}}-\\frac{9}{4}\\right)(-\\Delta_{\\mathbb{H}}+\\alpha)u\\cdot udV\\leq1. \\]\n  As applications, we obtain a sharpened Adams inequality on hype"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08149","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":"1703.08149","created_at":"2026-05-18T00:48:03.749208+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.08149v1","created_at":"2026-05-18T00:48:03.749208+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08149","created_at":"2026-05-18T00:48:03.749208+00:00"},{"alias_kind":"pith_short_12","alias_value":"HZLPUPWC5V2C","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"HZLPUPWC5V2CRZ6W","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"HZLPUPWC","created_at":"2026-05-18T12:31:21.493067+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/HZLPUPWC5V2CRZ6WZZDUR5OJNT","json":"https://pith.science/pith/HZLPUPWC5V2CRZ6WZZDUR5OJNT.json","graph_json":"https://pith.science/api/pith-number/HZLPUPWC5V2CRZ6WZZDUR5OJNT/graph.json","events_json":"https://pith.science/api/pith-number/HZLPUPWC5V2CRZ6WZZDUR5OJNT/events.json","paper":"https://pith.science/paper/HZLPUPWC"},"agent_actions":{"view_html":"https://pith.science/pith/HZLPUPWC5V2CRZ6WZZDUR5OJNT","download_json":"https://pith.science/pith/HZLPUPWC5V2CRZ6WZZDUR5OJNT.json","view_paper":"https://pith.science/paper/HZLPUPWC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.08149&json=true","fetch_graph":"https://pith.science/api/pith-number/HZLPUPWC5V2CRZ6WZZDUR5OJNT/graph.json","fetch_events":"https://pith.science/api/pith-number/HZLPUPWC5V2CRZ6WZZDUR5OJNT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HZLPUPWC5V2CRZ6WZZDUR5OJNT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HZLPUPWC5V2CRZ6WZZDUR5OJNT/action/storage_attestation","attest_author":"https://pith.science/pith/HZLPUPWC5V2CRZ6WZZDUR5OJNT/action/author_attestation","sign_citation":"https://pith.science/pith/HZLPUPWC5V2CRZ6WZZDUR5OJNT/action/citation_signature","submit_replication":"https://pith.science/pith/HZLPUPWC5V2CRZ6WZZDUR5OJNT/action/replication_record"}},"created_at":"2026-05-18T00:48:03.749208+00:00","updated_at":"2026-05-18T00:48:03.749208+00:00"}