{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:MSNASVE3VZFPQED25VZ5FSZXFV","short_pith_number":"pith:MSNASVE3","schema_version":"1.0","canonical_sha256":"649a09549bae4af8107aed73d2cb372d50d48e0373acfd3bd8a8b9e391c50b4c","source":{"kind":"arxiv","id":"1105.6042","version":1},"attestation_state":"computed","paper":{"title":"Weighted Integral Means of Mixed Areas and Lengths under Holomorphic Mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jie Xiao, Wen Xu","submitted_at":"2011-05-30T17:03:30Z","abstract_excerpt":"This note addresses monotonic growths and logarithmic convexities of the weighted ($(1-t^2)^\\alpha dt^2$, $-\\infty<\\alpha<\\infty$, $0<t<1$) integral means $\\mathsf{A}_{\\alpha,\\beta}(f,\\cdot)$ and $\\mathsf{L}_{\\alpha,\\beta}(f,\\cdot)$ of the mixed area $(\\pi r^2)^{-\\beta}A(f,r)$ and the mixed length $(2\\pi r)^{-\\beta}L(f,r)$ ($0\\le\\beta\\le 1$ and $0<r<1$) of $f(r\\mathbb D)$ and $\\partial f(r\\mathbb D)$ under a holomorphic map $f$ from the unit disk $\\mathbb D$ into the finite complex plane $\\mathbb C$."},"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":"1105.6042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-05-30T17:03:30Z","cross_cats_sorted":[],"title_canon_sha256":"c084b10d1e641906f86ef8827e18acb3d6f6a93818efd92284fc13a2e8eb46bd","abstract_canon_sha256":"c02f8ca69d7f3c971af788fa9ddf6864983dc4546dc076554964883196d76b68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:01.013664Z","signature_b64":"oqdITbYGgbPDMCytonxg0OpZuFLUG3R97VGXf1soG60q71upaAZZYAyO83Cfg2HlT7Fpf+I9nE34ObjMTemYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"649a09549bae4af8107aed73d2cb372d50d48e0373acfd3bd8a8b9e391c50b4c","last_reissued_at":"2026-05-18T04:21:01.013084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:01.013084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted Integral Means of Mixed Areas and Lengths under Holomorphic Mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jie Xiao, Wen Xu","submitted_at":"2011-05-30T17:03:30Z","abstract_excerpt":"This note addresses monotonic growths and logarithmic convexities of the weighted ($(1-t^2)^\\alpha dt^2$, $-\\infty<\\alpha<\\infty$, $0<t<1$) integral means $\\mathsf{A}_{\\alpha,\\beta}(f,\\cdot)$ and $\\mathsf{L}_{\\alpha,\\beta}(f,\\cdot)$ of the mixed area $(\\pi r^2)^{-\\beta}A(f,r)$ and the mixed length $(2\\pi r)^{-\\beta}L(f,r)$ ($0\\le\\beta\\le 1$ and $0<r<1$) of $f(r\\mathbb D)$ and $\\partial f(r\\mathbb D)$ under a holomorphic map $f$ from the unit disk $\\mathbb D$ into the finite complex plane $\\mathbb C$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6042","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":"1105.6042","created_at":"2026-05-18T04:21:01.013164+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.6042v1","created_at":"2026-05-18T04:21:01.013164+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6042","created_at":"2026-05-18T04:21:01.013164+00:00"},{"alias_kind":"pith_short_12","alias_value":"MSNASVE3VZFP","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"MSNASVE3VZFPQED2","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"MSNASVE3","created_at":"2026-05-18T12:26:34.985390+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/MSNASVE3VZFPQED25VZ5FSZXFV","json":"https://pith.science/pith/MSNASVE3VZFPQED25VZ5FSZXFV.json","graph_json":"https://pith.science/api/pith-number/MSNASVE3VZFPQED25VZ5FSZXFV/graph.json","events_json":"https://pith.science/api/pith-number/MSNASVE3VZFPQED25VZ5FSZXFV/events.json","paper":"https://pith.science/paper/MSNASVE3"},"agent_actions":{"view_html":"https://pith.science/pith/MSNASVE3VZFPQED25VZ5FSZXFV","download_json":"https://pith.science/pith/MSNASVE3VZFPQED25VZ5FSZXFV.json","view_paper":"https://pith.science/paper/MSNASVE3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.6042&json=true","fetch_graph":"https://pith.science/api/pith-number/MSNASVE3VZFPQED25VZ5FSZXFV/graph.json","fetch_events":"https://pith.science/api/pith-number/MSNASVE3VZFPQED25VZ5FSZXFV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MSNASVE3VZFPQED25VZ5FSZXFV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MSNASVE3VZFPQED25VZ5FSZXFV/action/storage_attestation","attest_author":"https://pith.science/pith/MSNASVE3VZFPQED25VZ5FSZXFV/action/author_attestation","sign_citation":"https://pith.science/pith/MSNASVE3VZFPQED25VZ5FSZXFV/action/citation_signature","submit_replication":"https://pith.science/pith/MSNASVE3VZFPQED25VZ5FSZXFV/action/replication_record"}},"created_at":"2026-05-18T04:21:01.013164+00:00","updated_at":"2026-05-18T04:21:01.013164+00:00"}