{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VSA73AHGEAT3567KEB4VQLUPJ3","short_pith_number":"pith:VSA73AHG","schema_version":"1.0","canonical_sha256":"ac81fd80e62027befbea2079582e8f4eccd371976d2855389a641faa02683c20","source":{"kind":"arxiv","id":"2507.19158","version":1},"attestation_state":"computed","paper":{"title":"On harmonic quasiregular mappings in Bergman spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Antti Rasila, Suman Das","submitted_at":"2025-07-25T11:03:03Z","abstract_excerpt":"A classical result of Hardy and Littlewood says that if $f=u+iv$ is analytic in the unit disk $\\mathbb{D}$ and $u$ is in the harmonic Bergman space $a^p$ ($0<p<\\infty$), then $v$ is also in $a^p$. This complements a celebrated result of M. Riesz on Hardy spaces, which only holds for $1<p<\\infty$. These results do not extend directly to complex-valued harmonic functions. We prove that the Hardy-Littlewood theorem holds for a harmonic function $f=u+iv$ if we place the assumption that $f$ is quasiregular in $\\mathbb{D}$. This makes further progress on the recent Riesz type theorems for harmonic q"},"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":"2507.19158","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-07-25T11:03:03Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"44d83efcd55c7dc7f18dcc369ea1780348778800c3a7fbffb1cb6513c8a71c5a","abstract_canon_sha256":"04ed36f889153fc0b858726c6f59e2fa9afce0f4f9285fc30d432a552d5f16ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:20.545478Z","signature_b64":"06/O9uIf2jZ7vIimqWKu8Rnwi+MvpXTDvjQrz6SR1qbdlXOuGYTscIf5rfoQhH6Uv1HLxb5PnpEPk9fVjtv1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac81fd80e62027befbea2079582e8f4eccd371976d2855389a641faa02683c20","last_reissued_at":"2026-07-05T11:43:20.544993Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:20.544993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On harmonic quasiregular mappings in Bergman spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Antti Rasila, Suman Das","submitted_at":"2025-07-25T11:03:03Z","abstract_excerpt":"A classical result of Hardy and Littlewood says that if $f=u+iv$ is analytic in the unit disk $\\mathbb{D}$ and $u$ is in the harmonic Bergman space $a^p$ ($0<p<\\infty$), then $v$ is also in $a^p$. This complements a celebrated result of M. Riesz on Hardy spaces, which only holds for $1<p<\\infty$. These results do not extend directly to complex-valued harmonic functions. We prove that the Hardy-Littlewood theorem holds for a harmonic function $f=u+iv$ if we place the assumption that $f$ is quasiregular in $\\mathbb{D}$. This makes further progress on the recent Riesz type theorems for harmonic q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19158","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.19158/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":"2507.19158","created_at":"2026-07-05T11:43:20.545060+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.19158v1","created_at":"2026-07-05T11:43:20.545060+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19158","created_at":"2026-07-05T11:43:20.545060+00:00"},{"alias_kind":"pith_short_12","alias_value":"VSA73AHGEAT3","created_at":"2026-07-05T11:43:20.545060+00:00"},{"alias_kind":"pith_short_16","alias_value":"VSA73AHGEAT3567K","created_at":"2026-07-05T11:43:20.545060+00:00"},{"alias_kind":"pith_short_8","alias_value":"VSA73AHG","created_at":"2026-07-05T11:43:20.545060+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/VSA73AHGEAT3567KEB4VQLUPJ3","json":"https://pith.science/pith/VSA73AHGEAT3567KEB4VQLUPJ3.json","graph_json":"https://pith.science/api/pith-number/VSA73AHGEAT3567KEB4VQLUPJ3/graph.json","events_json":"https://pith.science/api/pith-number/VSA73AHGEAT3567KEB4VQLUPJ3/events.json","paper":"https://pith.science/paper/VSA73AHG"},"agent_actions":{"view_html":"https://pith.science/pith/VSA73AHGEAT3567KEB4VQLUPJ3","download_json":"https://pith.science/pith/VSA73AHGEAT3567KEB4VQLUPJ3.json","view_paper":"https://pith.science/paper/VSA73AHG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.19158&json=true","fetch_graph":"https://pith.science/api/pith-number/VSA73AHGEAT3567KEB4VQLUPJ3/graph.json","fetch_events":"https://pith.science/api/pith-number/VSA73AHGEAT3567KEB4VQLUPJ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VSA73AHGEAT3567KEB4VQLUPJ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VSA73AHGEAT3567KEB4VQLUPJ3/action/storage_attestation","attest_author":"https://pith.science/pith/VSA73AHGEAT3567KEB4VQLUPJ3/action/author_attestation","sign_citation":"https://pith.science/pith/VSA73AHGEAT3567KEB4VQLUPJ3/action/citation_signature","submit_replication":"https://pith.science/pith/VSA73AHGEAT3567KEB4VQLUPJ3/action/replication_record"}},"created_at":"2026-07-05T11:43:20.545060+00:00","updated_at":"2026-07-05T11:43:20.545060+00:00"}