{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NJLTHKULC5PWXGBQF577R2HWVF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"aed212cd24fdb10788ca0ea2028d46d40c646694e0010d7a8d7dda576997f343","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-05T10:51:36Z","title_canon_sha256":"3ae4857cfa9b59f9229cb980809b26455109663ab72ec7d1220d3fd7a629f485"},"schema_version":"1.0","source":{"id":"1609.01090","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01090","created_at":"2026-05-18T00:58:28Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01090v2","created_at":"2026-05-18T00:58:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01090","created_at":"2026-05-18T00:58:28Z"},{"alias_kind":"pith_short_12","alias_value":"NJLTHKULC5PW","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NJLTHKULC5PWXGBQ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NJLTHKUL","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:b657c28b1c0dc1f1af68aa7874acf73b18a4bf794140db4d30c103dc989f3b7e","target":"graph","created_at":"2026-05-18T00:58:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We extend the helicoidal method that we previously developed to the quasi-Banach context, proving in this way multiple Banach and quasi-Banach vector-valued inequalities for paraproducts $\\Pi$ and for the bilinear Hilbert transform $BHT$. As an immediate application, we obtain mixed norm estimates for $\\Pi \\otimes \\Pi$ in the whole range of Lebesgue exponents.\n  One of the novelties in the quasi-Banach framework (that is, when $0<r<1$), which we expect to be useful in other contexts as well, is the \"linearization\" of the operator $ \\left( \\sum_k | T(f_k, g_k) |^r \\right)^{1/r}$ by dualizing it","authors_text":"Camil Muscalu, Cristina Benea","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-05T10:51:36Z","title":"Quasi-Banach Valued Inequalities via the Helicoidal method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01090","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6635fe7aabadc11a2684d034de0aa4405ffca456d6ea30260307ee1e45e03298","target":"record","created_at":"2026-05-18T00:58:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"aed212cd24fdb10788ca0ea2028d46d40c646694e0010d7a8d7dda576997f343","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-05T10:51:36Z","title_canon_sha256":"3ae4857cfa9b59f9229cb980809b26455109663ab72ec7d1220d3fd7a629f485"},"schema_version":"1.0","source":{"id":"1609.01090","kind":"arxiv","version":2}},"canonical_sha256":"6a5733aa8b175f6b98302f7ff8e8f6a940e141f9d10aa76e9a809aa762ddf37f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a5733aa8b175f6b98302f7ff8e8f6a940e141f9d10aa76e9a809aa762ddf37f","first_computed_at":"2026-05-18T00:58:28.411008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:28.411008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HWQdrzyYyvxMURzG8ojbWGw1SXuyp20nbeJ0pyQ9rYbj12xCtsiNJgSb/4JedxY/vR//WJkkxccxcttqIRXNBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:28.411613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01090","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6635fe7aabadc11a2684d034de0aa4405ffca456d6ea30260307ee1e45e03298","sha256:b657c28b1c0dc1f1af68aa7874acf73b18a4bf794140db4d30c103dc989f3b7e"],"state_sha256":"d1a1ec4d1e2aac0558ae8dcf81784d2b40d698d9d90f941243346a90c47b6c47"}