{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YNB2MEV6G2VTAWCFVCPOJ6UAFD","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":"999fe602c08a119ac21d50946135f0c4f783a2bd0f4971a50050d2ebac01c25f","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-06-30T21:18:45Z","title_canon_sha256":"ed6bc3163f7fb20f2c64910e61f16a0fc3971dd9acc8dff414a70a4d9eaff0dd"},"schema_version":"1.0","source":{"id":"2607.00194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.00194","created_at":"2026-07-02T00:18:38Z"},{"alias_kind":"arxiv_version","alias_value":"2607.00194v1","created_at":"2026-07-02T00:18:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.00194","created_at":"2026-07-02T00:18:38Z"},{"alias_kind":"pith_short_12","alias_value":"YNB2MEV6G2VT","created_at":"2026-07-02T00:18:38Z"},{"alias_kind":"pith_short_16","alias_value":"YNB2MEV6G2VTAWCF","created_at":"2026-07-02T00:18:38Z"},{"alias_kind":"pith_short_8","alias_value":"YNB2MEV6","created_at":"2026-07-02T00:18:38Z"}],"graph_snapshots":[{"event_id":"sha256:9ce85c3918f1452bb7884e9910fd147301ac4165e338de519c3242c8303fe754","target":"graph","created_at":"2026-07-02T00:18:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.00194/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study Hilbert transforms on graph products of finite von Neumann algebras, with particular interests on their boundedness on the associated noncommutative $L_p$-spaces for $1<p<\\infty$. We establish a generalized Cotlar identity for Hilbert transforms, valid on operators whose lengths exceed a constant depending only on the underlying graph. We further prove that graph products of finite von Neumann algebras satisfying a Haagerup-type inequality admit $L_p$-bounded Hilbert transforms, therefore extending the corresponding result of Mei and Ricard for free products of finite von Neumann alge","authors_text":"Runlian Xia, Xiao-Qi Lu","cross_cats":["math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-06-30T21:18:45Z","title":"Hilbert transforms on graph products of finite von Neumann algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00194","kind":"arxiv","version":1},"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":"sha256:73d10e415246f44a39851a10a99be5c7eb15dce12bee1b3e9a8c663fdec5d23f","target":"record","created_at":"2026-07-02T00:18:38Z","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":"999fe602c08a119ac21d50946135f0c4f783a2bd0f4971a50050d2ebac01c25f","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-06-30T21:18:45Z","title_canon_sha256":"ed6bc3163f7fb20f2c64910e61f16a0fc3971dd9acc8dff414a70a4d9eaff0dd"},"schema_version":"1.0","source":{"id":"2607.00194","kind":"arxiv","version":1}},"canonical_sha256":"c343a612be36ab305845a89ee4fa8028fba4c678e23a1c7406e1aa9e8d0e1a6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c343a612be36ab305845a89ee4fa8028fba4c678e23a1c7406e1aa9e8d0e1a6e","first_computed_at":"2026-07-02T00:18:38.643305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T00:18:38.643305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"py5nE8WMnsDA82eXulgdS06nHvnRtQxSEUlQMBMWn6/FRwPlNQ4k4ivCdx6DgkaA71lqP3dnMTRToYVAGExyAQ==","signature_status":"signed_v1","signed_at":"2026-07-02T00:18:38.643815Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.00194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73d10e415246f44a39851a10a99be5c7eb15dce12bee1b3e9a8c663fdec5d23f","sha256:9ce85c3918f1452bb7884e9910fd147301ac4165e338de519c3242c8303fe754"],"state_sha256":"17c0d55b420a90efd95aa2b219d9e0ca4b2040c9e61237b970a4231088d6b1a6"}