{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OQQYAANPPMRXJN5OEXEDNS2L72","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":"1700c8115d3e2e2122a8d24736fa3ef6688d71eb0ef45ee79fe34e751612408d","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-07-09T08:12:40Z","title_canon_sha256":"de278eddccf9a8125ef9ab5a5ec68bcb477bec3e8feb20e774fc5cfaa39f804e"},"schema_version":"1.0","source":{"id":"1507.02409","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02409","created_at":"2026-05-18T01:22:57Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02409v3","created_at":"2026-05-18T01:22:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02409","created_at":"2026-05-18T01:22:57Z"},{"alias_kind":"pith_short_12","alias_value":"OQQYAANPPMRX","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OQQYAANPPMRXJN5O","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OQQYAANP","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:b8db692cae4bf26fb1768fcec640af52d33cdcc58a0ff89815f5b57af6ac5081","target":"graph","created_at":"2026-05-18T01:22:57Z","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":"This paper deals with the operator-valued Hardy spaces introduced and studied by Tao Mei. Our principal result shows that the Poisson kernel in Mei's definition of these spaces can be replaced by any reasonable test function. As an application, we get a general characterization of Hardy spaces on quantum tori. The latter characterization plays a key role in our recent study of Triebel-Lizorkin spaces on quantum tori.","authors_text":"Quanhua Xu, Runlian Xia, Xiao Xiong","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-07-09T08:12:40Z","title":"Characterizations of operator-valued Hardy spaces and applications to harmonic analysis on quantum tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02409","kind":"arxiv","version":3},"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":"sha256:6e7701d4d9807e3d85556f30ebfb955d8bd56e76f951738c5e1216f10f9d4f61","target":"record","created_at":"2026-05-18T01:22:57Z","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":"1700c8115d3e2e2122a8d24736fa3ef6688d71eb0ef45ee79fe34e751612408d","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-07-09T08:12:40Z","title_canon_sha256":"de278eddccf9a8125ef9ab5a5ec68bcb477bec3e8feb20e774fc5cfaa39f804e"},"schema_version":"1.0","source":{"id":"1507.02409","kind":"arxiv","version":3}},"canonical_sha256":"74218001af7b2374b7ae25c836cb4bfe87b60bf054bfad5eace439ec7c18cd95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74218001af7b2374b7ae25c836cb4bfe87b60bf054bfad5eace439ec7c18cd95","first_computed_at":"2026-05-18T01:22:57.671808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:57.671808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ByOjd2895+pOBgpY/WDl4ePZmi1jJbNN97NfeeV3DR1R+91++U+ymoQFZFcMInn/QaUUFRC5RSBHr1PGqEM7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:57.672428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02409","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e7701d4d9807e3d85556f30ebfb955d8bd56e76f951738c5e1216f10f9d4f61","sha256:b8db692cae4bf26fb1768fcec640af52d33cdcc58a0ff89815f5b57af6ac5081"],"state_sha256":"af827d94ea90987861a5e9d1515e7a84fda4aaeeff59c4606be906d7a7fe4792"}