{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:B4DQJX2PRDA4NSP35Y3VUAXCKW","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":"9074c56fdca19463816c43a93511625906969e74a1f287e360f79c7875b8b131","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-01T23:02:04Z","title_canon_sha256":"2b3b78221751299b8813b368f5240354c04f257f0645fc8dbe95600ebfa9890d"},"schema_version":"1.0","source":{"id":"1605.00318","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00318","created_at":"2026-05-18T00:26:13Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00318v3","created_at":"2026-05-18T00:26:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00318","created_at":"2026-05-18T00:26:13Z"},{"alias_kind":"pith_short_12","alias_value":"B4DQJX2PRDA4","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"B4DQJX2PRDA4NSP3","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"B4DQJX2P","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:838d868fa3c741a42f1f450578050cf0d8b5cd1dea3b1b4dc46ca1bda2069390","target":"graph","created_at":"2026-05-18T00:26:13Z","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 study the bilinear Weyl product acting on quasi-Banach modulation spaces. We find sufficient conditions for continuity of the Weyl product and we derive necessary conditions. The results extend known results for Banach modulation spaces.","authors_text":"Joachim Toft, Patrik Wahlberg, Yuanyuan Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-01T23:02:04Z","title":"The Weyl product on quasi-Banach modulation spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00318","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:b82eae3a464168ca51a7dd4cab4694eaa0c58bd806b858a110a17357cf7c3725","target":"record","created_at":"2026-05-18T00:26:13Z","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":"9074c56fdca19463816c43a93511625906969e74a1f287e360f79c7875b8b131","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-01T23:02:04Z","title_canon_sha256":"2b3b78221751299b8813b368f5240354c04f257f0645fc8dbe95600ebfa9890d"},"schema_version":"1.0","source":{"id":"1605.00318","kind":"arxiv","version":3}},"canonical_sha256":"0f0704df4f88c1c6c9fbee375a02e255ab56b8e0b4a1766cfce54ad701f32fed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f0704df4f88c1c6c9fbee375a02e255ab56b8e0b4a1766cfce54ad701f32fed","first_computed_at":"2026-05-18T00:26:13.080053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:13.080053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Q+lEP4ub9DKeTg82ywL6nDXfL7qudXCvCuiT1dVACZY1l2SCRaRHTvMyzSghsoISQruAtlh4L7anWXbb6ecDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:13.080729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00318","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b82eae3a464168ca51a7dd4cab4694eaa0c58bd806b858a110a17357cf7c3725","sha256:838d868fa3c741a42f1f450578050cf0d8b5cd1dea3b1b4dc46ca1bda2069390"],"state_sha256":"e9e1a96639eeafb0a9f14117a0fcb47ca74a3252cfebc907ebb3f10dc91ace78"}