{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C6ZWNII6BJLLCNNU73IZLGS6UV","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":"7dd7f4dc0b1c477e27b51d05b242c295888b7875f0b206f580983b3381a1fd0e","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-01T16:04:16Z","title_canon_sha256":"d60025444769f7c92e5db2cc1b1e617e81016b11213a6a1741b1d491c58bda8b"},"schema_version":"1.0","source":{"id":"1701.00258","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00258","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00258v1","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00258","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"C6ZWNII6BJLL","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C6ZWNII6BJLLCNNU","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C6ZWNII6","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:336227f64a957e794a20284b80aace92747caff75bdceb2ae5918dfd1dd62d41","target":"graph","created_at":"2026-05-18T00:53:35Z","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 initiate the study of the completely bounded multipliers of the Haagerup tensor product $A(G)\\otimes_{\\rm h} A(G)$ of two copies of the Fourier algebra $A(G)$ of a locally compact group $G$. If $E$ is a closed subset of $G$ we let $E^{\\sharp} = \\{(s,t) : st\\in E\\}$ and show that if $E^{\\sharp}$ is a set of spectral synthesis for $A(G)\\otimes_{\\rm h} A(G)$ then $E$ is a set of local spectral synthesis for $A(G)$. Conversely, we prove that if $E$ is a set of spectral synthesis for $A(G)$ and $G$ is a Moore group then $E^{\\sharp}$ is a set of spectral synthesis for $A(G)\\otimes_{\\rm h} A(G)$. ","authors_text":"I. G. Todorov, L. Turowska, M. Alaghmandan","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-01T16:04:16Z","title":"Completely bounded bimodule maps and spectral synthesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00258","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":"sha256:5261c9d2ea6431d725d51aa63301b1667c89c36117248829235736020f62a50f","target":"record","created_at":"2026-05-18T00:53:35Z","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":"7dd7f4dc0b1c477e27b51d05b242c295888b7875f0b206f580983b3381a1fd0e","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-01T16:04:16Z","title_canon_sha256":"d60025444769f7c92e5db2cc1b1e617e81016b11213a6a1741b1d491c58bda8b"},"schema_version":"1.0","source":{"id":"1701.00258","kind":"arxiv","version":1}},"canonical_sha256":"17b366a11e0a56b135b4fed1959a5ea5497f66fb1bc9de407eb3e71781abcc3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17b366a11e0a56b135b4fed1959a5ea5497f66fb1bc9de407eb3e71781abcc3b","first_computed_at":"2026-05-18T00:53:35.961908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:35.961908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Ez4DPAQaab/gVrlDv4FFlf1oPe6C5aJn42UZFBlWdtOgiCwpFtdH88MEQtRpTa3/EksonnEC3C9AjqF0orZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:35.962379Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00258","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5261c9d2ea6431d725d51aa63301b1667c89c36117248829235736020f62a50f","sha256:336227f64a957e794a20284b80aace92747caff75bdceb2ae5918dfd1dd62d41"],"state_sha256":"a4a43bc39de7e240b4aec0de09c09607b55dbce38a1c433ad11c2e46a0afc0b7"}