{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:F6ESDWXQHPUQQ7JPEF4WBIASZT","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":"074fe0a5e0428585c898b0ce7ac5fb2c242f17166cb382ab22393dae78f8e744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-11-21T22:56:45Z","title_canon_sha256":"0f600ad64cf256ce860963a9eec14b4b1240a68f7e067925311776d000c33ce3"},"schema_version":"1.0","source":{"id":"2411.14624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14624","created_at":"2026-07-05T09:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14624v1","created_at":"2026-07-05T09:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14624","created_at":"2026-07-05T09:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"F6ESDWXQHPUQ","created_at":"2026-07-05T09:38:54Z"},{"alias_kind":"pith_short_16","alias_value":"F6ESDWXQHPUQQ7JP","created_at":"2026-07-05T09:38:54Z"},{"alias_kind":"pith_short_8","alias_value":"F6ESDWXQ","created_at":"2026-07-05T09:38:54Z"}],"graph_snapshots":[{"event_id":"sha256:21dedaa1d1cb184c39003fd20e703f0e3f9ec0df029e8cb73a5a63bdaf170540","target":"graph","created_at":"2026-07-05T09:38:54Z","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/2411.14624/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Fourier and Fourier-Stieltjes algebras over locally compact groupoids have been defined in a way that parallels their construction for groups. In this article, we extend the results on surjectivity or lack of surjectivity of the restriction map on the Fourier and Fourier-Stieltjes algebras of groups to the groupoid setting. In particular, we consider the maps that restrict the domain of these functions in the Fourier or Fourier-Stieltjes algebra of a groupoid to an isotropy subgroup. These maps are continuous contractive algebra homomorphisms. When the groupoid is \\'{e}tale, we show that t","authors_text":"Joseph DeGaetani, Mahya Ghandehari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-11-21T22:56:45Z","title":"On the restriction maps of the Fourier and Fourier-Stieltjes algebras over locally compact groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14624","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":"sha256:35f915758659982fd2f17757f3e79eb2edb9ebd9967a069a1fe6cccfbeb2c8bb","target":"record","created_at":"2026-07-05T09:38:54Z","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":"074fe0a5e0428585c898b0ce7ac5fb2c242f17166cb382ab22393dae78f8e744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-11-21T22:56:45Z","title_canon_sha256":"0f600ad64cf256ce860963a9eec14b4b1240a68f7e067925311776d000c33ce3"},"schema_version":"1.0","source":{"id":"2411.14624","kind":"arxiv","version":1}},"canonical_sha256":"2f8921daf03be9087d2f217960a012ccf725209e421b812a90370ddc5589e101","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f8921daf03be9087d2f217960a012ccf725209e421b812a90370ddc5589e101","first_computed_at":"2026-07-05T09:38:54.237907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:54.237907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7+g1d/f8mBemJY/7oDXGVGNVh69Wo05ijIUVHmG2T9VkDJRFq3rAQ0Km2asYDOYkyrugQPMrZZFuDdycnAZ5Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:54.238361Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35f915758659982fd2f17757f3e79eb2edb9ebd9967a069a1fe6cccfbeb2c8bb","sha256:21dedaa1d1cb184c39003fd20e703f0e3f9ec0df029e8cb73a5a63bdaf170540"],"state_sha256":"eb8bd9ec04e58ee389bd570d9db8e8b452c38165770f90f5d0594e59c3d9ff24"}