{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5H45RZ2UZ3JESHFE3ESVRD4FLR","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":"2e2646ff69e816e35fd40bfb20a68f3d80b308316df311d5426abbf37f2dacd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-11T16:00:14Z","title_canon_sha256":"1e9aebb1a14fe8dde513b29a657edece00476bbbc3b808014c08d6c37d85ef9a"},"schema_version":"1.0","source":{"id":"1801.03839","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.03839","created_at":"2026-05-18T00:26:13Z"},{"alias_kind":"arxiv_version","alias_value":"1801.03839v1","created_at":"2026-05-18T00:26:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.03839","created_at":"2026-05-18T00:26:13Z"},{"alias_kind":"pith_short_12","alias_value":"5H45RZ2UZ3JE","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5H45RZ2UZ3JESHFE","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5H45RZ2U","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:f248f827b22ebc81c15adaabd98a9c427f7525a3e42f02495f3bf4ed6c5cc939","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":"This paper presents a proof of an uncertainty principle of Donoho-Stark type involving $\\varepsilon$-concentration of localization operators. More general operators associated with time-frequency representations in the Cohen class are then considered. For these operators, which include all usual quantizations, we prove a boundedness result in the $L^p$ functional setting and a form of uncertainty principle analogous to that for localization operators.","authors_text":"Alessandro Oliaro, Evanthia Carypis, Paolo Boggiatto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-11T16:00:14Z","title":"Cohen class of time-frequency representations and operators: boundedness and uncertainty principles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03839","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":"sha256:2f3de5e7573bfe38eab48f72ef0d5489e3b9c8941b6f540b681498464145d0fd","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":"2e2646ff69e816e35fd40bfb20a68f3d80b308316df311d5426abbf37f2dacd0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-11T16:00:14Z","title_canon_sha256":"1e9aebb1a14fe8dde513b29a657edece00476bbbc3b808014c08d6c37d85ef9a"},"schema_version":"1.0","source":{"id":"1801.03839","kind":"arxiv","version":1}},"canonical_sha256":"e9f9d8e754ced2491ca4d925588f855c7c103953f15fa7a308cceb205520a699","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9f9d8e754ced2491ca4d925588f855c7c103953f15fa7a308cceb205520a699","first_computed_at":"2026-05-18T00:26:13.382479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:13.382479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sd3bukXpWgk9WM6A6HE0Ia+afxnJVjicSIOytn+twGQ3H6N/LeRpBpnQR1D4cu+boS96u3/EwQ6S6+BlDENdAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:13.383099Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.03839","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f3de5e7573bfe38eab48f72ef0d5489e3b9c8941b6f540b681498464145d0fd","sha256:f248f827b22ebc81c15adaabd98a9c427f7525a3e42f02495f3bf4ed6c5cc939"],"state_sha256":"7ffe19c618edffcac2c0d87e2432ae37e026e1dee8bd9cf33da3116cff235358"}