{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5YE772E3RAUAX3ADZZBLCD7EHK","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":"74dfd03671b2fe356513f14f8e996e4803ed3680cefa92523fbf79360fcdf57b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-01-27T06:52:08Z","title_canon_sha256":"ec5658e9da01c3e014b99b45047d08d18243a33277aa6effaf16cd2f0b0c95c8"},"schema_version":"1.0","source":{"id":"1601.07276","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07276","created_at":"2026-05-18T01:21:46Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07276v1","created_at":"2026-05-18T01:21:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07276","created_at":"2026-05-18T01:21:46Z"},{"alias_kind":"pith_short_12","alias_value":"5YE772E3RAUA","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5YE772E3RAUAX3AD","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5YE772E3","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:78596b6b8b956cdbaaa655da5c7139f196e0de96f727934bcbdb7039ddd64e68","target":"graph","created_at":"2026-05-18T01:21:46Z","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":"Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity Criterion. As an application we characterize upper frequently hypercyclic weighted backward shifts on sequence spaces, which in turn allows us to come up with various counter-examples in linear dynamics that are substantially simpler than those previously obtained in the literature. More generally, we introduce the notion of upper Furstenberg families $\\mathcal{A}$ and show that our main results hold for $\\mathcal{A","authors_text":"Antonio Bonilla, Karl-G. Grosse-Erdmann","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-01-27T06:52:08Z","title":"Upper frequent hypercyclicity and related notions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07276","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:d441c51d3225c01a4ced3deca3d3791f2f9c5ffb84509e73cc7299deb3f7a8b0","target":"record","created_at":"2026-05-18T01:21:46Z","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":"74dfd03671b2fe356513f14f8e996e4803ed3680cefa92523fbf79360fcdf57b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-01-27T06:52:08Z","title_canon_sha256":"ec5658e9da01c3e014b99b45047d08d18243a33277aa6effaf16cd2f0b0c95c8"},"schema_version":"1.0","source":{"id":"1601.07276","kind":"arxiv","version":1}},"canonical_sha256":"ee09ffe89b88280bec03ce42b10fe43ab59b8e9391156fab24b551f016472dac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee09ffe89b88280bec03ce42b10fe43ab59b8e9391156fab24b551f016472dac","first_computed_at":"2026-05-18T01:21:46.240090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:46.240090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e55EhdrLmtn2flt2BcdcWx0X7+uENJHmDL0yrhlkLqxfp0s/U+/8fSRd7RxO3Zlg+Jn+hIl0hnDybj6mK63AAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:46.240693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07276","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d441c51d3225c01a4ced3deca3d3791f2f9c5ffb84509e73cc7299deb3f7a8b0","sha256:78596b6b8b956cdbaaa655da5c7139f196e0de96f727934bcbdb7039ddd64e68"],"state_sha256":"5bcfacbcea6254ef82be1b68d8279325703c5293ab1962a72e236172bbca7006"}