{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CJ3JWY5XMBJQEFKKWFSPSGOVQ4","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":"6ab2e68273d1a06b7acdbc670ad9473a3160bb263d68f603848fa8e51c3722b6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-06T08:27:53Z","title_canon_sha256":"26b0f4c331993860faf6e3d240660f19deb000e3d65fe6423f61adcc6c453417"},"schema_version":"1.0","source":{"id":"1209.1221","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1221","created_at":"2026-05-18T03:46:06Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1221v1","created_at":"2026-05-18T03:46:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1221","created_at":"2026-05-18T03:46:06Z"},{"alias_kind":"pith_short_12","alias_value":"CJ3JWY5XMBJQ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CJ3JWY5XMBJQEFKK","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CJ3JWY5X","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:f1c92c2769bf7e16598eb9539f1677f5a7147762105e5d1fd36782baaec3b072","target":"graph","created_at":"2026-05-18T03:46:06Z","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":"A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\\in X$ such that the lower density of the set $\\{n\\in\\N:T^nx\\in U\\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and Grivaux have raised a question whether there is a frequently hypercyclic operator on any separable infinite dimensional Banach space. We prove that the spectrum of a frequently hypercyclic operator has no isolated points. It follows that there are no frequently hypercyclic operators on all complex and on some real hereditarily indecomposable Banach spaces, whic","authors_text":"Stanislav Shkarin","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-06T08:27:53Z","title":"On the spectrum of frequently hypercyclic operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1221","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":"sha256:11d0aa4a543bdcfb88c849c8948d975acbe136799b3bf13f300eea1985b88b73","target":"record","created_at":"2026-05-18T03:46:06Z","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":"6ab2e68273d1a06b7acdbc670ad9473a3160bb263d68f603848fa8e51c3722b6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-06T08:27:53Z","title_canon_sha256":"26b0f4c331993860faf6e3d240660f19deb000e3d65fe6423f61adcc6c453417"},"schema_version":"1.0","source":{"id":"1209.1221","kind":"arxiv","version":1}},"canonical_sha256":"12769b63b7605302154ab164f919d58701cd35815a898ac26c64fed2f3afd634","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12769b63b7605302154ab164f919d58701cd35815a898ac26c64fed2f3afd634","first_computed_at":"2026-05-18T03:46:06.185460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:06.185460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SvvxHVwK+2B0D4TzcGS7TdEDYoaX3CvvtJ+uGaIYZADHxXQJWpk4N74G8Dvjv9tdn9qY1u5BqNQQD/6HoQrsDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:06.185950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1221","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11d0aa4a543bdcfb88c849c8948d975acbe136799b3bf13f300eea1985b88b73","sha256:f1c92c2769bf7e16598eb9539f1677f5a7147762105e5d1fd36782baaec3b072"],"state_sha256":"3b06210703607e93b7c8a2d39e80c1cc8c9c923e9825e7a6f94aee7c0eb8b239"}