{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:D3U2LP7237QKCKSTA4KWZCTYUQ","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":"61ca22b2327de73429326d6981fd8fddac4bb2644e305109e6770216d1c99f5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-16T10:32:01Z","title_canon_sha256":"171734d902893ebe0643f10176a8f699ae25c6deeadcb7849308ad69c44c2dab"},"schema_version":"1.0","source":{"id":"1609.04986","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04986","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04986v1","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04986","created_at":"2026-05-18T00:49:42Z"},{"alias_kind":"pith_short_12","alias_value":"D3U2LP7237QK","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D3U2LP7237QKCKST","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D3U2LP72","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:e3bad68fb673d80d0d456a807f72bfca173dc6bd4a8980700d01966d61434e27","target":"graph","created_at":"2026-05-18T00:49:42Z","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 investigate the hypercyclic properties of commutator maps acting on separable ideals of operators. As the main result we prove the commutator map induced by scalar multiples of the backward shift operator fails to be hypercyclic on the space of compact operators on $\\ell^2$. We also establish some necessary conditions which identify large classes of operators that do not induce hypercyclic commutator maps.","authors_text":"Clifford Gilmore, Eero Saksman, Hans-Olav Tylli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-16T10:32:01Z","title":"Hypercyclicity Properties of Commutator Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04986","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":"sha256:44949be3421635e159870a23c382cb59dcf48142059bdae293094508d51c93a3","target":"record","created_at":"2026-05-18T00:49:42Z","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":"61ca22b2327de73429326d6981fd8fddac4bb2644e305109e6770216d1c99f5c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-09-16T10:32:01Z","title_canon_sha256":"171734d902893ebe0643f10176a8f699ae25c6deeadcb7849308ad69c44c2dab"},"schema_version":"1.0","source":{"id":"1609.04986","kind":"arxiv","version":1}},"canonical_sha256":"1ee9a5bffadfe0a12a5307156c8a78a404049c8c4a03e5c3d2b8de0fda8c2c2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ee9a5bffadfe0a12a5307156c8a78a404049c8c4a03e5c3d2b8de0fda8c2c2e","first_computed_at":"2026-05-18T00:49:42.119670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:42.119670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K0zpHQjgdh4ZChLQARLlrh7Vvpgsv8mhgwls/AnjyRCOQksC6m102HDI6zYVvuOOsISG1UaqvgzaitVrnb/BAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:42.120243Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04986","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44949be3421635e159870a23c382cb59dcf48142059bdae293094508d51c93a3","sha256:e3bad68fb673d80d0d456a807f72bfca173dc6bd4a8980700d01966d61434e27"],"state_sha256":"3f82c5b3e55d1626a5106f20a7ef241089bde9e4fce725840ebfb52c20a32a5e"}