{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WK5WH4GMIPFXXKAAIUFJPYGWGE","short_pith_number":"pith:WK5WH4GM","schema_version":"1.0","canonical_sha256":"b2bb63f0cc43cb7ba800450a97e0d631230dbd62188a600da6b52f321de74d58","source":{"kind":"arxiv","id":"1302.6447","version":2},"attestation_state":"computed","paper":{"title":"Hypercyclic subspaces on Fr\\'echet spaces without continuous norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Quentin Menet","submitted_at":"2013-02-26T14:49:31Z","abstract_excerpt":"Known results about hypercyclic subspaces concern either Fr\\'echet spaces with a continuous norm or the space \\omega. We fill the gap between these spaces by investigating Fr\\'echet spaces without continuous norm. To this end, we divide hypercyclic subspaces into two types: the hypercyclic subspaces M for which there exists a continuous seminorm p such that M\\cap \\ker p=\\{0\\} and the others. For each of these types of hypercyclic subspaces, we establish some criteria. This investigation permits us to generalize several results about hypercyclic subspaces on Fr\\'echet spaces with a continuous n"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.6447","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-26T14:49:31Z","cross_cats_sorted":[],"title_canon_sha256":"380434bad6834254134441473e53203b64fb7c5aedca5f350a02f87df0337716","abstract_canon_sha256":"38ef158c4297fdecce06dbff64dee208a8cdb7cdf5c3d9c0adc5366fed3a7bfd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:03.403167Z","signature_b64":"zjdDEBDoo8wLvQ+h9auz2F4PxHXy3/l1v12V+qjav5TOVmc4WEfP8yNj+DJhhJRytOhnx/vgLqVS+3cFjpi4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2bb63f0cc43cb7ba800450a97e0d631230dbd62188a600da6b52f321de74d58","last_reissued_at":"2026-05-18T03:06:03.402729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:03.402729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hypercyclic subspaces on Fr\\'echet spaces without continuous norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Quentin Menet","submitted_at":"2013-02-26T14:49:31Z","abstract_excerpt":"Known results about hypercyclic subspaces concern either Fr\\'echet spaces with a continuous norm or the space \\omega. We fill the gap between these spaces by investigating Fr\\'echet spaces without continuous norm. To this end, we divide hypercyclic subspaces into two types: the hypercyclic subspaces M for which there exists a continuous seminorm p such that M\\cap \\ker p=\\{0\\} and the others. For each of these types of hypercyclic subspaces, we establish some criteria. This investigation permits us to generalize several results about hypercyclic subspaces on Fr\\'echet spaces with a continuous n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6447","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1302.6447","created_at":"2026-05-18T03:06:03.402796+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.6447v2","created_at":"2026-05-18T03:06:03.402796+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6447","created_at":"2026-05-18T03:06:03.402796+00:00"},{"alias_kind":"pith_short_12","alias_value":"WK5WH4GMIPFX","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WK5WH4GMIPFXXKAA","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WK5WH4GM","created_at":"2026-05-18T12:28:04.890932+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE","json":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE.json","graph_json":"https://pith.science/api/pith-number/WK5WH4GMIPFXXKAAIUFJPYGWGE/graph.json","events_json":"https://pith.science/api/pith-number/WK5WH4GMIPFXXKAAIUFJPYGWGE/events.json","paper":"https://pith.science/paper/WK5WH4GM"},"agent_actions":{"view_html":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE","download_json":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE.json","view_paper":"https://pith.science/paper/WK5WH4GM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.6447&json=true","fetch_graph":"https://pith.science/api/pith-number/WK5WH4GMIPFXXKAAIUFJPYGWGE/graph.json","fetch_events":"https://pith.science/api/pith-number/WK5WH4GMIPFXXKAAIUFJPYGWGE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE/action/storage_attestation","attest_author":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE/action/author_attestation","sign_citation":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE/action/citation_signature","submit_replication":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE/action/replication_record"}},"created_at":"2026-05-18T03:06:03.402796+00:00","updated_at":"2026-05-18T03:06:03.402796+00:00"}