{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WK5WH4GMIPFXXKAAIUFJPYGWGE","short_pith_number":"pith:WK5WH4GM","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"},"canonical_sha256":"b2bb63f0cc43cb7ba800450a97e0d631230dbd62188a600da6b52f321de74d58","source":{"kind":"arxiv","id":"1302.6447","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6447","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6447v2","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6447","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"pith_short_12","alias_value":"WK5WH4GMIPFX","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WK5WH4GMIPFXXKAA","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WK5WH4GM","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WK5WH4GMIPFXXKAAIUFJPYGWGE","target":"record","payload":{"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"},"canonical_sha256":"b2bb63f0cc43cb7ba800450a97e0d631230dbd62188a600da6b52f321de74d58","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"},"source_kind":"arxiv","source_id":"1302.6447","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nR8GC+ocdtYIbjKHqzIIYqo1VBtVZ0PUONv1KWhDUD1UgwWmQo9Di4Wi/6A4Qd8tCk79iol64W/4VNbMOdmxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:48:51.871217Z"},"content_sha256":"2253b93dc075ae4560787d79f85812c13a321917b878d9914843dc6d754e0863","schema_version":"1.0","event_id":"sha256:2253b93dc075ae4560787d79f85812c13a321917b878d9914843dc6d754e0863"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WK5WH4GMIPFXXKAAIUFJPYGWGE","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qQ4tqyTa67vSu/pbdbf0ijR5+wgUe1rNbhbVM7B+zXrWitif7jZzAq/yddtLsUVVRtgk7DEAEgFgnTX9WWwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:48:51.871581Z"},"content_sha256":"83b9244844bf94721bb3409017d5feb1e905b2d776ae10fd61105fc69c9a6c34","schema_version":"1.0","event_id":"sha256:83b9244844bf94721bb3409017d5feb1e905b2d776ae10fd61105fc69c9a6c34"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE/bundle.json","state_url":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-01T12:48:51Z","links":{"resolver":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE","bundle":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE/bundle.json","state":"https://pith.science/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WK5WH4GMIPFXXKAAIUFJPYGWGE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WK5WH4GMIPFXXKAAIUFJPYGWGE","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":"38ef158c4297fdecce06dbff64dee208a8cdb7cdf5c3d9c0adc5366fed3a7bfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-26T14:49:31Z","title_canon_sha256":"380434bad6834254134441473e53203b64fb7c5aedca5f350a02f87df0337716"},"schema_version":"1.0","source":{"id":"1302.6447","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6447","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6447v2","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6447","created_at":"2026-05-18T03:06:03Z"},{"alias_kind":"pith_short_12","alias_value":"WK5WH4GMIPFX","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WK5WH4GMIPFXXKAA","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WK5WH4GM","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:83b9244844bf94721bb3409017d5feb1e905b2d776ae10fd61105fc69c9a6c34","target":"graph","created_at":"2026-05-18T03:06:03Z","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":"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","authors_text":"Quentin Menet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-26T14:49:31Z","title":"Hypercyclic subspaces on Fr\\'echet spaces without continuous norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6447","kind":"arxiv","version":2},"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":"sha256:2253b93dc075ae4560787d79f85812c13a321917b878d9914843dc6d754e0863","target":"record","created_at":"2026-05-18T03:06:03Z","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":"38ef158c4297fdecce06dbff64dee208a8cdb7cdf5c3d9c0adc5366fed3a7bfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-26T14:49:31Z","title_canon_sha256":"380434bad6834254134441473e53203b64fb7c5aedca5f350a02f87df0337716"},"schema_version":"1.0","source":{"id":"1302.6447","kind":"arxiv","version":2}},"canonical_sha256":"b2bb63f0cc43cb7ba800450a97e0d631230dbd62188a600da6b52f321de74d58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2bb63f0cc43cb7ba800450a97e0d631230dbd62188a600da6b52f321de74d58","first_computed_at":"2026-05-18T03:06:03.402729Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:03.402729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zjdDEBDoo8wLvQ+h9auz2F4PxHXy3/l1v12V+qjav5TOVmc4WEfP8yNj+DJhhJRytOhnx/vgLqVS+3cFjpi4Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:03.403167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6447","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2253b93dc075ae4560787d79f85812c13a321917b878d9914843dc6d754e0863","sha256:83b9244844bf94721bb3409017d5feb1e905b2d776ae10fd61105fc69c9a6c34"],"state_sha256":"c05909d10a33180e2c922fd6b5397843661dc724674c2139503cdb332f70f96c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uh9yXLhcD0iKIuKMDATUXAMGNcZSphWxVDacX+lXSpN7BdjTzJyw02yuRzHC/QizpRwCNHEZDhoo9Ex4sIRvCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T12:48:51.873514Z","bundle_sha256":"57f4047cb4e05c68e49e360e7c47fda76c84ef382aa7d774d913d50a1a2faf52"}}