{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KJHS3L6JXGUUHPTEKTS4RTNUKA","short_pith_number":"pith:KJHS3L6J","canonical_record":{"source":{"id":"1209.1462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:41:00Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"0d2691ca0bfa0abfe980ee3f55038a06448723325122ee0fc2073c6696b187db","abstract_canon_sha256":"e683fee3645738142dd55d7d989233a6990b4bdfd395f433a2af827081b46a36"},"schema_version":"1.0"},"canonical_sha256":"524f2dafc9b9a943be6454e5c8cdb450219ef0cfb1150b73e462659ae9edd756","source":{"kind":"arxiv","id":"1209.1462","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1462","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1462v1","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1462","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"KJHS3L6JXGUU","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KJHS3L6JXGUUHPTE","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KJHS3L6J","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KJHS3L6JXGUUHPTEKTS4RTNUKA","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1462","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:41:00Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"0d2691ca0bfa0abfe980ee3f55038a06448723325122ee0fc2073c6696b187db","abstract_canon_sha256":"e683fee3645738142dd55d7d989233a6990b4bdfd395f433a2af827081b46a36"},"schema_version":"1.0"},"canonical_sha256":"524f2dafc9b9a943be6454e5c8cdb450219ef0cfb1150b73e462659ae9edd756","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:04.700446Z","signature_b64":"xHZqXrBSe9qNzVecz9QMzucsjTgTobq6xiI0gx5gBGJJdlRDMm77gQyKopm41GOxBQTEVTJW90HYnCyyb/HLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"524f2dafc9b9a943be6454e5c8cdb450219ef0cfb1150b73e462659ae9edd756","last_reissued_at":"2026-05-18T03:46:04.699107Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:04.699107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1462","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qdW228N+KYALakL7B40Bm7YY3J/Q1DHeGKZg0lNKtsMCit8ScF5Wv+uIyCix8qt2wmKhL84hCI2bPY/xlJQNAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:14:49.188855Z"},"content_sha256":"6aefc5dbc8adc12bd795650c0fb40d670c34fba10f184b9cf01f13dfa39f1d75","schema_version":"1.0","event_id":"sha256:6aefc5dbc8adc12bd795650c0fb40d670c34fba10f184b9cf01f13dfa39f1d75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KJHS3L6JXGUUHPTEKTS4RTNUKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-sequential weak supercyclicity and hypercyclicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Stanislav Shkarin","submitted_at":"2012-09-07T08:41:00Z","abstract_excerpt":"A bounded linear operator $T$ acting on a Banach space $\\B$ is called weakly hypercyclic if there exists $x\\in \\B$ such that the orbit ${T^n x: n=0,1,...}$ is weakly dense in $\\B$ and $T$ is called weakly supercyclic if there is $x\\in \\B$ for which the projective orbit ${\\lambda T^n x: \\lambda \\in \\C, n=0,1,...}$ is weakly dense in $\\B$. If weak density is replaced by weak sequential density, then $T$ is said to be weakly sequentially hypercyclic or supercyclic respectively. It is shown that on a separable Hilbert space there are weakly supercyclic operators which are not weakly sequentially s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1462","kind":"arxiv","version":1},"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":"2026-05-18T03:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ySmlYyonVbpfNbsjWrKWYz8gp+p5vvJ6vVF0Asrm5J/n9JKipG1BdYYtDR/GH1Rw2bv3f4fVIoGWOoheY/RwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:14:49.189188Z"},"content_sha256":"573855ecb1efb57e4931ed64363a90c4987096cab3e84078ac3d497a406d767d","schema_version":"1.0","event_id":"sha256:573855ecb1efb57e4931ed64363a90c4987096cab3e84078ac3d497a406d767d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJHS3L6JXGUUHPTEKTS4RTNUKA/bundle.json","state_url":"https://pith.science/pith/KJHS3L6JXGUUHPTEKTS4RTNUKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJHS3L6JXGUUHPTEKTS4RTNUKA/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":"2026-06-23T23:14:49Z","links":{"resolver":"https://pith.science/pith/KJHS3L6JXGUUHPTEKTS4RTNUKA","bundle":"https://pith.science/pith/KJHS3L6JXGUUHPTEKTS4RTNUKA/bundle.json","state":"https://pith.science/pith/KJHS3L6JXGUUHPTEKTS4RTNUKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJHS3L6JXGUUHPTEKTS4RTNUKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KJHS3L6JXGUUHPTEKTS4RTNUKA","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":"e683fee3645738142dd55d7d989233a6990b4bdfd395f433a2af827081b46a36","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:41:00Z","title_canon_sha256":"0d2691ca0bfa0abfe980ee3f55038a06448723325122ee0fc2073c6696b187db"},"schema_version":"1.0","source":{"id":"1209.1462","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1462","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1462v1","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1462","created_at":"2026-05-18T03:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"KJHS3L6JXGUU","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KJHS3L6JXGUUHPTE","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KJHS3L6J","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:573855ecb1efb57e4931ed64363a90c4987096cab3e84078ac3d497a406d767d","target":"graph","created_at":"2026-05-18T03:46:04Z","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 $T$ acting on a Banach space $\\B$ is called weakly hypercyclic if there exists $x\\in \\B$ such that the orbit ${T^n x: n=0,1,...}$ is weakly dense in $\\B$ and $T$ is called weakly supercyclic if there is $x\\in \\B$ for which the projective orbit ${\\lambda T^n x: \\lambda \\in \\C, n=0,1,...}$ is weakly dense in $\\B$. If weak density is replaced by weak sequential density, then $T$ is said to be weakly sequentially hypercyclic or supercyclic respectively. It is shown that on a separable Hilbert space there are weakly supercyclic operators which are not weakly sequentially s","authors_text":"Stanislav Shkarin","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:41:00Z","title":"Non-sequential weak supercyclicity and hypercyclicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1462","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":"sha256:6aefc5dbc8adc12bd795650c0fb40d670c34fba10f184b9cf01f13dfa39f1d75","target":"record","created_at":"2026-05-18T03:46:04Z","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":"e683fee3645738142dd55d7d989233a6990b4bdfd395f433a2af827081b46a36","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:41:00Z","title_canon_sha256":"0d2691ca0bfa0abfe980ee3f55038a06448723325122ee0fc2073c6696b187db"},"schema_version":"1.0","source":{"id":"1209.1462","kind":"arxiv","version":1}},"canonical_sha256":"524f2dafc9b9a943be6454e5c8cdb450219ef0cfb1150b73e462659ae9edd756","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"524f2dafc9b9a943be6454e5c8cdb450219ef0cfb1150b73e462659ae9edd756","first_computed_at":"2026-05-18T03:46:04.699107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:04.699107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xHZqXrBSe9qNzVecz9QMzucsjTgTobq6xiI0gx5gBGJJdlRDMm77gQyKopm41GOxBQTEVTJW90HYnCyyb/HLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:04.700446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1462","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6aefc5dbc8adc12bd795650c0fb40d670c34fba10f184b9cf01f13dfa39f1d75","sha256:573855ecb1efb57e4931ed64363a90c4987096cab3e84078ac3d497a406d767d"],"state_sha256":"6bfb22552e45ca861e6d89acd02b60a650204e0a0ed18ac031d0206e4e8c3aae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TPDQnFVPiMWV8IuCDweUMiggyp+HW8PcTSrCTTAfyzLy0QuWZQbyBKQMZKOjWa+V99zjPAw2V2LvOF33ET0KAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T23:14:49.191053Z","bundle_sha256":"bcb43172ba94ec32ba85f4807cd4a37697633f39557a02803714d3559446923e"}}