{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NSLOQKCUMUOJGPDETXKFVPFGXI","short_pith_number":"pith:NSLOQKCU","canonical_record":{"source":{"id":"1202.3114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-14T18:42:58Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"dae6ee59c2d00680e694a5ad00ae605072c5d639743c2835de0dabfc51bd79b0","abstract_canon_sha256":"f6f3504c481f69ce2c78335005d20af5b387219afd8d7fbeeb2ef3df7984b066"},"schema_version":"1.0"},"canonical_sha256":"6c96e82854651c933c649dd45abca6ba24ac0ed31e12fe09cc878f02572d08dc","source":{"kind":"arxiv","id":"1202.3114","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3114","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3114v1","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3114","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"NSLOQKCUMUOJ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NSLOQKCUMUOJGPDE","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NSLOQKCU","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NSLOQKCUMUOJGPDETXKFVPFGXI","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-14T18:42:58Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"dae6ee59c2d00680e694a5ad00ae605072c5d639743c2835de0dabfc51bd79b0","abstract_canon_sha256":"f6f3504c481f69ce2c78335005d20af5b387219afd8d7fbeeb2ef3df7984b066"},"schema_version":"1.0"},"canonical_sha256":"6c96e82854651c933c649dd45abca6ba24ac0ed31e12fe09cc878f02572d08dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:36.323171Z","signature_b64":"vkF/w2DYHmadgrF0wM1NFeg3VtOZVq2W56xvmP7KKWs6wao1wDeCiRZ65rrnQtB317MmqUoRbPoSdxPSpI1rCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c96e82854651c933c649dd45abca6ba24ac0ed31e12fe09cc878f02572d08dc","last_reissued_at":"2026-05-17T23:53:36.322354Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:36.322354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3114","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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I6QD2z4JFuoycT/Qw5tplMScGVIf8kKeE8lAyWtpmQwgBTXR4cBPUoPGl9dOhwuIlngT9WB66X+ObOwwJry5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:47:07.217500Z"},"content_sha256":"40d04611db0cdd627ca1db164cae81677d70cc35248533c02b65fda30a6bc2a0","schema_version":"1.0","event_id":"sha256:40d04611db0cdd627ca1db164cae81677d70cc35248533c02b65fda30a6bc2a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NSLOQKCUMUOJGPDETXKFVPFGXI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-recurrence sets for weakly mixing linear dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"Sophie Grivaux","submitted_at":"2012-02-14T18:42:58Z","abstract_excerpt":"We study non-recurrence sets for weakly mixing dynamical systems by using linear dynamical systems. These are systems consisting of a bounded linear operator acting on a separable complex Banach space X, which becomes a probability space when endowed with a non-degenerate Gaussian measure. We generalize some recent results of Bergelson, del Junco, Lema\\'nczyk and Rosenblatt, and show in particular that sets \\{n_k\\} such that n_{k+1}/{n_k} tends to infinity, or such that n_{k} divides n_{k+1} for each k, are non-recurrence sets for weakly mixing linear dynamical systems. We also give examples, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3114","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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p9HEq0o5SsyhQLEGfgmEsRBAOIvPb8s123vr0i9L8wkH82EFHznGuTxWYv97teevAuGcmWsION57m5u4QFUGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:47:07.217843Z"},"content_sha256":"749f6cc588a3b63aef9b2fad18eb87ce6b751fbe0d71cbc97c1aa17ffca93d04","schema_version":"1.0","event_id":"sha256:749f6cc588a3b63aef9b2fad18eb87ce6b751fbe0d71cbc97c1aa17ffca93d04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSLOQKCUMUOJGPDETXKFVPFGXI/bundle.json","state_url":"https://pith.science/pith/NSLOQKCUMUOJGPDETXKFVPFGXI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSLOQKCUMUOJGPDETXKFVPFGXI/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":"2026-06-24T05:47:07Z","links":{"resolver":"https://pith.science/pith/NSLOQKCUMUOJGPDETXKFVPFGXI","bundle":"https://pith.science/pith/NSLOQKCUMUOJGPDETXKFVPFGXI/bundle.json","state":"https://pith.science/pith/NSLOQKCUMUOJGPDETXKFVPFGXI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSLOQKCUMUOJGPDETXKFVPFGXI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NSLOQKCUMUOJGPDETXKFVPFGXI","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":"f6f3504c481f69ce2c78335005d20af5b387219afd8d7fbeeb2ef3df7984b066","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-14T18:42:58Z","title_canon_sha256":"dae6ee59c2d00680e694a5ad00ae605072c5d639743c2835de0dabfc51bd79b0"},"schema_version":"1.0","source":{"id":"1202.3114","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3114","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3114v1","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3114","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"NSLOQKCUMUOJ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NSLOQKCUMUOJGPDE","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NSLOQKCU","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:749f6cc588a3b63aef9b2fad18eb87ce6b751fbe0d71cbc97c1aa17ffca93d04","target":"graph","created_at":"2026-05-17T23:53:36Z","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 study non-recurrence sets for weakly mixing dynamical systems by using linear dynamical systems. These are systems consisting of a bounded linear operator acting on a separable complex Banach space X, which becomes a probability space when endowed with a non-degenerate Gaussian measure. We generalize some recent results of Bergelson, del Junco, Lema\\'nczyk and Rosenblatt, and show in particular that sets \\{n_k\\} such that n_{k+1}/{n_k} tends to infinity, or such that n_{k} divides n_{k+1} for each k, are non-recurrence sets for weakly mixing linear dynamical systems. We also give examples, ","authors_text":"Sophie Grivaux","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-14T18:42:58Z","title":"Non-recurrence sets for weakly mixing linear dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3114","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":"sha256:40d04611db0cdd627ca1db164cae81677d70cc35248533c02b65fda30a6bc2a0","target":"record","created_at":"2026-05-17T23:53:36Z","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":"f6f3504c481f69ce2c78335005d20af5b387219afd8d7fbeeb2ef3df7984b066","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-14T18:42:58Z","title_canon_sha256":"dae6ee59c2d00680e694a5ad00ae605072c5d639743c2835de0dabfc51bd79b0"},"schema_version":"1.0","source":{"id":"1202.3114","kind":"arxiv","version":1}},"canonical_sha256":"6c96e82854651c933c649dd45abca6ba24ac0ed31e12fe09cc878f02572d08dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c96e82854651c933c649dd45abca6ba24ac0ed31e12fe09cc878f02572d08dc","first_computed_at":"2026-05-17T23:53:36.322354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.322354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vkF/w2DYHmadgrF0wM1NFeg3VtOZVq2W56xvmP7KKWs6wao1wDeCiRZ65rrnQtB317MmqUoRbPoSdxPSpI1rCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.323171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3114","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40d04611db0cdd627ca1db164cae81677d70cc35248533c02b65fda30a6bc2a0","sha256:749f6cc588a3b63aef9b2fad18eb87ce6b751fbe0d71cbc97c1aa17ffca93d04"],"state_sha256":"0755dd3c29a040788e641198113c6e6c34c6080cc3149a9bd4507e1d13e3cbcd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"udlF/yAEnpx37u1DcRtqzt5zl86owPRqCVkx2COGDNzxP3xeeWcnwE0aHpLujGNVZ/59w+eYJID6nJcv0KBDAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:47:07.219758Z","bundle_sha256":"e546e3b6c0dfe5f650b622e481c02a19b8076ab68374de4915101d07e89d0bae"}}