{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZCFT6Y7BIMWVPVKRJ4FQH5Q5YV","short_pith_number":"pith:ZCFT6Y7B","canonical_record":{"source":{"id":"1701.06853","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-24T13:02:54Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"b5e7fcf2f9deba7412c2beb6208a1b911de717f375eaab59b73b5da9c0cbcda6","abstract_canon_sha256":"fe1b9741a3656dec8ee422dcb93cf8673eb68fb59a37ea28886144d381e3ff70"},"schema_version":"1.0"},"canonical_sha256":"c88b3f63e1432d57d5514f0b03f61dc56ca01ef74844bb6593c4142dd2c22059","source":{"kind":"arxiv","id":"1701.06853","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06853","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06853v1","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06853","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZCFT6Y7BIMWV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCFT6Y7BIMWVPVKR","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCFT6Y7B","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZCFT6Y7BIMWVPVKRJ4FQH5Q5YV","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06853","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-24T13:02:54Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"b5e7fcf2f9deba7412c2beb6208a1b911de717f375eaab59b73b5da9c0cbcda6","abstract_canon_sha256":"fe1b9741a3656dec8ee422dcb93cf8673eb68fb59a37ea28886144d381e3ff70"},"schema_version":"1.0"},"canonical_sha256":"c88b3f63e1432d57d5514f0b03f61dc56ca01ef74844bb6593c4142dd2c22059","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:12.027205Z","signature_b64":"UblShNhR2bROfXJ4bsIz+bMUxt3rxge11PuM9hOHOVHewqpQ1/SlKFJucYs/EKY1/TyR+FaWFIp/ZlMIc1McCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c88b3f63e1432d57d5514f0b03f61dc56ca01ef74844bb6593c4142dd2c22059","last_reissued_at":"2026-05-18T00:52:12.026813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:12.026813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06853","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":"2026-05-18T00:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJabP2qXfVXXnWiR8p5IM7NH5R+1z0PHJFyCZ8sbF2vPQYnknnK2MeM9Jfd6jGteiK3T46yxTy1dDeN4eJb0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:13:13.861002Z"},"content_sha256":"a7ff11a597558b392cbf74303ce451a9c5e218019095be09559efbb704221fd6","schema_version":"1.0","event_id":"sha256:a7ff11a597558b392cbf74303ce451a9c5e218019095be09559efbb704221fd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZCFT6Y7BIMWVPVKRJ4FQH5Q5YV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Synchronization, Lyapunov exponents and stable manifolds for random dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Isabell Vorkastner, Michael Scheutzow","submitted_at":"2017-01-24T13:02:54Z","abstract_excerpt":"During the past decades, the question of existence and properties of a random attractor of a random dynamical system generated by an S(P)DE has received considerable attention, for example by the work of Gess and R\\\"ockner. Recently some authors investigated sufficient conditions which guarantee synchronization, i.e. existence of a random attractor which is a singleton. It is reasonable to conjecture that synchronization and negativity (or non-positivity) of the top Lyapunov exponent of the system should be closely related since both mean that the system is contracting in some sense. Based on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06853","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":"2026-05-18T00:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eZlNguL/MGXGU0q9e9CxtXIT1KfX1tP5pfgHiwTRwEUwbAF1eCVdb/pxB4/NUH9bufLvKmbZlhf9WOKPI+0nAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:13:13.861388Z"},"content_sha256":"18b83512290a5e0a06b210e035a17312deab93ea8219b6d56c501c463dea4485","schema_version":"1.0","event_id":"sha256:18b83512290a5e0a06b210e035a17312deab93ea8219b6d56c501c463dea4485"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZCFT6Y7BIMWVPVKRJ4FQH5Q5YV/bundle.json","state_url":"https://pith.science/pith/ZCFT6Y7BIMWVPVKRJ4FQH5Q5YV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZCFT6Y7BIMWVPVKRJ4FQH5Q5YV/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":"2026-05-30T22:13:13Z","links":{"resolver":"https://pith.science/pith/ZCFT6Y7BIMWVPVKRJ4FQH5Q5YV","bundle":"https://pith.science/pith/ZCFT6Y7BIMWVPVKRJ4FQH5Q5YV/bundle.json","state":"https://pith.science/pith/ZCFT6Y7BIMWVPVKRJ4FQH5Q5YV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZCFT6Y7BIMWVPVKRJ4FQH5Q5YV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZCFT6Y7BIMWVPVKRJ4FQH5Q5YV","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":"fe1b9741a3656dec8ee422dcb93cf8673eb68fb59a37ea28886144d381e3ff70","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-24T13:02:54Z","title_canon_sha256":"b5e7fcf2f9deba7412c2beb6208a1b911de717f375eaab59b73b5da9c0cbcda6"},"schema_version":"1.0","source":{"id":"1701.06853","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06853","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06853v1","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06853","created_at":"2026-05-18T00:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZCFT6Y7BIMWV","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZCFT6Y7BIMWVPVKR","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZCFT6Y7B","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:18b83512290a5e0a06b210e035a17312deab93ea8219b6d56c501c463dea4485","target":"graph","created_at":"2026-05-18T00:52:12Z","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":"During the past decades, the question of existence and properties of a random attractor of a random dynamical system generated by an S(P)DE has received considerable attention, for example by the work of Gess and R\\\"ockner. Recently some authors investigated sufficient conditions which guarantee synchronization, i.e. existence of a random attractor which is a singleton. It is reasonable to conjecture that synchronization and negativity (or non-positivity) of the top Lyapunov exponent of the system should be closely related since both mean that the system is contracting in some sense. Based on ","authors_text":"Isabell Vorkastner, Michael Scheutzow","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-24T13:02:54Z","title":"Synchronization, Lyapunov exponents and stable manifolds for random dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06853","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:a7ff11a597558b392cbf74303ce451a9c5e218019095be09559efbb704221fd6","target":"record","created_at":"2026-05-18T00:52:12Z","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":"fe1b9741a3656dec8ee422dcb93cf8673eb68fb59a37ea28886144d381e3ff70","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-24T13:02:54Z","title_canon_sha256":"b5e7fcf2f9deba7412c2beb6208a1b911de717f375eaab59b73b5da9c0cbcda6"},"schema_version":"1.0","source":{"id":"1701.06853","kind":"arxiv","version":1}},"canonical_sha256":"c88b3f63e1432d57d5514f0b03f61dc56ca01ef74844bb6593c4142dd2c22059","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c88b3f63e1432d57d5514f0b03f61dc56ca01ef74844bb6593c4142dd2c22059","first_computed_at":"2026-05-18T00:52:12.026813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:12.026813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UblShNhR2bROfXJ4bsIz+bMUxt3rxge11PuM9hOHOVHewqpQ1/SlKFJucYs/EKY1/TyR+FaWFIp/ZlMIc1McCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:12.027205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06853","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7ff11a597558b392cbf74303ce451a9c5e218019095be09559efbb704221fd6","sha256:18b83512290a5e0a06b210e035a17312deab93ea8219b6d56c501c463dea4485"],"state_sha256":"4ed415ed32b41f98a953aee5596be07c1f36f8ef1f4db64cb57bb9572005544a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bx9E45WJpCWIl5ADFiflJ/1BGV5KFfGog4dcsHk+KLaJL/PpFHQRvgeACNWLnzyiuN5yfvaYx+iMWGdAX3gnBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:13:13.863900Z","bundle_sha256":"fbcf2ab9118b612d3ca4953ae261670770dc981f927eff7d728354e58ccbc4a9"}}