{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:V7LY2SF4PWWGYD6ILWZQRMYMHI","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":"d80d82ee61189cd385b3d0885810dd1c5d0a86cca40bebe0bc292413f255a62b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-27T21:46:10Z","title_canon_sha256":"9d782dcd2804b494e2c121dd9fd327b3bdd0c7a1a5ecfd7d9eba26bfc22b9007"},"schema_version":"1.0","source":{"id":"1511.08831","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08831","created_at":"2026-05-18T01:23:07Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08831v2","created_at":"2026-05-18T01:23:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08831","created_at":"2026-05-18T01:23:07Z"},{"alias_kind":"pith_short_12","alias_value":"V7LY2SF4PWWG","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V7LY2SF4PWWGYD6I","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V7LY2SF4","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:381b839e6e07d9f0d24b71a4c1a4e9c56aeefa6cd8857b9dd26ef604a717eb21","target":"graph","created_at":"2026-05-18T01:23:07Z","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":"It has been shown by Le Jan that, given a memoryless-noise random dynamical system together with an ergodic distribution for the associated Markov transition probabilities, if the support of the ergodic distribution admits locally asymptotically stable trajectories, then there is a random attracting set consisting of finitely many points, whose basin of forward-time attraction includes a random full measure open set. In this paper, we present necessary and sufficient conditions for this attracting set to be a singleton; our result does not require the state space to be compact, but holds on ge","authors_text":"Julian Newman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-27T21:46:10Z","title":"Synchronisation of almost all trajectories of a random dynamical system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08831","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":"sha256:6488832702b009ccfbe6835d1cd49bbf4d69d2490db4f9bf19dc061fb2dc9d83","target":"record","created_at":"2026-05-18T01:23:07Z","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":"d80d82ee61189cd385b3d0885810dd1c5d0a86cca40bebe0bc292413f255a62b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-27T21:46:10Z","title_canon_sha256":"9d782dcd2804b494e2c121dd9fd327b3bdd0c7a1a5ecfd7d9eba26bfc22b9007"},"schema_version":"1.0","source":{"id":"1511.08831","kind":"arxiv","version":2}},"canonical_sha256":"afd78d48bc7dac6c0fc85db308b30c3a2a8a287920d86965171d4cc41e68f9fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afd78d48bc7dac6c0fc85db308b30c3a2a8a287920d86965171d4cc41e68f9fb","first_computed_at":"2026-05-18T01:23:07.784554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:07.784554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OLlY83RMQCaZj9j7MWT7eW6Na2dmw4OFKXUYoezYyKtHyi86QqgobYT89wZIkTHPNMllsuKbuFiWa3g+S/J0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:07.785231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08831","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6488832702b009ccfbe6835d1cd49bbf4d69d2490db4f9bf19dc061fb2dc9d83","sha256:381b839e6e07d9f0d24b71a4c1a4e9c56aeefa6cd8857b9dd26ef604a717eb21"],"state_sha256":"b88501e0b989fcdfea7626724c5ea969cd0fe292bdeb072662da090fa165ef64"}