{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:4SY3ABJCP77OCPPFSKAYTCSY3Z","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":"a0df87f867a3184832ae6889cd0c9a25e282b1db71e028a476551448d6ef3a1f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-12-20T16:17:12Z","title_canon_sha256":"cb70baac76a5a8c4294d52b97ceee32e05d34d8ca602b2b0eb5a1932a9d580bb"},"schema_version":"1.0","source":{"id":"2312.13153","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.13153","created_at":"2026-07-05T07:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"2312.13153v1","created_at":"2026-07-05T07:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.13153","created_at":"2026-07-05T07:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"4SY3ABJCP77O","created_at":"2026-07-05T07:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"4SY3ABJCP77OCPPF","created_at":"2026-07-05T07:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"4SY3ABJC","created_at":"2026-07-05T07:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:6b23fae0bd4fe25939f918486bf94527a18a570adf4c8abe97deac6d5557d539","target":"graph","created_at":"2026-07-05T07:26:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2312.13153/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the class $Erg^\\perp$ of automorphisms which are disjoint with all ergodic systems. We prove that the identities are the only multipliers of $Erg^\\perp,$ that is, each automorphism whose every joining with an element of $Erg^{\\perp}$ yields a system which is again an element of $Erg^{\\perp}$, must be an identity. Despite this fact, we show that $Erg^\\perp$ is closed by taking Cartesian products. Finally, we prove that there are non-identity elements in $Erg^\\perp$ whose self-joinings always yield elements in $Erg^\\perp$. This shows that there are non-trivial characteristic classes inc","authors_text":"Martyna G\\'orska, Przemys{\\l}aw Berk, Thierry de la Rue","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-12-20T16:17:12Z","title":"Joining properties of automorphisms disjoint with all ergodic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.13153","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":"sha256:4b51fba427afeab82cf9ade7273d53c103a3215c2db4c03b1cf92fb38962857e","target":"record","created_at":"2026-07-05T07:26:32Z","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":"a0df87f867a3184832ae6889cd0c9a25e282b1db71e028a476551448d6ef3a1f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-12-20T16:17:12Z","title_canon_sha256":"cb70baac76a5a8c4294d52b97ceee32e05d34d8ca602b2b0eb5a1932a9d580bb"},"schema_version":"1.0","source":{"id":"2312.13153","kind":"arxiv","version":1}},"canonical_sha256":"e4b1b005227ffee13de59281898a58de6956b55b0f9298d2e245c07aa5f513c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4b1b005227ffee13de59281898a58de6956b55b0f9298d2e245c07aa5f513c5","first_computed_at":"2026-07-05T07:26:32.697142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:26:32.697142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"poabZ4iM9fjsJUNC8hYps750ljSYpUJ+4oPik/cYe7HcyXRM/WHuuoVjif97QfVdF9v5bfGw7sjvVWnAuOwQCA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:26:32.697691Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.13153","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b51fba427afeab82cf9ade7273d53c103a3215c2db4c03b1cf92fb38962857e","sha256:6b23fae0bd4fe25939f918486bf94527a18a570adf4c8abe97deac6d5557d539"],"state_sha256":"2806148c80577bb00e55e212d0f22935d11017043eecdb56ed032aeaccdfeaf1"}