{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HTVODLKU2TIZLIWRXPLBXQPPJ4","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":"849e246552c82efa6b852461a7fa509c8bd4c623257f78285678cbbec2b05f52","cross_cats_sorted":["math.DS","math.GN","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2024-10-11T13:12:59Z","title_canon_sha256":"68b57ecfd56fbac18950b5a3d91e16b7c8fd6e20b8756914bb0b75298fa18c63"},"schema_version":"1.0","source":{"id":"2410.08789","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.08789","created_at":"2026-07-05T11:24:07Z"},{"alias_kind":"arxiv_version","alias_value":"2410.08789v3","created_at":"2026-07-05T11:24:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.08789","created_at":"2026-07-05T11:24:07Z"},{"alias_kind":"pith_short_12","alias_value":"HTVODLKU2TIZ","created_at":"2026-07-05T11:24:07Z"},{"alias_kind":"pith_short_16","alias_value":"HTVODLKU2TIZLIWR","created_at":"2026-07-05T11:24:07Z"},{"alias_kind":"pith_short_8","alias_value":"HTVODLKU","created_at":"2026-07-05T11:24:07Z"}],"graph_snapshots":[{"event_id":"sha256:dc8f0786abbf39b99ba325491bdc58de391e64fc2d7deb06498fcda35c5e7825","target":"graph","created_at":"2026-07-05T11:24:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.08789/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A trivial automorphism of the Boolean algebra $\\mathcal P(\\mathbb N) / \\mathrm{Fin}$ is an automorphism induced by the action of some function $\\mathbb N \\rightarrow \\mathbb N$. In models of forcing axioms all automorphisms are trivial, and therefore two trivial automorphisms are conjugate if and only if they have the same (modulo finite) cycle structure. We show that the Continuum Hypothesis implies that two trivial automorphisms are conjugate if and only if there are neither first-order obstructions nor index obstructions for their conjugacy. This is equivalent to given trivial automorphisms","authors_text":"Ilijas Farah, Will Brian","cross_cats":["math.DS","math.GN","math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2024-10-11T13:12:59Z","title":"Conjugating trivial automorphisms of $\\mathcal P(\\mathbb N)/\\mathrm{Fin}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.08789","kind":"arxiv","version":3},"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":"sha256:7a5ebaeb0391b09cd8b7e502ad6ff3229095dc95331c310c37ba244347793124","target":"record","created_at":"2026-07-05T11:24:07Z","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":"849e246552c82efa6b852461a7fa509c8bd4c623257f78285678cbbec2b05f52","cross_cats_sorted":["math.DS","math.GN","math.OA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2024-10-11T13:12:59Z","title_canon_sha256":"68b57ecfd56fbac18950b5a3d91e16b7c8fd6e20b8756914bb0b75298fa18c63"},"schema_version":"1.0","source":{"id":"2410.08789","kind":"arxiv","version":3}},"canonical_sha256":"3ceae1ad54d4d195a2d1bbd61bc1ef4f2d79b28ef1711fe870f418c85ac5fca2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ceae1ad54d4d195a2d1bbd61bc1ef4f2d79b28ef1711fe870f418c85ac5fca2","first_computed_at":"2026-07-05T11:24:07.097677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:24:07.097677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P3ycJznitLwBBuZzSJCPfrhrklHA4vVI/5o4DJJ488ITnLtte38jyfCzOm0vhVENiOP3j3XDIDY3dz/4HmYmDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:24:07.098520Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.08789","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a5ebaeb0391b09cd8b7e502ad6ff3229095dc95331c310c37ba244347793124","sha256:dc8f0786abbf39b99ba325491bdc58de391e64fc2d7deb06498fcda35c5e7825"],"state_sha256":"8b13e10974781f98642f14b3a2055210b36bd342834279b2b2f4e13c34b19c5d"}