{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:XD5LOG5G3TQZTPJRRGNFKLWLT2","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":"8ef1ae08793a9f8688f715a0e8653c85129ed8473a64c7d19df99341d94247fc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-04-11T01:24:54Z","title_canon_sha256":"a4d03baba607a031eb6875eccd81f2de860ee2a61cda9484c499d73c49dd97f0"},"schema_version":"1.0","source":{"id":"2204.04820","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.04820","created_at":"2026-07-05T04:17:22Z"},{"alias_kind":"arxiv_version","alias_value":"2204.04820v2","created_at":"2026-07-05T04:17:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.04820","created_at":"2026-07-05T04:17:22Z"},{"alias_kind":"pith_short_12","alias_value":"XD5LOG5G3TQZ","created_at":"2026-07-05T04:17:22Z"},{"alias_kind":"pith_short_16","alias_value":"XD5LOG5G3TQZTPJR","created_at":"2026-07-05T04:17:22Z"},{"alias_kind":"pith_short_8","alias_value":"XD5LOG5G","created_at":"2026-07-05T04:17:22Z"}],"graph_snapshots":[{"event_id":"sha256:368d19e3ba4c7f7a1783ad6474f7d80136572f4eecc46d546cc8f30a1230ab55","target":"graph","created_at":"2026-07-05T04:17:22Z","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/2204.04820/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a 3-manifold M, the twist group Twist(M) is the subgroup of the mapping class group Mod(M) generated by twists about embedded 2-spheres. We study the Nielsen realization problem for subgroups of Twist(M). We prove that a nontrivial subgroup G<Twist(M) is realized by diffeomorphisms if and only if G is cyclic and M is a connected sum of lens spaces. We also apply our methods to the Burnside problem for 3-manifolds and show that Diff(M) does not contain an infinite torsion group when M is reducible and not a connected sum of lens spaces.","authors_text":"Bena Tshishiku, Lei Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-04-11T01:24:54Z","title":"Nielsen Realization for sphere twists on 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.04820","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":"sha256:54fa08ed940ba55ecd7ea54c6b7c88f536014ae1ed5e1a9aeef7edd7b6463e47","target":"record","created_at":"2026-07-05T04:17:22Z","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":"8ef1ae08793a9f8688f715a0e8653c85129ed8473a64c7d19df99341d94247fc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2022-04-11T01:24:54Z","title_canon_sha256":"a4d03baba607a031eb6875eccd81f2de860ee2a61cda9484c499d73c49dd97f0"},"schema_version":"1.0","source":{"id":"2204.04820","kind":"arxiv","version":2}},"canonical_sha256":"b8fab71ba6dce199bd31899a552ecb9ebee48bae3293aa9525e372d9ccaabf40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8fab71ba6dce199bd31899a552ecb9ebee48bae3293aa9525e372d9ccaabf40","first_computed_at":"2026-07-05T04:17:22.123676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:17:22.123676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pEJqBXF3KEv9xyKQdnHSD+ADpFHLr3SCN4r9X1/VpaoHxbkWYrlIrW2Uvt7ZjTzb0rIcM4HQvChRQWE5HdwZDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:17:22.124133Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.04820","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54fa08ed940ba55ecd7ea54c6b7c88f536014ae1ed5e1a9aeef7edd7b6463e47","sha256:368d19e3ba4c7f7a1783ad6474f7d80136572f4eecc46d546cc8f30a1230ab55"],"state_sha256":"c467eb23dc12a340a94f7bef963ba7bfebd891e888c36246716295f7e30aaee2"}