{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AM6EJZDXTFFEETMOPMZBXSGGAQ","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":"3bb7b2f8dffb1458003215c0796e3dca8698406f2ac690f4d32049e3e4977585","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-15T10:28:08Z","title_canon_sha256":"77bf53a5959bb8c0d5adf6ac9f1f7cda9dc0ed012ced96d4ba6d7a28f8f315ee"},"schema_version":"1.0","source":{"id":"1211.3563","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3563","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3563v4","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3563","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"AM6EJZDXTFFE","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AM6EJZDXTFFEETMO","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AM6EJZDX","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:fb0aed80783e809dd9aa18168d11aed3b3e05145e0712a66e59ea52cdad198e2","target":"graph","created_at":"2026-05-18T02:50:43Z","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":"Assuming Borisov--Alexeev--Borisov conjecture, we prove that there is a constant $J=J(n)$ such that for any rationally connected variety $X$ of dimension $n$ and any finite subgroup $G\\subset Bir(X)$ there exists a normal abelian subgroup $A\\subset G$ of index at most $J$. In particular, we obtain that the Cremona group $Cr_3=Bir(P^3)$ enjoys the Jordan property.","authors_text":"Constantin Shramov, Yuri Prokhorov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-15T10:28:08Z","title":"Jordan property for Cremona groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3563","kind":"arxiv","version":4},"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:c63f70761dd29ccd30fca91c6eb15bcbe5f0414e587e87a42d0e14a05e4e26e5","target":"record","created_at":"2026-05-18T02:50:43Z","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":"3bb7b2f8dffb1458003215c0796e3dca8698406f2ac690f4d32049e3e4977585","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-15T10:28:08Z","title_canon_sha256":"77bf53a5959bb8c0d5adf6ac9f1f7cda9dc0ed012ced96d4ba6d7a28f8f315ee"},"schema_version":"1.0","source":{"id":"1211.3563","kind":"arxiv","version":4}},"canonical_sha256":"033c44e477994a424d8e7b321bc8c6040756a81a5b033256667412fc90b0acc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"033c44e477994a424d8e7b321bc8c6040756a81a5b033256667412fc90b0acc1","first_computed_at":"2026-05-18T02:50:43.259518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:43.259518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PaHOmAxAAZJwfxODIw49HSD47R0393xtYgQfGhR4h73NJwuSbN49YGfVkl0bt7Zrz1ztzKobKOCVTKsqvGdMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:43.260213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3563","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c63f70761dd29ccd30fca91c6eb15bcbe5f0414e587e87a42d0e14a05e4e26e5","sha256:fb0aed80783e809dd9aa18168d11aed3b3e05145e0712a66e59ea52cdad198e2"],"state_sha256":"d6dee9c6316695e103757c1d7fe895260bff985919a821f3391635724f4de478"}