{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AM6EJZDXTFFEETMOPMZBXSGGAQ","short_pith_number":"pith:AM6EJZDX","canonical_record":{"source":{"id":"1211.3563","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-15T10:28:08Z","cross_cats_sorted":[],"title_canon_sha256":"77bf53a5959bb8c0d5adf6ac9f1f7cda9dc0ed012ced96d4ba6d7a28f8f315ee","abstract_canon_sha256":"3bb7b2f8dffb1458003215c0796e3dca8698406f2ac690f4d32049e3e4977585"},"schema_version":"1.0"},"canonical_sha256":"033c44e477994a424d8e7b321bc8c6040756a81a5b033256667412fc90b0acc1","source":{"kind":"arxiv","id":"1211.3563","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AM6EJZDXTFFEETMOPMZBXSGGAQ","target":"record","payload":{"canonical_record":{"source":{"id":"1211.3563","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-15T10:28:08Z","cross_cats_sorted":[],"title_canon_sha256":"77bf53a5959bb8c0d5adf6ac9f1f7cda9dc0ed012ced96d4ba6d7a28f8f315ee","abstract_canon_sha256":"3bb7b2f8dffb1458003215c0796e3dca8698406f2ac690f4d32049e3e4977585"},"schema_version":"1.0"},"canonical_sha256":"033c44e477994a424d8e7b321bc8c6040756a81a5b033256667412fc90b0acc1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:43.260213Z","signature_b64":"PaHOmAxAAZJwfxODIw49HSD47R0393xtYgQfGhR4h73NJwuSbN49YGfVkl0bt7Zrz1ztzKobKOCVTKsqvGdMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"033c44e477994a424d8e7b321bc8c6040756a81a5b033256667412fc90b0acc1","last_reissued_at":"2026-05-18T02:50:43.259518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:43.259518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.3563","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"evsSYsGGVZjCAopplw5fj8oTCXgvzppi2nWkt3eokI+ukF+TyzFNn/ukonlK+IW2kjk0qGo/+gptyMyVMQ9PAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T11:25:19.460792Z"},"content_sha256":"c63f70761dd29ccd30fca91c6eb15bcbe5f0414e587e87a42d0e14a05e4e26e5","schema_version":"1.0","event_id":"sha256:c63f70761dd29ccd30fca91c6eb15bcbe5f0414e587e87a42d0e14a05e4e26e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AM6EJZDXTFFEETMOPMZBXSGGAQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jordan property for Cremona groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Constantin Shramov, Yuri Prokhorov","submitted_at":"2012-11-15T10:28:08Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3563","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WzqFL0dapbPCyEwvMobGnVSxNexMwJADaAt7lcKkIcTi6nlh0TJIBjgD8o40dHzDNs/fYVEojNPKuAw2ox8SCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T11:25:19.461375Z"},"content_sha256":"fb0aed80783e809dd9aa18168d11aed3b3e05145e0712a66e59ea52cdad198e2","schema_version":"1.0","event_id":"sha256:fb0aed80783e809dd9aa18168d11aed3b3e05145e0712a66e59ea52cdad198e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AM6EJZDXTFFEETMOPMZBXSGGAQ/bundle.json","state_url":"https://pith.science/pith/AM6EJZDXTFFEETMOPMZBXSGGAQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AM6EJZDXTFFEETMOPMZBXSGGAQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-24T11:25:19Z","links":{"resolver":"https://pith.science/pith/AM6EJZDXTFFEETMOPMZBXSGGAQ","bundle":"https://pith.science/pith/AM6EJZDXTFFEETMOPMZBXSGGAQ/bundle.json","state":"https://pith.science/pith/AM6EJZDXTFFEETMOPMZBXSGGAQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AM6EJZDXTFFEETMOPMZBXSGGAQ/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"titx5lw1h6gYKarO9MwV3NDmFvEUElj3PZTFTzUmjdoSkFy4l3j2RXXj3wizgyFgW8dMOnejpTCegc8nDPJxDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T11:25:19.465031Z","bundle_sha256":"00a40e2fbd989516f97c33f27fb77a67de5d724b44ef49d9a9890aae1506b66b"}}