{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7YNOHTFG2RAJXVYZPEEEH2CRJU","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":"c72a2efa8a5692ef349ca8f8523645314b7439fae967ada3ef68371a0cb654cb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-09T18:35:49Z","title_canon_sha256":"2686225b22812a742b6e302cfaf9f0c8e3f854f332096f8f608f501e4704407f"},"schema_version":"1.0","source":{"id":"1304.2691","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2691","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2691v1","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2691","created_at":"2026-05-18T03:28:31Z"},{"alias_kind":"pith_short_12","alias_value":"7YNOHTFG2RAJ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7YNOHTFG2RAJXVYZ","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7YNOHTFG","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:9737fbb7c7689f168894e2e39f9b4804c6c43fa73a7ad80c15bc28495d27dc5a","target":"graph","created_at":"2026-05-18T03:28:31Z","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":"The Bogomolov multiplier of a finite group $G$ is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of $G$. This invariant of $G$ plays an important role in birational geometry of quotient spaces $V/G$. We show that in many cases the vanishing of the Bogomolov multiplier is guaranteed by the rigidity of $G$ in the sense that it has no outer class-preserving automorphisms.","authors_text":"Boris Kunyavskii, Ming-chang Kang","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-09T18:35:49Z","title":"The Bogomolov multiplier of rigid finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2691","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":"sha256:0118c5d9a893d44e23f4285ca2a58d9e0568d1c2e7905d37b96b37a1edb1952b","target":"record","created_at":"2026-05-18T03:28:31Z","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":"c72a2efa8a5692ef349ca8f8523645314b7439fae967ada3ef68371a0cb654cb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-04-09T18:35:49Z","title_canon_sha256":"2686225b22812a742b6e302cfaf9f0c8e3f854f332096f8f608f501e4704407f"},"schema_version":"1.0","source":{"id":"1304.2691","kind":"arxiv","version":1}},"canonical_sha256":"fe1ae3cca6d4409bd719790843e8514d39d62f4e40cf0151b37e6fc5a8fccb8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe1ae3cca6d4409bd719790843e8514d39d62f4e40cf0151b37e6fc5a8fccb8d","first_computed_at":"2026-05-18T03:28:31.056944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:31.056944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FCERgBn1z3X0zPnrZWI2KeJxfIkvmp9w3oqRhoLL6tAu/4Xzr8Wc4HExoNwVO7wnt5KKBjUE5646Lb1NDCYaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:31.057863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2691","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0118c5d9a893d44e23f4285ca2a58d9e0568d1c2e7905d37b96b37a1edb1952b","sha256:9737fbb7c7689f168894e2e39f9b4804c6c43fa73a7ad80c15bc28495d27dc5a"],"state_sha256":"8e43fc1f11492ceb969982105b12bf29682325af6c4feccdfa786d2fd9fd18e8"}