{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YMTIZE75O6IMQHZWKYXZTSRUYD","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":"6a3f94c4dd506b9022ba5c790c2d56efc2e126ade1304c54dd489b95c2dfc5e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-29T20:21:18Z","title_canon_sha256":"2e5ddbd580d63e9a469e42fbbea6d79fbb4391482507ac80ea3754a023c5f4ee"},"schema_version":"1.0","source":{"id":"1810.12391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.12391","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1810.12391v1","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12391","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"YMTIZE75O6IM","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YMTIZE75O6IMQHZW","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YMTIZE75","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:b25a77caec12843ee36e04c0883fdd189c1b7a3ca6414b60f831ae223cd17559","target":"graph","created_at":"2026-05-18T00:02:02Z","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":"We study a family of affine varieties arising from a version of an old problem due to Birkhoff asking for the classification of embeddings of finite abelian p-groups. We show that all of these varieties are irreducible and have a dense orbit.","authors_text":"Grzegorz Bobinski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-29T20:21:18Z","title":"Algebras with irreducible module varieties III: Birkhoff varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12391","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":"sha256:865dce57667749247d6046bfd70150ed5c9ff3bc4aa09a24abaf44c28ff59cc5","target":"record","created_at":"2026-05-18T00:02:02Z","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":"6a3f94c4dd506b9022ba5c790c2d56efc2e126ade1304c54dd489b95c2dfc5e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-10-29T20:21:18Z","title_canon_sha256":"2e5ddbd580d63e9a469e42fbbea6d79fbb4391482507ac80ea3754a023c5f4ee"},"schema_version":"1.0","source":{"id":"1810.12391","kind":"arxiv","version":1}},"canonical_sha256":"c3268c93fd7790c81f36562f99ca34c0d75efddc55d2342562588a9ffc61b590","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3268c93fd7790c81f36562f99ca34c0d75efddc55d2342562588a9ffc61b590","first_computed_at":"2026-05-18T00:02:02.813571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:02.813571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LqX+cK7U/Vm3ycsOdWDEqcVE/K796zx7eJYuDsACDevIs+FDiFMW3o0eBft6zqD5yAcdY6RVcsqu332sV+b4CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:02.814057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.12391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:865dce57667749247d6046bfd70150ed5c9ff3bc4aa09a24abaf44c28ff59cc5","sha256:b25a77caec12843ee36e04c0883fdd189c1b7a3ca6414b60f831ae223cd17559"],"state_sha256":"bd4f99f2b03f34d0b5fd2d966f2bd05d36be404a2380deaa0abb6b9dae90f895"}