{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LAGZAWPQGLMBLTXWP5XX5T6CLC","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":"cdc41767494343b7b83bf54476ba4ef964ec7dd74588770dd02793429dd347c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-08T06:18:12Z","title_canon_sha256":"6e69e9478d91448bc22a454c505efea9c6841f5e533f61b288ebe127af3e5f7d"},"schema_version":"1.0","source":{"id":"1908.02942","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02942","created_at":"2026-07-05T00:11:21Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02942v2","created_at":"2026-07-05T00:11:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02942","created_at":"2026-07-05T00:11:21Z"},{"alias_kind":"pith_short_12","alias_value":"LAGZAWPQGLMB","created_at":"2026-07-05T00:11:21Z"},{"alias_kind":"pith_short_16","alias_value":"LAGZAWPQGLMBLTXW","created_at":"2026-07-05T00:11:21Z"},{"alias_kind":"pith_short_8","alias_value":"LAGZAWPQ","created_at":"2026-07-05T00:11:21Z"}],"graph_snapshots":[{"event_id":"sha256:32dd0faa743232638b65ed6cd837b1ef389e58f99ed218a66ee7bd9824418f7a","target":"graph","created_at":"2026-07-05T00:11:21Z","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/1908.02942/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we address the celebrated Albert problem for exceptional Jordan algebras (i.e. Albert algebras): Does every Albert division algebra contain a cubic cyclic subfield? We prove that for any Albert division algebra $A$ over a field $k$ of arbitrary characteristic, there is a suitable isotope that contains a cubic cyclic subfield. It follows from this that for any Albert division algebra $A$ over a field $k$, the structure group $\\text{\\bf Str}(A)$ always contains a subgroup of type $^3D_4$ defined over $k$.","authors_text":"Maneesh Thakur","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-08T06:18:12Z","title":"The cyclicity problem for Albert algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02942","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:a9f97afe21e6d5ddc7bcb720901a28dce69970efaf56a3fd996b44bc422f2bc7","target":"record","created_at":"2026-07-05T00:11:21Z","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":"cdc41767494343b7b83bf54476ba4ef964ec7dd74588770dd02793429dd347c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2019-08-08T06:18:12Z","title_canon_sha256":"6e69e9478d91448bc22a454c505efea9c6841f5e533f61b288ebe127af3e5f7d"},"schema_version":"1.0","source":{"id":"1908.02942","kind":"arxiv","version":2}},"canonical_sha256":"580d9059f032d815cef67f6f7ecfc25886c4f0a11f366881debf52553ad8d18f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"580d9059f032d815cef67f6f7ecfc25886c4f0a11f366881debf52553ad8d18f","first_computed_at":"2026-07-05T00:11:21.935626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:11:21.935626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"elH7RWPY4t0WJz49g5Ks7AE6ocp/LbTuZ6qGA+vJsJ3JYauuOm8URU5NcKZclzxFcj8xHjezPP2D0JixD4LoDA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:11:21.936053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.02942","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9f97afe21e6d5ddc7bcb720901a28dce69970efaf56a3fd996b44bc422f2bc7","sha256:32dd0faa743232638b65ed6cd837b1ef389e58f99ed218a66ee7bd9824418f7a"],"state_sha256":"4a0701d6c791c06a7a38b96bd93eb2024cbf986ecfd27ab501a8e8a2cb3b7e10"}