{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:K6356VXH2FXUR6P5XET2Q32H2T","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":"b7d1df93a52ab2b2aa6b3e6b9f8660b39bee62ca3bac0b03ab68e9a4cf65e877","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-10-12T18:14:01Z","title_canon_sha256":"7bb553a4d7b71d9f4ef67b508b2a964df2171e37f7ea5c693db3ab7b77026408"},"schema_version":"1.0","source":{"id":"1610.03810","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03810","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03810v2","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03810","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"K6356VXH2FXU","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"K6356VXH2FXUR6P5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"K6356VXH","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:214b5d7db05d36b89a3f9fbf6b7ce4f7ea063fba988da26c546e17562c17a9a9","target":"graph","created_at":"2026-05-18T00:41:58Z","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":"Let $p$ and $q$ be distinct prime numbers. We study the Galois objects and cocycle deformations of the noncommutative, noncocommutative, semisimple Hopf algebras of odd dimension $p^3$ and of dimension $pq^2$. We obtain that the $p+1$ non-isomorphic self-dual semisimple Hopf algebras of dimension $p^3$ classified by Masuoka have no non-trivial cocycle deformations, extending his previous results for the 8-dimensional Kac-Paljutkin Hopf algebra. This is done as a consequence of the classification of categorical Morita equivalence classes among semisimple Hopf algebras of odd dimension $p^3$, es","authors_text":"Adriana Mej\\'ia Casta\\~no, Chelsea Walton, Maria D. Vega, Sonia Natale, Susan Montgomery","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-10-12T18:14:01Z","title":"Cocycle deformations and Galois objects for semisimple Hopf algebras of dimension $p^3$ and $pq^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03810","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:c95c7b63e2cff5d5e767404ecb37ed17d056f18d9a385546a8eb7fbcf8045dec","target":"record","created_at":"2026-05-18T00:41:58Z","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":"b7d1df93a52ab2b2aa6b3e6b9f8660b39bee62ca3bac0b03ab68e9a4cf65e877","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-10-12T18:14:01Z","title_canon_sha256":"7bb553a4d7b71d9f4ef67b508b2a964df2171e37f7ea5c693db3ab7b77026408"},"schema_version":"1.0","source":{"id":"1610.03810","kind":"arxiv","version":2}},"canonical_sha256":"57b7df56e7d16f48f9fdb927a86f47d4e734e40888c446a4c3bab4e6b4d56d85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57b7df56e7d16f48f9fdb927a86f47d4e734e40888c446a4c3bab4e6b4d56d85","first_computed_at":"2026-05-18T00:41:58.211348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:58.211348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ov5pfeg1eVN2FAnZElcCrWDu6nS04F4Elj6VCYViAJwIzVNxk1FRv+ypnrEUP0N4LmraRf03eHycrHzUp3LoDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:58.212133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03810","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c95c7b63e2cff5d5e767404ecb37ed17d056f18d9a385546a8eb7fbcf8045dec","sha256:214b5d7db05d36b89a3f9fbf6b7ce4f7ea063fba988da26c546e17562c17a9a9"],"state_sha256":"efa605b68c49ec10a597cc8bc4c7a476dd606596088ff9b9118e6751846343b2"}