{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UBUGB4DRHKVYKNDSMS2F5E24UB","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":"b2d546b33000e98e3473df89b2a2a055851c0de4f50c1888fe9d665cd8ebd47f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-07-12T10:37:44Z","title_canon_sha256":"4f13a39944691ad790631221197f400a1ed59f67ae9c1d8ff2fd396003394169"},"schema_version":"1.0","source":{"id":"1107.2240","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2240","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2240v2","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2240","created_at":"2026-05-18T00:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"UBUGB4DRHKVY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UBUGB4DRHKVYKNDS","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UBUGB4DR","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:534c60744830fb982602132e9900bbaafcc630fd84128b7fb1907ab9d6c89a0f","target":"graph","created_at":"2026-05-18T00:22:07Z","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 compute the Hochschild cohomology algebras of Ringel-self-dual blocks of polynomial representations of $\\GL_2$ over an algebraically closed field of characteristic $p>2$, that is, of any block whose number of simple modules is a power of $p$. These algebras are finite-dimensional and we provide an explicit description of their bases and multiplications.","authors_text":"Vanessa Miemietz, Will Turner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-07-12T10:37:44Z","title":"Hochschild cohomology of polynomial representations of $GL_2(\\bar{\\mathbb{F}}_p)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2240","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":"sha256:4fbf3ba52092dcc854cbfb3d71a062384bbfad03084895632b6a2204f5f65adf","target":"record","created_at":"2026-05-18T00:22:07Z","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":"b2d546b33000e98e3473df89b2a2a055851c0de4f50c1888fe9d665cd8ebd47f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-07-12T10:37:44Z","title_canon_sha256":"4f13a39944691ad790631221197f400a1ed59f67ae9c1d8ff2fd396003394169"},"schema_version":"1.0","source":{"id":"1107.2240","kind":"arxiv","version":2}},"canonical_sha256":"a06860f0713aab85347264b45e935ca04e9e8ffe0bb9967730f6b7ae6352991a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a06860f0713aab85347264b45e935ca04e9e8ffe0bb9967730f6b7ae6352991a","first_computed_at":"2026-05-18T00:22:07.214121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:07.214121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ESaLC2ZPfpuIqBAR1XDqX0C5MY/DYDwzqaBHpeiluBFr1fHu70BF/Uh8IBeQ+SkN7hskOGYZI3XYt1OG2EVVDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:07.214742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2240","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fbf3ba52092dcc854cbfb3d71a062384bbfad03084895632b6a2204f5f65adf","sha256:534c60744830fb982602132e9900bbaafcc630fd84128b7fb1907ab9d6c89a0f"],"state_sha256":"be211a85dc44a3e910c1ab55fccd0c2cec6aba6ee24ccade6748f1e875685200"}