{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:32CLHJQS3SWBX3YXGP7XJOFDWM","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":"6a6e71011bebd9ffe2c3a7559f6e6e947db2b213e500dcbd0be971d4f27b178b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-11-11T07:47:23Z","title_canon_sha256":"5a1529eea68667a268b29e7444c7554854515daa51c32ddf7b220823d6fde3fe"},"schema_version":"1.0","source":{"id":"1011.2588","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2588","created_at":"2026-05-18T04:36:09Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2588v1","created_at":"2026-05-18T04:36:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2588","created_at":"2026-05-18T04:36:09Z"},{"alias_kind":"pith_short_12","alias_value":"32CLHJQS3SWB","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"32CLHJQS3SWBX3YX","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"32CLHJQS","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:79d0e4382da1d15d15ef80bc2a964e86b82ab96087a863539ad206b5a6f90fce","target":"graph","created_at":"2026-05-18T04:36:09Z","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":"In this paper we show that a certain algebra being a comodule algebra over the Taft Hopf algebra of dimension $n^2$ is equivalent to a set of identities related to the $q$-binomial coefficient, when $q$ is a primitive $n^{th}$ root of 1. We then give a direct combinatorial proof of these identities.","authors_text":"Andrea Jedwab, Susan Montgomery","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-11-11T07:47:23Z","title":"A $q$-Identity Related to a Comodule"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2588","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:e197a792559858c536b6204c571e9c10d598cb0365fc9b6ca2ee1f472a76dd7e","target":"record","created_at":"2026-05-18T04:36:09Z","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":"6a6e71011bebd9ffe2c3a7559f6e6e947db2b213e500dcbd0be971d4f27b178b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-11-11T07:47:23Z","title_canon_sha256":"5a1529eea68667a268b29e7444c7554854515daa51c32ddf7b220823d6fde3fe"},"schema_version":"1.0","source":{"id":"1011.2588","kind":"arxiv","version":1}},"canonical_sha256":"de84b3a612dcac1bef1733ff74b8a3b32efbbd0648fdbcd424d509df29fea2a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de84b3a612dcac1bef1733ff74b8a3b32efbbd0648fdbcd424d509df29fea2a5","first_computed_at":"2026-05-18T04:36:09.971114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:09.971114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Iu4niE3RZKShkV4JFAqSfB+9NL+GdnMqE7VHexUkSTqR8lYpHG5oG7WjCJTsLga90Sszb5T+Uj57BQAzEefLAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:09.971757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2588","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e197a792559858c536b6204c571e9c10d598cb0365fc9b6ca2ee1f472a76dd7e","sha256:79d0e4382da1d15d15ef80bc2a964e86b82ab96087a863539ad206b5a6f90fce"],"state_sha256":"a119b8f5b600955de8277278597a3d52cde2db876256836b4a121d93e5c40f73"}