{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KNH5CNNJPHC3LQ5F7KZI4W6S46","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":"34b819a6230741920c0f71393e197c6ab9240c7da61fe1e01f235ca318f71270","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-05-07T09:22:52Z","title_canon_sha256":"6dac4c2613696d3d2358eec512d902acbdf30df1c2ac3cffa3170367043c4e2f"},"schema_version":"1.0","source":{"id":"1305.1444","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1444","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1444v6","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1444","created_at":"2026-05-18T02:41:10Z"},{"alias_kind":"pith_short_12","alias_value":"KNH5CNNJPHC3","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KNH5CNNJPHC3LQ5F","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KNH5CNNJ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:55ef6d5089400dce20727ca42a4cad0610331eebbe6d3ded4435052cdd12f58c","target":"graph","created_at":"2026-05-18T02:41:10Z","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 the paper, the representation rings (or the Green rings) for a family of Hopf algebras of tame type, the 2-rank Taft algebra (at $q=-1$) and its two relatives twisted by 2-cocycles are explicitly described via a representation theoretic analysis. It turns out that the Green rings can serve to detect effectively the twist-equivalent Hopf algebras here.","authors_text":"Naihong Hu, Yunnan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-05-07T09:22:52Z","title":"The Green rings of the 2-rank Taft algebra and its two relatives twisted"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1444","kind":"arxiv","version":6},"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":"sha256:366365ea8510d7c9a9b76d1755020e9e6047a6aab7b6ec61babb012c8f1dc4ec","target":"record","created_at":"2026-05-18T02:41:10Z","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":"34b819a6230741920c0f71393e197c6ab9240c7da61fe1e01f235ca318f71270","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-05-07T09:22:52Z","title_canon_sha256":"6dac4c2613696d3d2358eec512d902acbdf30df1c2ac3cffa3170367043c4e2f"},"schema_version":"1.0","source":{"id":"1305.1444","kind":"arxiv","version":6}},"canonical_sha256":"534fd135a979c5b5c3a5fab28e5bd2e798d28d3df022b546c2552828ee17233d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"534fd135a979c5b5c3a5fab28e5bd2e798d28d3df022b546c2552828ee17233d","first_computed_at":"2026-05-18T02:41:10.317367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:10.317367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EPSf96mKIVYI48kO5Z8iinU/PvyOQ9IqAPsEVRP0SoWB7vsVYgf+JFGbbc13KObcR8bxERc2+kFDFZWUoXQ7DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:10.317758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1444","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:366365ea8510d7c9a9b76d1755020e9e6047a6aab7b6ec61babb012c8f1dc4ec","sha256:55ef6d5089400dce20727ca42a4cad0610331eebbe6d3ded4435052cdd12f58c"],"state_sha256":"70f92fd7bae1fc364d4931fc66d51d0af73ba6ba432011bc3a14dbfb25d5ec2a"}