{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:T3DC6AQ32GDIZK4VHB564RXCJJ","short_pith_number":"pith:T3DC6AQ3","canonical_record":{"source":{"id":"1302.1769","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-02-07T14:58:09Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"eaa38a0b0872a25cfbcdd0f52f0eec38c0708341d1fa53b859fb859d006c441b","abstract_canon_sha256":"c688c1d5236dce374f2a5dabd69af6e20b9a4848191cab77dc92485bca0307f9"},"schema_version":"1.0"},"canonical_sha256":"9ec62f021bd1868cab95387bee46e24a5eda34f0d51b1b8fa8958294c370dc66","source":{"kind":"arxiv","id":"1302.1769","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1769","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1769v3","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1769","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"pith_short_12","alias_value":"T3DC6AQ32GDI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T3DC6AQ32GDIZK4V","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T3DC6AQ3","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:T3DC6AQ32GDIZK4VHB564RXCJJ","target":"record","payload":{"canonical_record":{"source":{"id":"1302.1769","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-02-07T14:58:09Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"eaa38a0b0872a25cfbcdd0f52f0eec38c0708341d1fa53b859fb859d006c441b","abstract_canon_sha256":"c688c1d5236dce374f2a5dabd69af6e20b9a4848191cab77dc92485bca0307f9"},"schema_version":"1.0"},"canonical_sha256":"9ec62f021bd1868cab95387bee46e24a5eda34f0d51b1b8fa8958294c370dc66","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:32.843076Z","signature_b64":"72uFt9UMEA1Ool/VR2YIoz8nOV3gbfd1JeFx+4SDENmC4S4cx8IaapVQeAbXyQxHOZZG08qhxVTurlmWqcZzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ec62f021bd1868cab95387bee46e24a5eda34f0d51b1b8fa8958294c370dc66","last_reissued_at":"2026-05-18T02:56:32.842436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:32.842436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.1769","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5mNRHNf/S8oCMB8UNPGzjudEIH9tLeqA5QJ/vQtTqQYx4neXIDGza3LF11jq/lHSkobWBQdVa+4VDkTs2CX4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:03:07.412069Z"},"content_sha256":"67220ef04e29f3362921bd52f94ccbab79a30aa5787c82644762872af7b449d5","schema_version":"1.0","event_id":"sha256:67220ef04e29f3362921bd52f94ccbab79a30aa5787c82644762872af7b449d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:T3DC6AQ32GDIZK4VHB564RXCJJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Christian Kassel","submitted_at":"2013-02-07T14:58:09Z","abstract_excerpt":"We define polynomial H-identities for comodule algebras over a Hopf algebra H and establish general properties for the corresponding T-ideals. In the case H is a Taft algebra or the Hopf algebra E(n), we exhibit a finite set of polynomial H-identities which distinguish the Galois objects over H up to isomorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1769","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w4IShAVH3fj0JmJq0fkCE9b6EFBzAple2+DJh0s26K4SbrXLXsdTknkwF4ix1mkgRViETsBxSfktXzzYHmYICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T01:03:07.412424Z"},"content_sha256":"dd6c33c96f3c447a5bfd843dc47f0df320452ad6acd40ae0849fc50adf4dd6b4","schema_version":"1.0","event_id":"sha256:dd6c33c96f3c447a5bfd843dc47f0df320452ad6acd40ae0849fc50adf4dd6b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3DC6AQ32GDIZK4VHB564RXCJJ/bundle.json","state_url":"https://pith.science/pith/T3DC6AQ32GDIZK4VHB564RXCJJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3DC6AQ32GDIZK4VHB564RXCJJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T01:03:07Z","links":{"resolver":"https://pith.science/pith/T3DC6AQ32GDIZK4VHB564RXCJJ","bundle":"https://pith.science/pith/T3DC6AQ32GDIZK4VHB564RXCJJ/bundle.json","state":"https://pith.science/pith/T3DC6AQ32GDIZK4VHB564RXCJJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3DC6AQ32GDIZK4VHB564RXCJJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T3DC6AQ32GDIZK4VHB564RXCJJ","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":"c688c1d5236dce374f2a5dabd69af6e20b9a4848191cab77dc92485bca0307f9","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-02-07T14:58:09Z","title_canon_sha256":"eaa38a0b0872a25cfbcdd0f52f0eec38c0708341d1fa53b859fb859d006c441b"},"schema_version":"1.0","source":{"id":"1302.1769","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1769","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1769v3","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1769","created_at":"2026-05-18T02:56:32Z"},{"alias_kind":"pith_short_12","alias_value":"T3DC6AQ32GDI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T3DC6AQ32GDIZK4V","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T3DC6AQ3","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:dd6c33c96f3c447a5bfd843dc47f0df320452ad6acd40ae0849fc50adf4dd6b4","target":"graph","created_at":"2026-05-18T02:56:32Z","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 define polynomial H-identities for comodule algebras over a Hopf algebra H and establish general properties for the corresponding T-ideals. In the case H is a Taft algebra or the Hopf algebra E(n), we exhibit a finite set of polynomial H-identities which distinguish the Galois objects over H up to isomorphism.","authors_text":"Christian Kassel","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-02-07T14:58:09Z","title":"Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1769","kind":"arxiv","version":3},"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":"sha256:67220ef04e29f3362921bd52f94ccbab79a30aa5787c82644762872af7b449d5","target":"record","created_at":"2026-05-18T02:56:32Z","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":"c688c1d5236dce374f2a5dabd69af6e20b9a4848191cab77dc92485bca0307f9","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-02-07T14:58:09Z","title_canon_sha256":"eaa38a0b0872a25cfbcdd0f52f0eec38c0708341d1fa53b859fb859d006c441b"},"schema_version":"1.0","source":{"id":"1302.1769","kind":"arxiv","version":3}},"canonical_sha256":"9ec62f021bd1868cab95387bee46e24a5eda34f0d51b1b8fa8958294c370dc66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ec62f021bd1868cab95387bee46e24a5eda34f0d51b1b8fa8958294c370dc66","first_computed_at":"2026-05-18T02:56:32.842436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:32.842436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"72uFt9UMEA1Ool/VR2YIoz8nOV3gbfd1JeFx+4SDENmC4S4cx8IaapVQeAbXyQxHOZZG08qhxVTurlmWqcZzBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:32.843076Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1769","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67220ef04e29f3362921bd52f94ccbab79a30aa5787c82644762872af7b449d5","sha256:dd6c33c96f3c447a5bfd843dc47f0df320452ad6acd40ae0849fc50adf4dd6b4"],"state_sha256":"7703291825b3722e21e4ee70f7b1adb646d42aca6aec0889f8c57765687591f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TM0PjLUQTAXIgja1OK3ummxfrJOpf40A3nloZNg2iYT3RSliYsy7bqdqOl1uEuJ+yeb3vzKHWSMPw4j57f8QAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T01:03:07.414259Z","bundle_sha256":"589100441c2ad680a905a0f5ddf6d86fe8de56c9a7b055a0f3e15798e62e686c"}}