{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:AEZ4OBRLJQ6P4IXA6YLOPWGV2A","short_pith_number":"pith:AEZ4OBRL","canonical_record":{"source":{"id":"2602.10850","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-02-11T13:36:15Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"7e89340781881cde67b02890823cb0423cf9df7c96f3414fb8fe68cac4bcf5c8","abstract_canon_sha256":"c75e277bb8d579cfe6c337785074bf52066da99bd737101175e92ec6c65a6010"},"schema_version":"1.0"},"canonical_sha256":"0133c7062b4c3cfe22e0f616e7d8d5d02b9b566af1e8d8c4c6039a673a085091","source":{"kind":"arxiv","id":"2602.10850","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.10850","created_at":"2026-06-12T01:09:22Z"},{"alias_kind":"arxiv_version","alias_value":"2602.10850v2","created_at":"2026-06-12T01:09:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.10850","created_at":"2026-06-12T01:09:22Z"},{"alias_kind":"pith_short_12","alias_value":"AEZ4OBRLJQ6P","created_at":"2026-06-12T01:09:22Z"},{"alias_kind":"pith_short_16","alias_value":"AEZ4OBRLJQ6P4IXA","created_at":"2026-06-12T01:09:22Z"},{"alias_kind":"pith_short_8","alias_value":"AEZ4OBRL","created_at":"2026-06-12T01:09:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:AEZ4OBRLJQ6P4IXA6YLOPWGV2A","target":"record","payload":{"canonical_record":{"source":{"id":"2602.10850","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-02-11T13:36:15Z","cross_cats_sorted":["math.QA","math.RT"],"title_canon_sha256":"7e89340781881cde67b02890823cb0423cf9df7c96f3414fb8fe68cac4bcf5c8","abstract_canon_sha256":"c75e277bb8d579cfe6c337785074bf52066da99bd737101175e92ec6c65a6010"},"schema_version":"1.0"},"canonical_sha256":"0133c7062b4c3cfe22e0f616e7d8d5d02b9b566af1e8d8c4c6039a673a085091","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:09:22.394732Z","signature_b64":"eU/Z7q5J6Mmj6OTslpfrlh4LNt3dIgrWsTUnJI6hlmGEMChpX8c7q6XcomIUuaQRm4MGrfA7UYgr9KSStjphAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0133c7062b4c3cfe22e0f616e7d8d5d02b9b566af1e8d8c4c6039a673a085091","last_reissued_at":"2026-06-12T01:09:22.393876Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:09:22.393876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.10850","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-12T01:09:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zotZdQ2vMBaTKhpJjT/Axbu+mouR9AShs5Y4y6khxE8HIS9E35tKW1/v/3vT91kSZYS1rz5LeNIvGsuJOvTnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:30:29.150770Z"},"content_sha256":"9ad86112ba1347d51c8ffb2c3c6e8798ba72b54e380acbf2959fc651cf11f752","schema_version":"1.0","event_id":"sha256:9ad86112ba1347d51c8ffb2c3c6e8798ba72b54e380acbf2959fc651cf11f752"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:AEZ4OBRLJQ6P4IXA6YLOPWGV2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iterated Hopf Ore Extensions over Group Rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Can Hatipo\\u{g}lu, Christian Lomp","submitted_at":"2026-02-11T13:36:15Z","abstract_excerpt":"We introduce and study a class of Hopf algebras $H(G, \\chi, \\eta, b, c, \\beta)$ which are two-step Ore extensions of a group algebra $\\mathbb{K}[G]$. This construction unifies and generalizes some known families of Hopf algebras such as generalized Taft algebras and Hopf algebras related to $\\mathfrak{sl}_2$ constructed by Wang, Wu, and Tan. We analyze the ring theoretical properties of these algebras and classify all finite dimensional simple modules over them. We also consider the tensor products of simple modules in the zero derivation case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.10850","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.10850/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-12T01:09:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"84BPfxbQkv+t3/7LKODv1FRJJyuzOo7rYpJ3fJOkkYajMGrfwrAJw2VMtDMHPuG5nFK89jgvJ8pvbDslHCKODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:30:29.151138Z"},"content_sha256":"364414a781df4595e8b52ff905d711974f504efca5df4528845b27fe1b591f52","schema_version":"1.0","event_id":"sha256:364414a781df4595e8b52ff905d711974f504efca5df4528845b27fe1b591f52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AEZ4OBRLJQ6P4IXA6YLOPWGV2A/bundle.json","state_url":"https://pith.science/pith/AEZ4OBRLJQ6P4IXA6YLOPWGV2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AEZ4OBRLJQ6P4IXA6YLOPWGV2A/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":"2026-06-20T18:30:29Z","links":{"resolver":"https://pith.science/pith/AEZ4OBRLJQ6P4IXA6YLOPWGV2A","bundle":"https://pith.science/pith/AEZ4OBRLJQ6P4IXA6YLOPWGV2A/bundle.json","state":"https://pith.science/pith/AEZ4OBRLJQ6P4IXA6YLOPWGV2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AEZ4OBRLJQ6P4IXA6YLOPWGV2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AEZ4OBRLJQ6P4IXA6YLOPWGV2A","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":"c75e277bb8d579cfe6c337785074bf52066da99bd737101175e92ec6c65a6010","cross_cats_sorted":["math.QA","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-02-11T13:36:15Z","title_canon_sha256":"7e89340781881cde67b02890823cb0423cf9df7c96f3414fb8fe68cac4bcf5c8"},"schema_version":"1.0","source":{"id":"2602.10850","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.10850","created_at":"2026-06-12T01:09:22Z"},{"alias_kind":"arxiv_version","alias_value":"2602.10850v2","created_at":"2026-06-12T01:09:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.10850","created_at":"2026-06-12T01:09:22Z"},{"alias_kind":"pith_short_12","alias_value":"AEZ4OBRLJQ6P","created_at":"2026-06-12T01:09:22Z"},{"alias_kind":"pith_short_16","alias_value":"AEZ4OBRLJQ6P4IXA","created_at":"2026-06-12T01:09:22Z"},{"alias_kind":"pith_short_8","alias_value":"AEZ4OBRL","created_at":"2026-06-12T01:09:22Z"}],"graph_snapshots":[{"event_id":"sha256:364414a781df4595e8b52ff905d711974f504efca5df4528845b27fe1b591f52","target":"graph","created_at":"2026-06-12T01:09:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2602.10850/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce and study a class of Hopf algebras $H(G, \\chi, \\eta, b, c, \\beta)$ which are two-step Ore extensions of a group algebra $\\mathbb{K}[G]$. This construction unifies and generalizes some known families of Hopf algebras such as generalized Taft algebras and Hopf algebras related to $\\mathfrak{sl}_2$ constructed by Wang, Wu, and Tan. We analyze the ring theoretical properties of these algebras and classify all finite dimensional simple modules over them. We also consider the tensor products of simple modules in the zero derivation case.","authors_text":"Can Hatipo\\u{g}lu, Christian Lomp","cross_cats":["math.QA","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-02-11T13:36:15Z","title":"Iterated Hopf Ore Extensions over Group Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.10850","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":"sha256:9ad86112ba1347d51c8ffb2c3c6e8798ba72b54e380acbf2959fc651cf11f752","target":"record","created_at":"2026-06-12T01:09:22Z","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":"c75e277bb8d579cfe6c337785074bf52066da99bd737101175e92ec6c65a6010","cross_cats_sorted":["math.QA","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-02-11T13:36:15Z","title_canon_sha256":"7e89340781881cde67b02890823cb0423cf9df7c96f3414fb8fe68cac4bcf5c8"},"schema_version":"1.0","source":{"id":"2602.10850","kind":"arxiv","version":2}},"canonical_sha256":"0133c7062b4c3cfe22e0f616e7d8d5d02b9b566af1e8d8c4c6039a673a085091","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0133c7062b4c3cfe22e0f616e7d8d5d02b9b566af1e8d8c4c6039a673a085091","first_computed_at":"2026-06-12T01:09:22.393876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:22.393876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eU/Z7q5J6Mmj6OTslpfrlh4LNt3dIgrWsTUnJI6hlmGEMChpX8c7q6XcomIUuaQRm4MGrfA7UYgr9KSStjphAQ==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:22.394732Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.10850","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ad86112ba1347d51c8ffb2c3c6e8798ba72b54e380acbf2959fc651cf11f752","sha256:364414a781df4595e8b52ff905d711974f504efca5df4528845b27fe1b591f52"],"state_sha256":"4ba98962e9b82e570cf2aed2b01355af307953e32565160849baad515531fb9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nutg4LOHvCD9PVAjQ6VydRR7UEDVHP48+kR73vIakAnsbvEnQZtTCHDxnLVEwDFnO4oOUfxS56faO156RpfJCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T18:30:29.153042Z","bundle_sha256":"f9d27f2dd8682bde0cd46cb65cdc5d68c1174f5b38ce8adce51a4493e11dfae8"}}