{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:C73DWHFWMR7TLAMPVGIJGX65WO","short_pith_number":"pith:C73DWHFW","canonical_record":{"source":{"id":"2505.00645","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-05-01T16:35:47Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"a8746a239000a8a64d6fd62f3aa5ae3438a4a22ca313596033f054efb3b11a4d","abstract_canon_sha256":"0f83fb8bdb7acd4d9ae3f4f7cb0b65e1df1034b0eb3a11a9ef8fae346ba6ba3e"},"schema_version":"1.0"},"canonical_sha256":"17f63b1cb6647f35818fa990935fddb390831e7d41f9746916e286cc5d836ae1","source":{"kind":"arxiv","id":"2505.00645","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.00645","created_at":"2026-06-04T01:08:28Z"},{"alias_kind":"arxiv_version","alias_value":"2505.00645v2","created_at":"2026-06-04T01:08:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.00645","created_at":"2026-06-04T01:08:28Z"},{"alias_kind":"pith_short_12","alias_value":"C73DWHFWMR7T","created_at":"2026-06-04T01:08:28Z"},{"alias_kind":"pith_short_16","alias_value":"C73DWHFWMR7TLAMP","created_at":"2026-06-04T01:08:28Z"},{"alias_kind":"pith_short_8","alias_value":"C73DWHFW","created_at":"2026-06-04T01:08:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:C73DWHFWMR7TLAMPVGIJGX65WO","target":"record","payload":{"canonical_record":{"source":{"id":"2505.00645","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-05-01T16:35:47Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"a8746a239000a8a64d6fd62f3aa5ae3438a4a22ca313596033f054efb3b11a4d","abstract_canon_sha256":"0f83fb8bdb7acd4d9ae3f4f7cb0b65e1df1034b0eb3a11a9ef8fae346ba6ba3e"},"schema_version":"1.0"},"canonical_sha256":"17f63b1cb6647f35818fa990935fddb390831e7d41f9746916e286cc5d836ae1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:08:28.914643Z","signature_b64":"m9SIpPQlb8v11OXLa08UF7qlUor/kDIoi9ETsvF+t1K+EZgHCFPR/uhfArNhfmhkrxLllcqAmB7niFUPfmpTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17f63b1cb6647f35818fa990935fddb390831e7d41f9746916e286cc5d836ae1","last_reissued_at":"2026-06-04T01:08:28.914081Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:08:28.914081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.00645","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":"2026-06-04T01:08:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j1v32fjbP7cvriJ0JQf2ahVdUzdF0m/LtNeHU+4VT+WRXdRgw0Qw1GJMFNvMC9xascjOlF0JGGF2o4By76unCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:25:35.387742Z"},"content_sha256":"9241a49362efa524fc17b2adb85b79cf28e9f53b5f2847e0d6efedce49600b0b","schema_version":"1.0","event_id":"sha256:9241a49362efa524fc17b2adb85b79cf28e9f53b5f2847e0d6efedce49600b0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:C73DWHFWMR7TLAMPVGIJGX65WO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Kac-Paljutkin algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Christian Lomp","submitted_at":"2025-05-01T16:35:47Z","abstract_excerpt":"In this note, we construct a family of semisimple Hopf algebras $H_{n,m}$ of dimension $n^m m!$ over a field of characteristic zero containing a primitive $n$th root of unity, where $n, m \\geq 2$ are integers. The well-known eight-dimensional Kac--Paljutkin algebra arises as the special case $H_{2,2}$, while the Hopf algebras previously constructed by Pansera correspond to the instances $H_{n,2}$. Each algebra $H_{n,m}$ is defined as an extension of the group algebra $\\mathbb{K} \\Sigma_m$ of the symmetric group by the $m$-fold tensor product $R = \\mathbb{K} \\mathbb{Z}_n^{\\otimes m}$, where $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00645","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/2505.00645/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":"2026-06-04T01:08:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"59LjgS09PeQQ83JlVdvv+8IkJ+ukvZTGeT1Ft85voQxXR9dD1zGoxSg9L699rExjEkF1KeVg99yyU7fRlioEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:25:35.388119Z"},"content_sha256":"2d36cd10e95b8bcb09da45b76293fe1a9d2370c4df2faa0c78bfa7d2e18d0a42","schema_version":"1.0","event_id":"sha256:2d36cd10e95b8bcb09da45b76293fe1a9d2370c4df2faa0c78bfa7d2e18d0a42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C73DWHFWMR7TLAMPVGIJGX65WO/bundle.json","state_url":"https://pith.science/pith/C73DWHFWMR7TLAMPVGIJGX65WO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C73DWHFWMR7TLAMPVGIJGX65WO/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":"2026-06-21T02:25:35Z","links":{"resolver":"https://pith.science/pith/C73DWHFWMR7TLAMPVGIJGX65WO","bundle":"https://pith.science/pith/C73DWHFWMR7TLAMPVGIJGX65WO/bundle.json","state":"https://pith.science/pith/C73DWHFWMR7TLAMPVGIJGX65WO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C73DWHFWMR7TLAMPVGIJGX65WO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:C73DWHFWMR7TLAMPVGIJGX65WO","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":"0f83fb8bdb7acd4d9ae3f4f7cb0b65e1df1034b0eb3a11a9ef8fae346ba6ba3e","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-05-01T16:35:47Z","title_canon_sha256":"a8746a239000a8a64d6fd62f3aa5ae3438a4a22ca313596033f054efb3b11a4d"},"schema_version":"1.0","source":{"id":"2505.00645","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.00645","created_at":"2026-06-04T01:08:28Z"},{"alias_kind":"arxiv_version","alias_value":"2505.00645v2","created_at":"2026-06-04T01:08:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.00645","created_at":"2026-06-04T01:08:28Z"},{"alias_kind":"pith_short_12","alias_value":"C73DWHFWMR7T","created_at":"2026-06-04T01:08:28Z"},{"alias_kind":"pith_short_16","alias_value":"C73DWHFWMR7TLAMP","created_at":"2026-06-04T01:08:28Z"},{"alias_kind":"pith_short_8","alias_value":"C73DWHFW","created_at":"2026-06-04T01:08:28Z"}],"graph_snapshots":[{"event_id":"sha256:2d36cd10e95b8bcb09da45b76293fe1a9d2370c4df2faa0c78bfa7d2e18d0a42","target":"graph","created_at":"2026-06-04T01:08:28Z","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/2505.00645/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note, we construct a family of semisimple Hopf algebras $H_{n,m}$ of dimension $n^m m!$ over a field of characteristic zero containing a primitive $n$th root of unity, where $n, m \\geq 2$ are integers. The well-known eight-dimensional Kac--Paljutkin algebra arises as the special case $H_{2,2}$, while the Hopf algebras previously constructed by Pansera correspond to the instances $H_{n,2}$. Each algebra $H_{n,m}$ is defined as an extension of the group algebra $\\mathbb{K} \\Sigma_m$ of the symmetric group by the $m$-fold tensor product $R = \\mathbb{K} \\mathbb{Z}_n^{\\otimes m}$, where $\\m","authors_text":"Christian Lomp","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-05-01T16:35:47Z","title":"Generalized Kac-Paljutkin algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.00645","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":"sha256:9241a49362efa524fc17b2adb85b79cf28e9f53b5f2847e0d6efedce49600b0b","target":"record","created_at":"2026-06-04T01:08:28Z","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":"0f83fb8bdb7acd4d9ae3f4f7cb0b65e1df1034b0eb3a11a9ef8fae346ba6ba3e","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-05-01T16:35:47Z","title_canon_sha256":"a8746a239000a8a64d6fd62f3aa5ae3438a4a22ca313596033f054efb3b11a4d"},"schema_version":"1.0","source":{"id":"2505.00645","kind":"arxiv","version":2}},"canonical_sha256":"17f63b1cb6647f35818fa990935fddb390831e7d41f9746916e286cc5d836ae1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17f63b1cb6647f35818fa990935fddb390831e7d41f9746916e286cc5d836ae1","first_computed_at":"2026-06-04T01:08:28.914081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:08:28.914081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m9SIpPQlb8v11OXLa08UF7qlUor/kDIoi9ETsvF+t1K+EZgHCFPR/uhfArNhfmhkrxLllcqAmB7niFUPfmpTDw==","signature_status":"signed_v1","signed_at":"2026-06-04T01:08:28.914643Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.00645","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9241a49362efa524fc17b2adb85b79cf28e9f53b5f2847e0d6efedce49600b0b","sha256:2d36cd10e95b8bcb09da45b76293fe1a9d2370c4df2faa0c78bfa7d2e18d0a42"],"state_sha256":"785924de62efc4d1761a82170b2779b7484e5031362c18855aea8e8e955443ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HaPPTw4UAauVDkkHfezz7s5wHzCOO1Rh3wzmacD93jrb8mHEv4Y2HI4wLATmUJ6WTAYOjtKD2O58bvX/4d/SAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T02:25:35.390163Z","bundle_sha256":"bfc635436fa63fde93e1fc37f8294f46b6707847ada09c42b80633e80f854e41"}}