{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:V3EQXIUILERLGY5UYKML7XDHYO","short_pith_number":"pith:V3EQXIUI","schema_version":"1.0","canonical_sha256":"aec90ba2885922b363b4c298bfdc67c3aaf18aec85825777db8e18451571b918","source":{"kind":"arxiv","id":"1810.03350","version":1},"attestation_state":"computed","paper":{"title":"A Hopf algebra without modular pair in involution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Sebastian Halbig, Ulrich Kraehmer","submitted_at":"2018-10-08T09:53:09Z","abstract_excerpt":"The aim of this short note is to communicate an example of a finite-dimensional Hopf algebra that does not admit a modular pair in involution in the sense of Connes and Moscovici."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.03350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-10-08T09:53:09Z","cross_cats_sorted":[],"title_canon_sha256":"3a4caa031988fb39394a9f089682d5c6c9f3bb6073c5aad55d1d875330d88606","abstract_canon_sha256":"ede44f2862b8e6e50d64676b66210f0f6bc48764f2ebe587e57dc9f0d127fbd1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:51.598374Z","signature_b64":"sNn4icwWzyYg3v+OaKFp4Lsna8gdt9fyvkbTs+RTmUBiD9oxAo8sd68hdJ37ZuHuap21nMMP/PT2QFkxtAAvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aec90ba2885922b363b4c298bfdc67c3aaf18aec85825777db8e18451571b918","last_reissued_at":"2026-05-18T00:03:51.597637Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:51.597637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Hopf algebra without modular pair in involution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Sebastian Halbig, Ulrich Kraehmer","submitted_at":"2018-10-08T09:53:09Z","abstract_excerpt":"The aim of this short note is to communicate an example of a finite-dimensional Hopf algebra that does not admit a modular pair in involution in the sense of Connes and Moscovici."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03350","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.03350","created_at":"2026-05-18T00:03:51.597760+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.03350v1","created_at":"2026-05-18T00:03:51.597760+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03350","created_at":"2026-05-18T00:03:51.597760+00:00"},{"alias_kind":"pith_short_12","alias_value":"V3EQXIUILERL","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"V3EQXIUILERLGY5U","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"V3EQXIUI","created_at":"2026-05-18T12:32:56.356000+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V3EQXIUILERLGY5UYKML7XDHYO","json":"https://pith.science/pith/V3EQXIUILERLGY5UYKML7XDHYO.json","graph_json":"https://pith.science/api/pith-number/V3EQXIUILERLGY5UYKML7XDHYO/graph.json","events_json":"https://pith.science/api/pith-number/V3EQXIUILERLGY5UYKML7XDHYO/events.json","paper":"https://pith.science/paper/V3EQXIUI"},"agent_actions":{"view_html":"https://pith.science/pith/V3EQXIUILERLGY5UYKML7XDHYO","download_json":"https://pith.science/pith/V3EQXIUILERLGY5UYKML7XDHYO.json","view_paper":"https://pith.science/paper/V3EQXIUI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.03350&json=true","fetch_graph":"https://pith.science/api/pith-number/V3EQXIUILERLGY5UYKML7XDHYO/graph.json","fetch_events":"https://pith.science/api/pith-number/V3EQXIUILERLGY5UYKML7XDHYO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V3EQXIUILERLGY5UYKML7XDHYO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V3EQXIUILERLGY5UYKML7XDHYO/action/storage_attestation","attest_author":"https://pith.science/pith/V3EQXIUILERLGY5UYKML7XDHYO/action/author_attestation","sign_citation":"https://pith.science/pith/V3EQXIUILERLGY5UYKML7XDHYO/action/citation_signature","submit_replication":"https://pith.science/pith/V3EQXIUILERLGY5UYKML7XDHYO/action/replication_record"}},"created_at":"2026-05-18T00:03:51.597760+00:00","updated_at":"2026-05-18T00:03:51.597760+00:00"}