{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:EQAJSVNNKDGGQCJFCU7AEB5AJE","short_pith_number":"pith:EQAJSVNN","schema_version":"1.0","canonical_sha256":"24009955ad50cc680925153e0207a04913b3a04ce07b4ba1609b1d1f664cead9","source":{"kind":"arxiv","id":"0810.3740","version":2},"attestation_state":"computed","paper":{"title":"Abstract integrals in algebra: coalgebras, Hopf algebras and compact groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Miodrag C. Iovanov","submitted_at":"2008-10-21T03:49:25Z","abstract_excerpt":"We generalize the results on existence and uniqueness of integrals from compact groups and Hopf algebras in a pure (co)algebraic setting, and find a series of new results on (quasi)-co-Frobenius and semiperfect coalgebras. For a coalgebra $C$, we introduce the generalized space of integrals $\\int_M=\\Hom^C(C,M)$ associated to a right $C$-comodule $M$ and study connections between \"uniqueness of integrals\" $\\dim(\\int_M)\\leq \\dim(M)$ and \"existence of integrals\" $\\dim(\\int_M)\\geq \\dim(M)$ for all $M$ and representation theoretic properties of $C$: (quasi)-co-Frobenius, semiperfect. We show that a"},"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":"0810.3740","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-10-21T03:49:25Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"76a57c3d8a43aa5991786121a48e85e1c1af9a88ac83fcbfeb388ec9bee129eb","abstract_canon_sha256":"416ba4775bf80ae3bb0a2fb95a0b1f923fb328a372c09e2ee89b256755b2ffa5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:45.045949Z","signature_b64":"shYQVUVY8MRVZXS8TuJPDgtty4GrYTZ2Pv321l4aJSyMV4/pgqHVxg4ThJnwkOt44/hLqAzU2b/0Xp+JDZ6mBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24009955ad50cc680925153e0207a04913b3a04ce07b4ba1609b1d1f664cead9","last_reissued_at":"2026-05-18T04:12:45.045383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:45.045383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Abstract integrals in algebra: coalgebras, Hopf algebras and compact groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Miodrag C. Iovanov","submitted_at":"2008-10-21T03:49:25Z","abstract_excerpt":"We generalize the results on existence and uniqueness of integrals from compact groups and Hopf algebras in a pure (co)algebraic setting, and find a series of new results on (quasi)-co-Frobenius and semiperfect coalgebras. For a coalgebra $C$, we introduce the generalized space of integrals $\\int_M=\\Hom^C(C,M)$ associated to a right $C$-comodule $M$ and study connections between \"uniqueness of integrals\" $\\dim(\\int_M)\\leq \\dim(M)$ and \"existence of integrals\" $\\dim(\\int_M)\\geq \\dim(M)$ for all $M$ and representation theoretic properties of $C$: (quasi)-co-Frobenius, semiperfect. We show that a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.3740","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":""},"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":"0810.3740","created_at":"2026-05-18T04:12:45.045473+00:00"},{"alias_kind":"arxiv_version","alias_value":"0810.3740v2","created_at":"2026-05-18T04:12:45.045473+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.3740","created_at":"2026-05-18T04:12:45.045473+00:00"},{"alias_kind":"pith_short_12","alias_value":"EQAJSVNNKDGG","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"EQAJSVNNKDGGQCJF","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"EQAJSVNN","created_at":"2026-05-18T12:25:57.157939+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/EQAJSVNNKDGGQCJFCU7AEB5AJE","json":"https://pith.science/pith/EQAJSVNNKDGGQCJFCU7AEB5AJE.json","graph_json":"https://pith.science/api/pith-number/EQAJSVNNKDGGQCJFCU7AEB5AJE/graph.json","events_json":"https://pith.science/api/pith-number/EQAJSVNNKDGGQCJFCU7AEB5AJE/events.json","paper":"https://pith.science/paper/EQAJSVNN"},"agent_actions":{"view_html":"https://pith.science/pith/EQAJSVNNKDGGQCJFCU7AEB5AJE","download_json":"https://pith.science/pith/EQAJSVNNKDGGQCJFCU7AEB5AJE.json","view_paper":"https://pith.science/paper/EQAJSVNN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0810.3740&json=true","fetch_graph":"https://pith.science/api/pith-number/EQAJSVNNKDGGQCJFCU7AEB5AJE/graph.json","fetch_events":"https://pith.science/api/pith-number/EQAJSVNNKDGGQCJFCU7AEB5AJE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EQAJSVNNKDGGQCJFCU7AEB5AJE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EQAJSVNNKDGGQCJFCU7AEB5AJE/action/storage_attestation","attest_author":"https://pith.science/pith/EQAJSVNNKDGGQCJFCU7AEB5AJE/action/author_attestation","sign_citation":"https://pith.science/pith/EQAJSVNNKDGGQCJFCU7AEB5AJE/action/citation_signature","submit_replication":"https://pith.science/pith/EQAJSVNNKDGGQCJFCU7AEB5AJE/action/replication_record"}},"created_at":"2026-05-18T04:12:45.045473+00:00","updated_at":"2026-05-18T04:12:45.045473+00:00"}