{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WJLK7K5PNR2YMVVIAJQCDOM2AQ","short_pith_number":"pith:WJLK7K5P","schema_version":"1.0","canonical_sha256":"b256afabaf6c758656a8026021b99a041c45e1773280005733899c384482afc9","source":{"kind":"arxiv","id":"1901.07855","version":2},"attestation_state":"computed","paper":{"title":"On faithfully balanced modules, F-cotilting and F-Auslander algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Biao Ma, Julia Sauter","submitted_at":"2019-01-23T13:00:40Z","abstract_excerpt":"We revisit faithfully balanced modules. These are faithful modules having the double centralizer property. For finite-dimensional algebras our main tool is the category ${\\rm cogen}^1(M)$ of modules with a copresentation by summands of finite sums of $M$ on which ${\\rm Hom}(-,M)$ is exact. For a faithfully balanced module $M$ the functor ${\\rm Hom}(-,M)$ is a duality on these categories - for cotilting modules this is the Brenner-Butler theorem. We also study new classes of faithfully balanced modules combining cogenerators and cotilting modules. Then we turn to relative homological algebra in"},"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":"1901.07855","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-01-23T13:00:40Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"a0598e25c11ae262883486025f6a1c99a98bfc3b87c06bdd1d3db10a0a9a6b61","abstract_canon_sha256":"67eb8fcd9024d2188008063ee8ff87b50939f6239a84d85ecb790e0929441f4c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:42.681951Z","signature_b64":"mFsWkPya+ePjHk9ra/02BBb7Hold+L2eFIe0JQP5Q/qLxLt6978KomWHkJbrlwB+2wgJE6JkvtR+BuS7x/VXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b256afabaf6c758656a8026021b99a041c45e1773280005733899c384482afc9","last_reissued_at":"2026-05-17T23:43:42.681212Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:42.681212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On faithfully balanced modules, F-cotilting and F-Auslander algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Biao Ma, Julia Sauter","submitted_at":"2019-01-23T13:00:40Z","abstract_excerpt":"We revisit faithfully balanced modules. These are faithful modules having the double centralizer property. For finite-dimensional algebras our main tool is the category ${\\rm cogen}^1(M)$ of modules with a copresentation by summands of finite sums of $M$ on which ${\\rm Hom}(-,M)$ is exact. For a faithfully balanced module $M$ the functor ${\\rm Hom}(-,M)$ is a duality on these categories - for cotilting modules this is the Brenner-Butler theorem. We also study new classes of faithfully balanced modules combining cogenerators and cotilting modules. Then we turn to relative homological algebra in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07855","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":"1901.07855","created_at":"2026-05-17T23:43:42.681327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.07855v2","created_at":"2026-05-17T23:43:42.681327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07855","created_at":"2026-05-17T23:43:42.681327+00:00"},{"alias_kind":"pith_short_12","alias_value":"WJLK7K5PNR2Y","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"WJLK7K5PNR2YMVVI","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"WJLK7K5P","created_at":"2026-05-18T12:33:30.264802+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/WJLK7K5PNR2YMVVIAJQCDOM2AQ","json":"https://pith.science/pith/WJLK7K5PNR2YMVVIAJQCDOM2AQ.json","graph_json":"https://pith.science/api/pith-number/WJLK7K5PNR2YMVVIAJQCDOM2AQ/graph.json","events_json":"https://pith.science/api/pith-number/WJLK7K5PNR2YMVVIAJQCDOM2AQ/events.json","paper":"https://pith.science/paper/WJLK7K5P"},"agent_actions":{"view_html":"https://pith.science/pith/WJLK7K5PNR2YMVVIAJQCDOM2AQ","download_json":"https://pith.science/pith/WJLK7K5PNR2YMVVIAJQCDOM2AQ.json","view_paper":"https://pith.science/paper/WJLK7K5P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.07855&json=true","fetch_graph":"https://pith.science/api/pith-number/WJLK7K5PNR2YMVVIAJQCDOM2AQ/graph.json","fetch_events":"https://pith.science/api/pith-number/WJLK7K5PNR2YMVVIAJQCDOM2AQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WJLK7K5PNR2YMVVIAJQCDOM2AQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WJLK7K5PNR2YMVVIAJQCDOM2AQ/action/storage_attestation","attest_author":"https://pith.science/pith/WJLK7K5PNR2YMVVIAJQCDOM2AQ/action/author_attestation","sign_citation":"https://pith.science/pith/WJLK7K5PNR2YMVVIAJQCDOM2AQ/action/citation_signature","submit_replication":"https://pith.science/pith/WJLK7K5PNR2YMVVIAJQCDOM2AQ/action/replication_record"}},"created_at":"2026-05-17T23:43:42.681327+00:00","updated_at":"2026-05-17T23:43:42.681327+00:00"}