{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:4L2CKY6ODZHTC6TQJK2XQFKXC3","short_pith_number":"pith:4L2CKY6O","schema_version":"1.0","canonical_sha256":"e2f42563ce1e4f317a704ab578155716fef96d2447247a2e13c3f90136ae1926","source":{"kind":"arxiv","id":"1311.7681","version":1},"attestation_state":"computed","paper":{"title":"Bar and cobar constructions for curved algebras and coalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.KT","authors_text":"Volodymyr Lyubashenko","submitted_at":"2013-11-29T20:11:26Z","abstract_excerpt":"We provide bar and cobar constructions as functors between some categories of curved algebras and curved augmented coalgebras over a graded commutative ring. These functors are adjoint to each other."},"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":"1311.7681","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-11-29T20:11:26Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"986023958cdf38148222b57aa7e7fae51135480d21f52a8b5bd6ee91cbd18f85","abstract_canon_sha256":"89d78a08c5ba906877642e10e7a3607ea8d179574c1e463715d3e4f5afda477b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:34.044553Z","signature_b64":"juaQmQr2Y51nIwEnjnkJU7qVzIrYhjexnC9VrCVjw6NgxNDo3a1gr89fqIvto6W07xs38sa9eKgXZ4YpWssXDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2f42563ce1e4f317a704ab578155716fef96d2447247a2e13c3f90136ae1926","last_reissued_at":"2026-05-18T02:59:34.043695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:34.043695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bar and cobar constructions for curved algebras and coalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.KT","authors_text":"Volodymyr Lyubashenko","submitted_at":"2013-11-29T20:11:26Z","abstract_excerpt":"We provide bar and cobar constructions as functors between some categories of curved algebras and curved augmented coalgebras over a graded commutative ring. These functors are adjoint to each other."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7681","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":"1311.7681","created_at":"2026-05-18T02:59:34.043837+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.7681v1","created_at":"2026-05-18T02:59:34.043837+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7681","created_at":"2026-05-18T02:59:34.043837+00:00"},{"alias_kind":"pith_short_12","alias_value":"4L2CKY6ODZHT","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"4L2CKY6ODZHTC6TQ","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"4L2CKY6O","created_at":"2026-05-18T12:27:34.582898+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/4L2CKY6ODZHTC6TQJK2XQFKXC3","json":"https://pith.science/pith/4L2CKY6ODZHTC6TQJK2XQFKXC3.json","graph_json":"https://pith.science/api/pith-number/4L2CKY6ODZHTC6TQJK2XQFKXC3/graph.json","events_json":"https://pith.science/api/pith-number/4L2CKY6ODZHTC6TQJK2XQFKXC3/events.json","paper":"https://pith.science/paper/4L2CKY6O"},"agent_actions":{"view_html":"https://pith.science/pith/4L2CKY6ODZHTC6TQJK2XQFKXC3","download_json":"https://pith.science/pith/4L2CKY6ODZHTC6TQJK2XQFKXC3.json","view_paper":"https://pith.science/paper/4L2CKY6O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.7681&json=true","fetch_graph":"https://pith.science/api/pith-number/4L2CKY6ODZHTC6TQJK2XQFKXC3/graph.json","fetch_events":"https://pith.science/api/pith-number/4L2CKY6ODZHTC6TQJK2XQFKXC3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4L2CKY6ODZHTC6TQJK2XQFKXC3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4L2CKY6ODZHTC6TQJK2XQFKXC3/action/storage_attestation","attest_author":"https://pith.science/pith/4L2CKY6ODZHTC6TQJK2XQFKXC3/action/author_attestation","sign_citation":"https://pith.science/pith/4L2CKY6ODZHTC6TQJK2XQFKXC3/action/citation_signature","submit_replication":"https://pith.science/pith/4L2CKY6ODZHTC6TQJK2XQFKXC3/action/replication_record"}},"created_at":"2026-05-18T02:59:34.043837+00:00","updated_at":"2026-05-18T02:59:34.043837+00:00"}