{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:Y253O7XN7ORAAD3MCQPUXM47CJ","short_pith_number":"pith:Y253O7XN","schema_version":"1.0","canonical_sha256":"c6bbb77eedfba2000f6c141f4bb39f124a640ffc85b149dadebc4bedb18903f5","source":{"kind":"arxiv","id":"1109.4850","version":1},"attestation_state":"computed","paper":{"title":"Distributivity versus associativity in the homology theory of algebraic structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Jozef H. Przytycki","submitted_at":"2011-09-22T15:38:50Z","abstract_excerpt":"While homology theory of associative structures, such as groups and rings, has been extensively studied in the past beginning with the work of Hopf, Eilenberg, and Hochschild, homology of non-associative distributive structures, such as quandles, were neglected until recently. Distributive structures have been studied for a long time. In 1880, C.S. Peirce emphasized the importance of (right) self-distributivity in algebraic structures. However, homology for these universal algebras was introduced only sixteen years ago by Fenn, Rourke, and Sanderson. We develop this theory in the historical co"},"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":"1109.4850","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2011-09-22T15:38:50Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"d8558890d15d7c7f437c365ac42de51d1b094a36ba695f90cf0865455b9546e2","abstract_canon_sha256":"a904fd86a30cd5170017e3f3711c1628dbf0120dbcf4a3a3e0cf1af61ead6e26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:32.793541Z","signature_b64":"3tjYctOhud4MWCLCJpq9Wbi4Xt7V76tyXlGHgZwrBhpQTo6fJI+7ENtRQz5fPh7HDLQF6p/bjkcJBez9NK7xDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6bbb77eedfba2000f6c141f4bb39f124a640ffc85b149dadebc4bedb18903f5","last_reissued_at":"2026-05-18T04:12:32.793055Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:32.793055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distributivity versus associativity in the homology theory of algebraic structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Jozef H. Przytycki","submitted_at":"2011-09-22T15:38:50Z","abstract_excerpt":"While homology theory of associative structures, such as groups and rings, has been extensively studied in the past beginning with the work of Hopf, Eilenberg, and Hochschild, homology of non-associative distributive structures, such as quandles, were neglected until recently. Distributive structures have been studied for a long time. In 1880, C.S. Peirce emphasized the importance of (right) self-distributivity in algebraic structures. However, homology for these universal algebras was introduced only sixteen years ago by Fenn, Rourke, and Sanderson. We develop this theory in the historical co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4850","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":"1109.4850","created_at":"2026-05-18T04:12:32.793129+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.4850v1","created_at":"2026-05-18T04:12:32.793129+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4850","created_at":"2026-05-18T04:12:32.793129+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y253O7XN7ORA","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y253O7XN7ORAAD3M","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y253O7XN","created_at":"2026-05-18T12:26:47.523578+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/Y253O7XN7ORAAD3MCQPUXM47CJ","json":"https://pith.science/pith/Y253O7XN7ORAAD3MCQPUXM47CJ.json","graph_json":"https://pith.science/api/pith-number/Y253O7XN7ORAAD3MCQPUXM47CJ/graph.json","events_json":"https://pith.science/api/pith-number/Y253O7XN7ORAAD3MCQPUXM47CJ/events.json","paper":"https://pith.science/paper/Y253O7XN"},"agent_actions":{"view_html":"https://pith.science/pith/Y253O7XN7ORAAD3MCQPUXM47CJ","download_json":"https://pith.science/pith/Y253O7XN7ORAAD3MCQPUXM47CJ.json","view_paper":"https://pith.science/paper/Y253O7XN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.4850&json=true","fetch_graph":"https://pith.science/api/pith-number/Y253O7XN7ORAAD3MCQPUXM47CJ/graph.json","fetch_events":"https://pith.science/api/pith-number/Y253O7XN7ORAAD3MCQPUXM47CJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y253O7XN7ORAAD3MCQPUXM47CJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y253O7XN7ORAAD3MCQPUXM47CJ/action/storage_attestation","attest_author":"https://pith.science/pith/Y253O7XN7ORAAD3MCQPUXM47CJ/action/author_attestation","sign_citation":"https://pith.science/pith/Y253O7XN7ORAAD3MCQPUXM47CJ/action/citation_signature","submit_replication":"https://pith.science/pith/Y253O7XN7ORAAD3MCQPUXM47CJ/action/replication_record"}},"created_at":"2026-05-18T04:12:32.793129+00:00","updated_at":"2026-05-18T04:12:32.793129+00:00"}