{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:C523W4LO3WC7H6MJH3X6YXSCDJ","short_pith_number":"pith:C523W4LO","schema_version":"1.0","canonical_sha256":"1775bb716edd85f3f9893eefec5e421a56f9f88d1edd25adab7a1607ba23e507","source":{"kind":"arxiv","id":"0909.3485","version":2},"attestation_state":"computed","paper":{"title":"Homological perturbation theory for algebras over operads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Alexander Berglund","submitted_at":"2009-09-18T17:06:35Z","abstract_excerpt":"We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O. To solve this problem, we introduce what we call thick maps of O-algebras and special thick maps that we call pseudo-derivations, which serve as appropriate generalizations of algebra homotopies for the purposes of homological perturbation theory.\n  As an application, we derive explicit formulas for transferring Cobar(C)-algebra structures along contractions, where C is an"},"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":"0909.3485","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-18T17:06:35Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"37344e85bc0099c1f19bf559dedb2308c61f7f95eb8752686141582c5b7949d6","abstract_canon_sha256":"5935ab73d8f461f27472fc0678170bd09714ad1f9338fc5f8625fbe30764857f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:30.973023Z","signature_b64":"rZehWuUFok1pH5AnuX+5W3nwAMXevsVHhKOj+HT0R2Lx9BL70WWAa9Ndril/DNL+fr896s2YZmo7+sYLAG3eAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1775bb716edd85f3f9893eefec5e421a56f9f88d1edd25adab7a1607ba23e507","last_reissued_at":"2026-05-18T01:22:30.972522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:30.972522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Homological perturbation theory for algebras over operads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Alexander Berglund","submitted_at":"2009-09-18T17:06:35Z","abstract_excerpt":"We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O. To solve this problem, we introduce what we call thick maps of O-algebras and special thick maps that we call pseudo-derivations, which serve as appropriate generalizations of algebra homotopies for the purposes of homological perturbation theory.\n  As an application, we derive explicit formulas for transferring Cobar(C)-algebra structures along contractions, where C is an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3485","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":"0909.3485","created_at":"2026-05-18T01:22:30.972596+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.3485v2","created_at":"2026-05-18T01:22:30.972596+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.3485","created_at":"2026-05-18T01:22:30.972596+00:00"},{"alias_kind":"pith_short_12","alias_value":"C523W4LO3WC7","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"C523W4LO3WC7H6MJ","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"C523W4LO","created_at":"2026-05-18T12:25:58.837520+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/C523W4LO3WC7H6MJH3X6YXSCDJ","json":"https://pith.science/pith/C523W4LO3WC7H6MJH3X6YXSCDJ.json","graph_json":"https://pith.science/api/pith-number/C523W4LO3WC7H6MJH3X6YXSCDJ/graph.json","events_json":"https://pith.science/api/pith-number/C523W4LO3WC7H6MJH3X6YXSCDJ/events.json","paper":"https://pith.science/paper/C523W4LO"},"agent_actions":{"view_html":"https://pith.science/pith/C523W4LO3WC7H6MJH3X6YXSCDJ","download_json":"https://pith.science/pith/C523W4LO3WC7H6MJH3X6YXSCDJ.json","view_paper":"https://pith.science/paper/C523W4LO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.3485&json=true","fetch_graph":"https://pith.science/api/pith-number/C523W4LO3WC7H6MJH3X6YXSCDJ/graph.json","fetch_events":"https://pith.science/api/pith-number/C523W4LO3WC7H6MJH3X6YXSCDJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C523W4LO3WC7H6MJH3X6YXSCDJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C523W4LO3WC7H6MJH3X6YXSCDJ/action/storage_attestation","attest_author":"https://pith.science/pith/C523W4LO3WC7H6MJH3X6YXSCDJ/action/author_attestation","sign_citation":"https://pith.science/pith/C523W4LO3WC7H6MJH3X6YXSCDJ/action/citation_signature","submit_replication":"https://pith.science/pith/C523W4LO3WC7H6MJH3X6YXSCDJ/action/replication_record"}},"created_at":"2026-05-18T01:22:30.972596+00:00","updated_at":"2026-05-18T01:22:30.972596+00:00"}