{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NLXN67CEPPRXFFY7ZMX4X7TYYT","short_pith_number":"pith:NLXN67CE","schema_version":"1.0","canonical_sha256":"6aeedf7c447be372971fcb2fcbfe78c4c0b2304437a050b69b89d351f64c8079","source":{"kind":"arxiv","id":"1701.01374","version":3},"attestation_state":"computed","paper":{"title":"Six operations formalism for generalized operads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Benjamin C. Ward","submitted_at":"2017-01-05T16:41:52Z","abstract_excerpt":"This paper shows that generalizations of operads equipped with their respective bar/cobar dualities are related by a six operations formalism analogous to that of classical contexts in algebraic geometry. As a consequence of our constructions, we prove intertwining theorems which govern derived Koszul duality of push-forwards and pull-backs."},"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":"1701.01374","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-01-05T16:41:52Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"64895d0f91086c113f0cec1a7efe957a7c7808b83580fc7b133f1f8b5a8b7f44","abstract_canon_sha256":"df5443d50269cde61be5cad9a56eae18dcfe6fcaafbfe05635055fa8704af334"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:59.896252Z","signature_b64":"r4Mlvn7OgFBZG8si3OZa2XFUe4zQmRWFSA8JBfCx219KtSOu64AQBux0yt3fA+yEz4odKSbRACy37TVoahHIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6aeedf7c447be372971fcb2fcbfe78c4c0b2304437a050b69b89d351f64c8079","last_reissued_at":"2026-05-17T23:49:59.895817Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:59.895817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Six operations formalism for generalized operads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Benjamin C. Ward","submitted_at":"2017-01-05T16:41:52Z","abstract_excerpt":"This paper shows that generalizations of operads equipped with their respective bar/cobar dualities are related by a six operations formalism analogous to that of classical contexts in algebraic geometry. As a consequence of our constructions, we prove intertwining theorems which govern derived Koszul duality of push-forwards and pull-backs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01374","kind":"arxiv","version":3},"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":"1701.01374","created_at":"2026-05-17T23:49:59.895880+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.01374v3","created_at":"2026-05-17T23:49:59.895880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01374","created_at":"2026-05-17T23:49:59.895880+00:00"},{"alias_kind":"pith_short_12","alias_value":"NLXN67CEPPRX","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"NLXN67CEPPRXFFY7","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"NLXN67CE","created_at":"2026-05-18T12:31:31.346846+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/NLXN67CEPPRXFFY7ZMX4X7TYYT","json":"https://pith.science/pith/NLXN67CEPPRXFFY7ZMX4X7TYYT.json","graph_json":"https://pith.science/api/pith-number/NLXN67CEPPRXFFY7ZMX4X7TYYT/graph.json","events_json":"https://pith.science/api/pith-number/NLXN67CEPPRXFFY7ZMX4X7TYYT/events.json","paper":"https://pith.science/paper/NLXN67CE"},"agent_actions":{"view_html":"https://pith.science/pith/NLXN67CEPPRXFFY7ZMX4X7TYYT","download_json":"https://pith.science/pith/NLXN67CEPPRXFFY7ZMX4X7TYYT.json","view_paper":"https://pith.science/paper/NLXN67CE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.01374&json=true","fetch_graph":"https://pith.science/api/pith-number/NLXN67CEPPRXFFY7ZMX4X7TYYT/graph.json","fetch_events":"https://pith.science/api/pith-number/NLXN67CEPPRXFFY7ZMX4X7TYYT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NLXN67CEPPRXFFY7ZMX4X7TYYT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NLXN67CEPPRXFFY7ZMX4X7TYYT/action/storage_attestation","attest_author":"https://pith.science/pith/NLXN67CEPPRXFFY7ZMX4X7TYYT/action/author_attestation","sign_citation":"https://pith.science/pith/NLXN67CEPPRXFFY7ZMX4X7TYYT/action/citation_signature","submit_replication":"https://pith.science/pith/NLXN67CEPPRXFFY7ZMX4X7TYYT/action/replication_record"}},"created_at":"2026-05-17T23:49:59.895880+00:00","updated_at":"2026-05-17T23:49:59.895880+00:00"}