{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VHXWYQXV6EO2TTI22NI5XE6M5B","short_pith_number":"pith:VHXWYQXV","schema_version":"1.0","canonical_sha256":"a9ef6c42f5f11da9cd1ad351db93cce86f8f2f41740b2b6b310dc4640e6191c3","source":{"kind":"arxiv","id":"2504.16935","version":3},"attestation_state":"computed","paper":{"title":"Higher Koszul duality and $n$-affineness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT","math.KT"],"primary_cat":"math.AG","authors_text":"Emanuele Pavia, James Pascaleff, Nicol\\`o Sibilla","submitted_at":"2025-03-25T11:00:45Z","abstract_excerpt":"In this paper we study $\\mathbb{E}_n$-Koszul duality in the topological setting, and the closely related question of \\emph{$n$-affineness} for Betti stacks. The $\\mathbb{E}_n$-Koszul dual of the algebra of chains on the $n$-fold loop space of a space $X$ is the algebra of cochains on $X$. It was expected that $\\mathbb{E}_n$-Koszul duality should induce a kind of Morita equivalence between categories of iterated modules, but even the precise formulation of such a statement was not known. We give a rigorous formulation, and a proof, of such an $\\mathbb{E}_n$-Koszul duality in the topological set"},"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":"2504.16935","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-03-25T11:00:45Z","cross_cats_sorted":["math.AT","math.CT","math.KT"],"title_canon_sha256":"2f794189e2ae19914336451a24e03e0bbb9087c15c3edde39c877bd14816628a","abstract_canon_sha256":"10e49c0d64a862653fa76db4b63130e6ac527b09cd28d9e1b4658fdd6cbee1e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:13:45.077079Z","signature_b64":"lbOWBXihQWSER2YnG7zu00Qk2JXf1z79EBsTRPsoS4tERKpBuH48KkCAylO/pCdy0dzNjq2HoZ0V7AONE20sCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9ef6c42f5f11da9cd1ad351db93cce86f8f2f41740b2b6b310dc4640e6191c3","last_reissued_at":"2026-06-23T03:13:45.076637Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:13:45.076637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher Koszul duality and $n$-affineness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT","math.KT"],"primary_cat":"math.AG","authors_text":"Emanuele Pavia, James Pascaleff, Nicol\\`o Sibilla","submitted_at":"2025-03-25T11:00:45Z","abstract_excerpt":"In this paper we study $\\mathbb{E}_n$-Koszul duality in the topological setting, and the closely related question of \\emph{$n$-affineness} for Betti stacks. The $\\mathbb{E}_n$-Koszul dual of the algebra of chains on the $n$-fold loop space of a space $X$ is the algebra of cochains on $X$. It was expected that $\\mathbb{E}_n$-Koszul duality should induce a kind of Morita equivalence between categories of iterated modules, but even the precise formulation of such a statement was not known. We give a rigorous formulation, and a proof, of such an $\\mathbb{E}_n$-Koszul duality in the topological set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16935","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.16935/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2504.16935","created_at":"2026-06-23T03:13:45.076696+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.16935v3","created_at":"2026-06-23T03:13:45.076696+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16935","created_at":"2026-06-23T03:13:45.076696+00:00"},{"alias_kind":"pith_short_12","alias_value":"VHXWYQXV6EO2","created_at":"2026-06-23T03:13:45.076696+00:00"},{"alias_kind":"pith_short_16","alias_value":"VHXWYQXV6EO2TTI2","created_at":"2026-06-23T03:13:45.076696+00:00"},{"alias_kind":"pith_short_8","alias_value":"VHXWYQXV","created_at":"2026-06-23T03:13:45.076696+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/VHXWYQXV6EO2TTI22NI5XE6M5B","json":"https://pith.science/pith/VHXWYQXV6EO2TTI22NI5XE6M5B.json","graph_json":"https://pith.science/api/pith-number/VHXWYQXV6EO2TTI22NI5XE6M5B/graph.json","events_json":"https://pith.science/api/pith-number/VHXWYQXV6EO2TTI22NI5XE6M5B/events.json","paper":"https://pith.science/paper/VHXWYQXV"},"agent_actions":{"view_html":"https://pith.science/pith/VHXWYQXV6EO2TTI22NI5XE6M5B","download_json":"https://pith.science/pith/VHXWYQXV6EO2TTI22NI5XE6M5B.json","view_paper":"https://pith.science/paper/VHXWYQXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.16935&json=true","fetch_graph":"https://pith.science/api/pith-number/VHXWYQXV6EO2TTI22NI5XE6M5B/graph.json","fetch_events":"https://pith.science/api/pith-number/VHXWYQXV6EO2TTI22NI5XE6M5B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VHXWYQXV6EO2TTI22NI5XE6M5B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VHXWYQXV6EO2TTI22NI5XE6M5B/action/storage_attestation","attest_author":"https://pith.science/pith/VHXWYQXV6EO2TTI22NI5XE6M5B/action/author_attestation","sign_citation":"https://pith.science/pith/VHXWYQXV6EO2TTI22NI5XE6M5B/action/citation_signature","submit_replication":"https://pith.science/pith/VHXWYQXV6EO2TTI22NI5XE6M5B/action/replication_record"}},"created_at":"2026-06-23T03:13:45.076696+00:00","updated_at":"2026-06-23T03:13:45.076696+00:00"}