{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:PSOUJKM3IG2Q3BILB3ZXQEP7BL","short_pith_number":"pith:PSOUJKM3","schema_version":"1.0","canonical_sha256":"7c9d44a99b41b50d850b0ef37811ff0acff465638bbf6dc348fba0f5cd46dbee","source":{"kind":"arxiv","id":"2501.02129","version":1},"attestation_state":"computed","paper":{"title":"Equivariant operads, symmetric sequences, and Boardman-Vogt tensor products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Natalie Stewart","submitted_at":"2025-01-03T22:47:12Z","abstract_excerpt":"We advance the foundational study of be Nardin-Shah's $\\infty$-category of $G$-operads and their associated $\\infty$-categories of algebras. In particular, we construct the underlying $G$-symmetric sequence of a (one color) $G$-operad, yielding a monadic functor; we use this to lift Bonventre's genuine operadic nerve to a conservative functor of $\\infty$-categories, restricting to an equivalence between categories of discrete $G$-operads. Using this, we extend Blumberg-Hill's program concerning $\\mathcal{N}_\\infty$-operads to arbitrary sub-operads of the terminal $G$-operad, which we show are "},"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":"2501.02129","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-01-03T22:47:12Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"53b8fc61a59fbff76e1ae9c4ae20e0fa670abfc02251023c96b987ba2b9ba8ca","abstract_canon_sha256":"1869a898f5f1c824619b286ccd2f967d7a6f240c4e5a3eca2e2fd835f272b40e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:02.648896Z","signature_b64":"6haBeHRdUzg5GXpDPGHgjHiNgh9aq1zPXXE6ORbFLkNfJkzWIuQ1Hrxcld4InLraXCasbz3cSzqaZBK0aQQJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c9d44a99b41b50d850b0ef37811ff0acff465638bbf6dc348fba0f5cd46dbee","last_reissued_at":"2026-07-05T09:57:02.648393Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:02.648393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivariant operads, symmetric sequences, and Boardman-Vogt tensor products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Natalie Stewart","submitted_at":"2025-01-03T22:47:12Z","abstract_excerpt":"We advance the foundational study of be Nardin-Shah's $\\infty$-category of $G$-operads and their associated $\\infty$-categories of algebras. In particular, we construct the underlying $G$-symmetric sequence of a (one color) $G$-operad, yielding a monadic functor; we use this to lift Bonventre's genuine operadic nerve to a conservative functor of $\\infty$-categories, restricting to an equivalence between categories of discrete $G$-operads. Using this, we extend Blumberg-Hill's program concerning $\\mathcal{N}_\\infty$-operads to arbitrary sub-operads of the terminal $G$-operad, which we show are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.02129","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.02129/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":"2501.02129","created_at":"2026-07-05T09:57:02.648447+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.02129v1","created_at":"2026-07-05T09:57:02.648447+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.02129","created_at":"2026-07-05T09:57:02.648447+00:00"},{"alias_kind":"pith_short_12","alias_value":"PSOUJKM3IG2Q","created_at":"2026-07-05T09:57:02.648447+00:00"},{"alias_kind":"pith_short_16","alias_value":"PSOUJKM3IG2Q3BIL","created_at":"2026-07-05T09:57:02.648447+00:00"},{"alias_kind":"pith_short_8","alias_value":"PSOUJKM3","created_at":"2026-07-05T09:57:02.648447+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2512.15573","citing_title":"Multiplicative Equivariant Thom Spectra & Structured Real Orientations","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PSOUJKM3IG2Q3BILB3ZXQEP7BL","json":"https://pith.science/pith/PSOUJKM3IG2Q3BILB3ZXQEP7BL.json","graph_json":"https://pith.science/api/pith-number/PSOUJKM3IG2Q3BILB3ZXQEP7BL/graph.json","events_json":"https://pith.science/api/pith-number/PSOUJKM3IG2Q3BILB3ZXQEP7BL/events.json","paper":"https://pith.science/paper/PSOUJKM3"},"agent_actions":{"view_html":"https://pith.science/pith/PSOUJKM3IG2Q3BILB3ZXQEP7BL","download_json":"https://pith.science/pith/PSOUJKM3IG2Q3BILB3ZXQEP7BL.json","view_paper":"https://pith.science/paper/PSOUJKM3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.02129&json=true","fetch_graph":"https://pith.science/api/pith-number/PSOUJKM3IG2Q3BILB3ZXQEP7BL/graph.json","fetch_events":"https://pith.science/api/pith-number/PSOUJKM3IG2Q3BILB3ZXQEP7BL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PSOUJKM3IG2Q3BILB3ZXQEP7BL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PSOUJKM3IG2Q3BILB3ZXQEP7BL/action/storage_attestation","attest_author":"https://pith.science/pith/PSOUJKM3IG2Q3BILB3ZXQEP7BL/action/author_attestation","sign_citation":"https://pith.science/pith/PSOUJKM3IG2Q3BILB3ZXQEP7BL/action/citation_signature","submit_replication":"https://pith.science/pith/PSOUJKM3IG2Q3BILB3ZXQEP7BL/action/replication_record"}},"created_at":"2026-07-05T09:57:02.648447+00:00","updated_at":"2026-07-05T09:57:02.648447+00:00"}