{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PSOUJKM3IG2Q3BILB3ZXQEP7BL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1869a898f5f1c824619b286ccd2f967d7a6f240c4e5a3eca2e2fd835f272b40e","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-01-03T22:47:12Z","title_canon_sha256":"53b8fc61a59fbff76e1ae9c4ae20e0fa670abfc02251023c96b987ba2b9ba8ca"},"schema_version":"1.0","source":{"id":"2501.02129","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.02129","created_at":"2026-07-05T09:57:02Z"},{"alias_kind":"arxiv_version","alias_value":"2501.02129v1","created_at":"2026-07-05T09:57:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.02129","created_at":"2026-07-05T09:57:02Z"},{"alias_kind":"pith_short_12","alias_value":"PSOUJKM3IG2Q","created_at":"2026-07-05T09:57:02Z"},{"alias_kind":"pith_short_16","alias_value":"PSOUJKM3IG2Q3BIL","created_at":"2026-07-05T09:57:02Z"},{"alias_kind":"pith_short_8","alias_value":"PSOUJKM3","created_at":"2026-07-05T09:57:02Z"}],"graph_snapshots":[{"event_id":"sha256:0f29bdc2ca65181d66899e816a0bd1dfd52dcd5d9cdfe6a85f7bf743e2b77b38","target":"graph","created_at":"2026-07-05T09:57:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.02129/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","authors_text":"Natalie Stewart","cross_cats":["math.AT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-01-03T22:47:12Z","title":"Equivariant operads, symmetric sequences, and Boardman-Vogt tensor products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.02129","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7bc1d95b1b455d0c8ff071b9c9a607c339c2fa0934e7f9e36c4208d485b51b56","target":"record","created_at":"2026-07-05T09:57:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1869a898f5f1c824619b286ccd2f967d7a6f240c4e5a3eca2e2fd835f272b40e","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-01-03T22:47:12Z","title_canon_sha256":"53b8fc61a59fbff76e1ae9c4ae20e0fa670abfc02251023c96b987ba2b9ba8ca"},"schema_version":"1.0","source":{"id":"2501.02129","kind":"arxiv","version":1}},"canonical_sha256":"7c9d44a99b41b50d850b0ef37811ff0acff465638bbf6dc348fba0f5cd46dbee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c9d44a99b41b50d850b0ef37811ff0acff465638bbf6dc348fba0f5cd46dbee","first_computed_at":"2026-07-05T09:57:02.648393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:57:02.648393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6haBeHRdUzg5GXpDPGHgjHiNgh9aq1zPXXE6ORbFLkNfJkzWIuQ1Hrxcld4InLraXCasbz3cSzqaZBK0aQQJDw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:57:02.648896Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.02129","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bc1d95b1b455d0c8ff071b9c9a607c339c2fa0934e7f9e36c4208d485b51b56","sha256:0f29bdc2ca65181d66899e816a0bd1dfd52dcd5d9cdfe6a85f7bf743e2b77b38"],"state_sha256":"69cd6270591603a46b13add546c0e5c0f5bb68a95bdd9d279c2322e6483a2a4c"}