{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5Q3VPRT5HUAMIKLFGWLFF4NUSQ","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":"0275ac8755133183528b9e4970893a774a27dacf78037933f53f9fd50dbb51c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-02-24T18:48:44Z","title_canon_sha256":"5bfbea8ddf48e87f8ad0db6d460bb6daae71490f624bf13bc9ea94025f3e1a96"},"schema_version":"1.0","source":{"id":"2502.17415","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.17415","created_at":"2026-07-05T10:31:26Z"},{"alias_kind":"arxiv_version","alias_value":"2502.17415v2","created_at":"2026-07-05T10:31:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.17415","created_at":"2026-07-05T10:31:26Z"},{"alias_kind":"pith_short_12","alias_value":"5Q3VPRT5HUAM","created_at":"2026-07-05T10:31:26Z"},{"alias_kind":"pith_short_16","alias_value":"5Q3VPRT5HUAMIKLF","created_at":"2026-07-05T10:31:26Z"},{"alias_kind":"pith_short_8","alias_value":"5Q3VPRT5","created_at":"2026-07-05T10:31:26Z"}],"graph_snapshots":[{"event_id":"sha256:73f9d4287b1d694345570f084b94b043b614d92f9a665d3559114f805bd3abff","target":"graph","created_at":"2026-07-05T10:31:26Z","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/2502.17415/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a discrete colored operad $P$, we construct an adjunction between the category of dendroidal sets over the nerve of $P$ and the category of simplicial $P$-algebras, and prove that when $P$ is $\\Sigma$-free it establishes a Quillen equivalence with respect to the covariant model structure on the former category and the projective model structure on the latter. When $P=A$ is a discrete category, this recovers a Quillen equivalence previously established by Heuts-Moerdijk, of which we provide an independent proof.\n  To prove the constructed adjunction is a Quillen equivalence, we show that th","authors_text":"Francesca Pratali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-02-24T18:48:44Z","title":"Rectification of dendroidal left fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.17415","kind":"arxiv","version":2},"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:cd51502172919eab3fee1ee3799712da7c6f09713c71cf7f015ea3e13789b5f4","target":"record","created_at":"2026-07-05T10:31:26Z","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":"0275ac8755133183528b9e4970893a774a27dacf78037933f53f9fd50dbb51c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-02-24T18:48:44Z","title_canon_sha256":"5bfbea8ddf48e87f8ad0db6d460bb6daae71490f624bf13bc9ea94025f3e1a96"},"schema_version":"1.0","source":{"id":"2502.17415","kind":"arxiv","version":2}},"canonical_sha256":"ec3757c67d3d00c42965359652f1b494049b17839699497f1d651426bd538547","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec3757c67d3d00c42965359652f1b494049b17839699497f1d651426bd538547","first_computed_at":"2026-07-05T10:31:26.943208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:31:26.943208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cJ6jdMJUy98uP3sIrcgxEP1l2i9+EDdv8jFQx2zC1yNrT/YaQtF7PC/hRLq8E1k1zIOTuE2oCY1pI4g9U8DACw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:31:26.943827Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.17415","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd51502172919eab3fee1ee3799712da7c6f09713c71cf7f015ea3e13789b5f4","sha256:73f9d4287b1d694345570f084b94b043b614d92f9a665d3559114f805bd3abff"],"state_sha256":"19e47aa2f5f636fcb42d24cad3e5f98930bcef483988383ff5c19d2294b1411a"}