{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:C5DE5E3NRSWEMUG25UJRPJBFCS","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":"c16cffde5ac26593243d9362054ce4e1f673ff87cfd857e9b787dea3e7a36643","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CT","submitted_at":"2025-04-09T01:45:40Z","title_canon_sha256":"7d24722d12adae9b17a1b097eb28d27f6a4c198c5b88af1ded014ebafb94d650"},"schema_version":"1.0","source":{"id":"2504.06522","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.06522","created_at":"2026-07-05T10:46:28Z"},{"alias_kind":"arxiv_version","alias_value":"2504.06522v1","created_at":"2026-07-05T10:46:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.06522","created_at":"2026-07-05T10:46:28Z"},{"alias_kind":"pith_short_12","alias_value":"C5DE5E3NRSWE","created_at":"2026-07-05T10:46:28Z"},{"alias_kind":"pith_short_16","alias_value":"C5DE5E3NRSWEMUG2","created_at":"2026-07-05T10:46:28Z"},{"alias_kind":"pith_short_8","alias_value":"C5DE5E3N","created_at":"2026-07-05T10:46:28Z"}],"graph_snapshots":[{"event_id":"sha256:fe6404fe00ede29c00aeaab310beb06b8a447eae147fa26df6cf9e856005a960","target":"graph","created_at":"2026-07-05T10:46:28Z","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/2504.06522/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Modular operads are an extension of operads. In the same way that operads, as dendroidal sets, can be considered as presheaves over the category of trees, so can modular operads be considered as presheaves over a category of graphs.\n  This paper contains a definition of the Kan condition for infinity modular operads, as well as a proof of the Nerve Theorem for modular operads, and the equivalence of the modular Kan and Segal conditions. Appendix A contains the same material for cyclic operads.","authors_text":"Michelle Strumila","cross_cats":["math.AT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CT","submitted_at":"2025-04-09T01:45:40Z","title":"Quasi Modular Operads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.06522","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:ba338c79f72289fc2360da47556423e07df24be4c38420314b42a86aa7a23c40","target":"record","created_at":"2026-07-05T10:46:28Z","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":"c16cffde5ac26593243d9362054ce4e1f673ff87cfd857e9b787dea3e7a36643","cross_cats_sorted":["math.AT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CT","submitted_at":"2025-04-09T01:45:40Z","title_canon_sha256":"7d24722d12adae9b17a1b097eb28d27f6a4c198c5b88af1ded014ebafb94d650"},"schema_version":"1.0","source":{"id":"2504.06522","kind":"arxiv","version":1}},"canonical_sha256":"17464e936d8cac4650daed1317a42514a8708f3ee7127538523a82f32ebaf5f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17464e936d8cac4650daed1317a42514a8708f3ee7127538523a82f32ebaf5f5","first_computed_at":"2026-07-05T10:46:28.287948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:46:28.287948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yb3pS4pAYvM9pKFdXT53z2XuXeV+7GPZ6+g03RIDGcADbLGOARKNG+Xw23YgS0f6ofvBjhHXrfPxjmC6HSNpAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:46:28.288459Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.06522","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba338c79f72289fc2360da47556423e07df24be4c38420314b42a86aa7a23c40","sha256:fe6404fe00ede29c00aeaab310beb06b8a447eae147fa26df6cf9e856005a960"],"state_sha256":"3983bfc8052d72e98a37d815db48eec4cc893beae5ce3d309cf1b62b3a354a87"}