{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5XYGBPA6PBLIR4VDGMZOCZZGVX","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":"59ef5fdcffd490ce99cfb3191f8c6693a56bcb6ceaf8546edf8d954715fc97ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-07-14T18:06:38Z","title_canon_sha256":"d3d3b08dfb56567e987d35615d66e451f891cd47b1b32067273af8aae7679fdf"},"schema_version":"1.0","source":{"id":"1607.06034","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06034","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06034v3","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06034","created_at":"2026-05-18T01:02:20Z"},{"alias_kind":"pith_short_12","alias_value":"5XYGBPA6PBLI","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5XYGBPA6PBLIR4VD","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5XYGBPA6","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:f87a62c4abb5d7354b75af7649b1879151b3e617c46bfc3415235fef917b36c5","target":"graph","created_at":"2026-05-18T01:02:20Z","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"},"paper":{"abstract_excerpt":"We define the notion of Cartesian 2-fibrations, and prove a weak analogue of straightening. Using Barwick's notion of operator categories and the notion of a Cartesian 2-fibration, we extend the notion of $\\infty$-operads to the $(\\infty,2)$-categorical context. These $(\\infty,2)$-operads are used to define and study 2-rings in the $\\infty$-categorical context.","authors_text":"Sanath Devalapurkar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-07-14T18:06:38Z","title":"2-fold complete Segal operads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06034","kind":"arxiv","version":3},"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":"sha256:1214a8d9401cd2dd990387bc7cb16450d5f2fa5d21ff97eba2eb595469b72f4a","target":"record","created_at":"2026-05-18T01:02:20Z","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":"59ef5fdcffd490ce99cfb3191f8c6693a56bcb6ceaf8546edf8d954715fc97ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-07-14T18:06:38Z","title_canon_sha256":"d3d3b08dfb56567e987d35615d66e451f891cd47b1b32067273af8aae7679fdf"},"schema_version":"1.0","source":{"id":"1607.06034","kind":"arxiv","version":3}},"canonical_sha256":"edf060bc1e785688f2a33332e16726adc3ad64e7d94814ffe98730c466be5249","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edf060bc1e785688f2a33332e16726adc3ad64e7d94814ffe98730c466be5249","first_computed_at":"2026-05-18T01:02:20.601351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:20.601351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hm8ikUMo8AKnMvt+NzwilwJBOr9MDS5n68lVMBHH6KpYWch6zEQUEe6uYpQLbStRQI3wz0qN+ITPWTbGpF00AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:20.601997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06034","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1214a8d9401cd2dd990387bc7cb16450d5f2fa5d21ff97eba2eb595469b72f4a","sha256:f87a62c4abb5d7354b75af7649b1879151b3e617c46bfc3415235fef917b36c5"],"state_sha256":"f9f99abbe3b67b24c7f452d72b5f8b9c7c3e1d8098376b662cc8f3fa370de66a"}