{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:IGUE4BRVKSG6YBDU3MPQH6FQKT","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":"1730ca0d68a0a73792673d4aab38b5a7de71f99dc111b5fe19590e22b3098bda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-10-09T03:45:15Z","title_canon_sha256":"78760bfc810eaa51bdfb5a2dcff7c76c05559d8de8b0f80de51892b9d0f12246"},"schema_version":"1.0","source":{"id":"2310.05384","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.05384","created_at":"2026-07-05T08:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"2310.05384v3","created_at":"2026-07-05T08:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.05384","created_at":"2026-07-05T08:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"IGUE4BRVKSG6","created_at":"2026-07-05T08:05:03Z"},{"alias_kind":"pith_short_16","alias_value":"IGUE4BRVKSG6YBDU","created_at":"2026-07-05T08:05:03Z"},{"alias_kind":"pith_short_8","alias_value":"IGUE4BRV","created_at":"2026-07-05T08:05:03Z"}],"graph_snapshots":[{"event_id":"sha256:9bf2503eff39d241579ad879dff189128ac58bb7dfb9e06eb90c4ed5258021b4","target":"graph","created_at":"2026-07-05T08:05:03Z","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/2310.05384/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The categorified theories known as \"doctrines\" specify a category equipped with extra structure, analogous to how ordinary theories specify a set with extra structure. We introduce a new framework for doctrines based on double category theory. A cartesian double theory is defined to be a small double category with finite products and a model of a cartesian double theory to be a finite product-preserving lax functor out of it. Many familiar categorical structures are models of cartesian double theories, including categories, presheaves, monoidal categories, braided and symmetric monoidal catego","authors_text":"Evan Patterson, Michael Lambert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-10-09T03:45:15Z","title":"Cartesian double theories: A double-categorical framework for categorical doctrines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.05384","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":"sha256:4c15d808849f2330d627e60a329d91bcc7d5a68a12810ed260676f8958847465","target":"record","created_at":"2026-07-05T08:05:03Z","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":"1730ca0d68a0a73792673d4aab38b5a7de71f99dc111b5fe19590e22b3098bda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-10-09T03:45:15Z","title_canon_sha256":"78760bfc810eaa51bdfb5a2dcff7c76c05559d8de8b0f80de51892b9d0f12246"},"schema_version":"1.0","source":{"id":"2310.05384","kind":"arxiv","version":3}},"canonical_sha256":"41a84e0635548dec0474db1f03f8b054c8300a0c0946b7f506f2c9c0eeaeb05a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41a84e0635548dec0474db1f03f8b054c8300a0c0946b7f506f2c9c0eeaeb05a","first_computed_at":"2026-07-05T08:05:03.588046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:05:03.588046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I/icuqJS2LimHgt7t0HkeYCbDTpTVHPwTRWafLpXAoyBYtSJxQCY5hXORhhigDNTA1Y3RbhMOGHys8QTSoXRAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:05:03.588478Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.05384","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c15d808849f2330d627e60a329d91bcc7d5a68a12810ed260676f8958847465","sha256:9bf2503eff39d241579ad879dff189128ac58bb7dfb9e06eb90c4ed5258021b4"],"state_sha256":"c267ae1ec77b2289242d0f0dc409fcca30e67ae04d010f0ca1230da9fdd0a6f0"}