{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:K3DUXJNNFHEYEL4VBQ2A4WXIXC","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":"5d6b24b8d71d90ec759e4476d3c2e7f405e38d6f21b192650c5255a8aa50d6ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-25T07:53:41Z","title_canon_sha256":"34abca45347a021d3647b1b488950339128a7e0bb4432011649a02619f62f3e1"},"schema_version":"1.0","source":{"id":"2606.26717","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.26717","created_at":"2026-06-26T01:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.26717v1","created_at":"2026-06-26T01:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26717","created_at":"2026-06-26T01:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"K3DUXJNNFHEY","created_at":"2026-06-26T01:15:57Z"},{"alias_kind":"pith_short_16","alias_value":"K3DUXJNNFHEYEL4V","created_at":"2026-06-26T01:15:57Z"},{"alias_kind":"pith_short_8","alias_value":"K3DUXJNN","created_at":"2026-06-26T01:15:57Z"}],"graph_snapshots":[{"event_id":"sha256:31c4410fa1a09c465318839ea0185c36280dd06d0c29cf2458b65acf6136502c","target":"graph","created_at":"2026-06-26T01:15:57Z","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/2606.26717/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce isoregular theories, in which it is possible to express existential quantification up to unique isomorphism, as typically used to characterise category-theoretic universal constructions, such as limits. We then develop a functorial semantics for isoregular theories and prove that their 2-categories of models are accessible with flexible limits. We apply these results by showing that a number of 2-categories of interest in general category theory, categorical algebra, and categorical logic are models of isoregular theories, thereby establishing that they are accessible 2-categories","authors_text":"Giacomo Tendas, Nicola Gambino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-25T07:53:41Z","title":"Isoregular theories, accessible 2-categories, and free constructions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26717","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:b0261f7aecccb5a986605518ed50bc7bc7d5cffd69e46ea630d18fb9a8becfeb","target":"record","created_at":"2026-06-26T01:15:57Z","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":"5d6b24b8d71d90ec759e4476d3c2e7f405e38d6f21b192650c5255a8aa50d6ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-25T07:53:41Z","title_canon_sha256":"34abca45347a021d3647b1b488950339128a7e0bb4432011649a02619f62f3e1"},"schema_version":"1.0","source":{"id":"2606.26717","kind":"arxiv","version":1}},"canonical_sha256":"56c74ba5ad29c9822f950c340e5ae8b8880424cbbf6c9f0e85ee3eaee0ac7804","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56c74ba5ad29c9822f950c340e5ae8b8880424cbbf6c9f0e85ee3eaee0ac7804","first_computed_at":"2026-06-26T01:15:57.839706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:15:57.839706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2KnesGrOsVvBOUol6pN/ORd7L0AH6PrRTtVkAg54lxUra3L7hZk4PLnGvuCR1VzUCi0h1dNz+RmpuBgl+ZVNDA==","signature_status":"signed_v1","signed_at":"2026-06-26T01:15:57.840122Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.26717","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0261f7aecccb5a986605518ed50bc7bc7d5cffd69e46ea630d18fb9a8becfeb","sha256:31c4410fa1a09c465318839ea0185c36280dd06d0c29cf2458b65acf6136502c"],"state_sha256":"9eeb697b243e807debf6d6f719a81f7bf6ed28e5cd37ea16203688b2d7bffb56"}