{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:K3DUXJNNFHEYEL4VBQ2A4WXIXC","short_pith_number":"pith:K3DUXJNN","schema_version":"1.0","canonical_sha256":"56c74ba5ad29c9822f950c340e5ae8b8880424cbbf6c9f0e85ee3eaee0ac7804","source":{"kind":"arxiv","id":"2606.26717","version":1},"attestation_state":"computed","paper":{"title":"Isoregular theories, accessible 2-categories, and free constructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Giacomo Tendas, Nicola Gambino","submitted_at":"2026-06-25T07:53:41Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.26717","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-06-25T07:53:41Z","cross_cats_sorted":[],"title_canon_sha256":"34abca45347a021d3647b1b488950339128a7e0bb4432011649a02619f62f3e1","abstract_canon_sha256":"5d6b24b8d71d90ec759e4476d3c2e7f405e38d6f21b192650c5255a8aa50d6ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:15:57.840122Z","signature_b64":"2KnesGrOsVvBOUol6pN/ORd7L0AH6PrRTtVkAg54lxUra3L7hZk4PLnGvuCR1VzUCi0h1dNz+RmpuBgl+ZVNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56c74ba5ad29c9822f950c340e5ae8b8880424cbbf6c9f0e85ee3eaee0ac7804","last_reissued_at":"2026-06-26T01:15:57.839706Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:15:57.839706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isoregular theories, accessible 2-categories, and free constructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Giacomo Tendas, Nicola Gambino","submitted_at":"2026-06-25T07:53:41Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26717","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.26717/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.26717","created_at":"2026-06-26T01:15:57.839769+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.26717v1","created_at":"2026-06-26T01:15:57.839769+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.26717","created_at":"2026-06-26T01:15:57.839769+00:00"},{"alias_kind":"pith_short_12","alias_value":"K3DUXJNNFHEY","created_at":"2026-06-26T01:15:57.839769+00:00"},{"alias_kind":"pith_short_16","alias_value":"K3DUXJNNFHEYEL4V","created_at":"2026-06-26T01:15:57.839769+00:00"},{"alias_kind":"pith_short_8","alias_value":"K3DUXJNN","created_at":"2026-06-26T01:15:57.839769+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/K3DUXJNNFHEYEL4VBQ2A4WXIXC","json":"https://pith.science/pith/K3DUXJNNFHEYEL4VBQ2A4WXIXC.json","graph_json":"https://pith.science/api/pith-number/K3DUXJNNFHEYEL4VBQ2A4WXIXC/graph.json","events_json":"https://pith.science/api/pith-number/K3DUXJNNFHEYEL4VBQ2A4WXIXC/events.json","paper":"https://pith.science/paper/K3DUXJNN"},"agent_actions":{"view_html":"https://pith.science/pith/K3DUXJNNFHEYEL4VBQ2A4WXIXC","download_json":"https://pith.science/pith/K3DUXJNNFHEYEL4VBQ2A4WXIXC.json","view_paper":"https://pith.science/paper/K3DUXJNN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.26717&json=true","fetch_graph":"https://pith.science/api/pith-number/K3DUXJNNFHEYEL4VBQ2A4WXIXC/graph.json","fetch_events":"https://pith.science/api/pith-number/K3DUXJNNFHEYEL4VBQ2A4WXIXC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K3DUXJNNFHEYEL4VBQ2A4WXIXC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K3DUXJNNFHEYEL4VBQ2A4WXIXC/action/storage_attestation","attest_author":"https://pith.science/pith/K3DUXJNNFHEYEL4VBQ2A4WXIXC/action/author_attestation","sign_citation":"https://pith.science/pith/K3DUXJNNFHEYEL4VBQ2A4WXIXC/action/citation_signature","submit_replication":"https://pith.science/pith/K3DUXJNNFHEYEL4VBQ2A4WXIXC/action/replication_record"}},"created_at":"2026-06-26T01:15:57.839769+00:00","updated_at":"2026-06-26T01:15:57.839769+00:00"}