{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:V2UEQ3ELDOBBFHN52RUFRV2EMY","short_pith_number":"pith:V2UEQ3EL","schema_version":"1.0","canonical_sha256":"aea8486c8b1b82129dbdd46858d744660306a2becfa5436ab4020f5fdcceb2dd","source":{"kind":"arxiv","id":"1012.3185","version":1},"attestation_state":"computed","paper":{"title":"A categorical approach to internality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.LO","authors_text":"Moshe Kamensky","submitted_at":"2010-12-14T22:04:50Z","abstract_excerpt":"Model theoretic internality provides conditions under which the group of automorphisms of a model over a reduct is itself a definable group. In this paper we formulate a categorical analogue of the condition of internality, and prove an analogous result on the categorical level. The model theoretic statement is recovered by considering the category of definable sets."},"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":"1012.3185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-12-14T22:04:50Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"f17d7cb723cf0cb1234e02a1c56b5f32a9bed090d0e1a44e4c0f3d92ce2e9532","abstract_canon_sha256":"e980e6af3090525afeb5e62505e750bcd1097520b65a5acd52ba3d75afcc6da6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:17.567160Z","signature_b64":"Oce52e38hjar63kvmVnSfSD1UPE17ntc8LOIgEYJHwwHuZof8IYS/G1punec9tDNJ+WJGLFsKGb1ykzIJuIBBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aea8486c8b1b82129dbdd46858d744660306a2becfa5436ab4020f5fdcceb2dd","last_reissued_at":"2026-05-18T04:33:17.566614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:17.566614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A categorical approach to internality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.LO","authors_text":"Moshe Kamensky","submitted_at":"2010-12-14T22:04:50Z","abstract_excerpt":"Model theoretic internality provides conditions under which the group of automorphisms of a model over a reduct is itself a definable group. In this paper we formulate a categorical analogue of the condition of internality, and prove an analogous result on the categorical level. The model theoretic statement is recovered by considering the category of definable sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3185","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":""},"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":"1012.3185","created_at":"2026-05-18T04:33:17.566700+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.3185v1","created_at":"2026-05-18T04:33:17.566700+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3185","created_at":"2026-05-18T04:33:17.566700+00:00"},{"alias_kind":"pith_short_12","alias_value":"V2UEQ3ELDOBB","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"V2UEQ3ELDOBBFHN5","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"V2UEQ3EL","created_at":"2026-05-18T12:26:15.391820+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/V2UEQ3ELDOBBFHN52RUFRV2EMY","json":"https://pith.science/pith/V2UEQ3ELDOBBFHN52RUFRV2EMY.json","graph_json":"https://pith.science/api/pith-number/V2UEQ3ELDOBBFHN52RUFRV2EMY/graph.json","events_json":"https://pith.science/api/pith-number/V2UEQ3ELDOBBFHN52RUFRV2EMY/events.json","paper":"https://pith.science/paper/V2UEQ3EL"},"agent_actions":{"view_html":"https://pith.science/pith/V2UEQ3ELDOBBFHN52RUFRV2EMY","download_json":"https://pith.science/pith/V2UEQ3ELDOBBFHN52RUFRV2EMY.json","view_paper":"https://pith.science/paper/V2UEQ3EL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.3185&json=true","fetch_graph":"https://pith.science/api/pith-number/V2UEQ3ELDOBBFHN52RUFRV2EMY/graph.json","fetch_events":"https://pith.science/api/pith-number/V2UEQ3ELDOBBFHN52RUFRV2EMY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V2UEQ3ELDOBBFHN52RUFRV2EMY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V2UEQ3ELDOBBFHN52RUFRV2EMY/action/storage_attestation","attest_author":"https://pith.science/pith/V2UEQ3ELDOBBFHN52RUFRV2EMY/action/author_attestation","sign_citation":"https://pith.science/pith/V2UEQ3ELDOBBFHN52RUFRV2EMY/action/citation_signature","submit_replication":"https://pith.science/pith/V2UEQ3ELDOBBFHN52RUFRV2EMY/action/replication_record"}},"created_at":"2026-05-18T04:33:17.566700+00:00","updated_at":"2026-05-18T04:33:17.566700+00:00"}