{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PN5URK6PSDSMXTFP2I4IABCU5T","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":"16e3d36905ed2c438ba12180d66b4fed49de11cb3b44732ec8f3933304f47c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-07-24T14:49:36Z","title_canon_sha256":"a3d753b77418a34bc51bd95b23d594ff3390c3c9d3804a0e7b3adfdc67071acd"},"schema_version":"1.0","source":{"id":"1507.06863","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06863","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06863v3","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06863","created_at":"2026-05-18T00:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"PN5URK6PSDSM","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PN5URK6PSDSMXTFP","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PN5URK6P","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:d6a39baa6455a8008176241176e079e42239581ca77b408b99ea4cd694225d37","target":"graph","created_at":"2026-05-18T00:55:39Z","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":"Let T be an NIP L-theory and T' be an enrichment. We give a sufficient condition on T' for the underlying L-type of any definable (respectively invariant) type over a model of T' to be definable (respectively invariant) as an L-type. Besides, we generalise work of Simon and Starchenko on the density of definable types among non forking types to this relative setting. These results are then applied to Scanlon's model completion of valued differential fields.","authors_text":"Pierre Simon, Silvain Rideau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-07-24T14:49:36Z","title":"Definable and invariant types in enrichments of NIP theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06863","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":"sha256:0219b150596e68ef97143c13ae37c4801644e15283f820a1a104fc180aa6a8fb","target":"record","created_at":"2026-05-18T00:55:39Z","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":"16e3d36905ed2c438ba12180d66b4fed49de11cb3b44732ec8f3933304f47c2f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-07-24T14:49:36Z","title_canon_sha256":"a3d753b77418a34bc51bd95b23d594ff3390c3c9d3804a0e7b3adfdc67071acd"},"schema_version":"1.0","source":{"id":"1507.06863","kind":"arxiv","version":3}},"canonical_sha256":"7b7b48abcf90e4cbccafd238800454ecdbb980a0d19323c8c583b73c6cb2317f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b7b48abcf90e4cbccafd238800454ecdbb980a0d19323c8c583b73c6cb2317f","first_computed_at":"2026-05-18T00:55:39.471387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:39.471387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pu+uFpsITnM+15QLh1yc8MAuSffIT90Dj3g3I3lIz44jzLhPeqX+4hhRLYYrQMBkLgxHYs+SwfBSrvyT1zHfAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:39.471925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06863","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0219b150596e68ef97143c13ae37c4801644e15283f820a1a104fc180aa6a8fb","sha256:d6a39baa6455a8008176241176e079e42239581ca77b408b99ea4cd694225d37"],"state_sha256":"8a2310b2297ab5ccda573989e3dd7b98e71b9db1b9de52d2eb5e1146ca0d9002"}