{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:T6G73HZHOVKF33LG3O53MIINMS","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":"d6ebf7fbaeb1e95ff308167592db6eb9aa7e8c56b6eb0f7d792feb142822632d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-02-13T07:38:09Z","title_canon_sha256":"899d54f80ad0c5745ce9b53a0b2452722af09623b7cd5a43c7bfc41dec7c0e8d"},"schema_version":"1.0","source":{"id":"1202.2650","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.2650","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"arxiv_version","alias_value":"1202.2650v1","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2650","created_at":"2026-05-18T04:02:25Z"},{"alias_kind":"pith_short_12","alias_value":"T6G73HZHOVKF","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"T6G73HZHOVKF33LG","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"T6G73HZH","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:2d90984584152ddc7e236df8c422535c00ad77bc0e4abe9cebee6f5641dfd852","target":"graph","created_at":"2026-05-18T04:02:25Z","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":"We continue investigating the structure of externally definable sets in NIP theories and preservation of NIP after expanding by new predicates. Most importantly: types over finite sets are uniformly definable; over a model, a family of non-forking instances of a formula (with parameters ranging over a type-definable set) can be covered with finitely many invariant types; we give some criteria for the boundedness of an expansion by a new predicate in a distal theory; naming an arbitrary small indiscernible sequence preserves NIP, while naming a large one doesn't; there are models of NIP theorie","authors_text":"Artem Chernikov, Pierre Simon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-02-13T07:38:09Z","title":"Externally definable sets and dependent pairs II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2650","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":"sha256:2f5f42b61af5dd9afbcded92504dca9790911e43dbf1a41b261d50a4638261de","target":"record","created_at":"2026-05-18T04:02:25Z","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":"d6ebf7fbaeb1e95ff308167592db6eb9aa7e8c56b6eb0f7d792feb142822632d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-02-13T07:38:09Z","title_canon_sha256":"899d54f80ad0c5745ce9b53a0b2452722af09623b7cd5a43c7bfc41dec7c0e8d"},"schema_version":"1.0","source":{"id":"1202.2650","kind":"arxiv","version":1}},"canonical_sha256":"9f8dfd9f2775545ded66dbbbb6210d64ba2358f4f1e4a54db63179e9d6cf1abb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f8dfd9f2775545ded66dbbbb6210d64ba2358f4f1e4a54db63179e9d6cf1abb","first_computed_at":"2026-05-18T04:02:25.990826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:25.990826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6h6wkpoMErUPR+oRLkBp7V3ECEPuxaU2jk93cPUN0XHB9VRag+nze+7R5Y5nPzDka2gI6yF7tA6031Wt2AtuBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:25.991362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.2650","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f5f42b61af5dd9afbcded92504dca9790911e43dbf1a41b261d50a4638261de","sha256:2d90984584152ddc7e236df8c422535c00ad77bc0e4abe9cebee6f5641dfd852"],"state_sha256":"6aced7dca2db7fed28020d41257a6c717af50322533a5f7283e445539124ca88"}