{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:BDF6A4CX2JCHQTLRSVQPMVFECF","short_pith_number":"pith:BDF6A4CX","schema_version":"1.0","canonical_sha256":"08cbe07057d244784d719560f654a4116560792f2b21a12a5f7d98f81ffc3863","source":{"kind":"arxiv","id":"1007.4468","version":2},"attestation_state":"computed","paper":{"title":"Externally definable sets and dependent pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Artem Chernikov, Pierre Simon","submitted_at":"2010-07-26T14:12:33Z","abstract_excerpt":"We prove that externally definable sets in first order NIP theories have honest definitions, giving a new proof of Shelah's expansion theorem. Also we discuss a weak notion of stable embeddedness true in this context. Those results are then used to prove a general theorem on dependent pairs, which in particular answers a question of Baldwin and Benedikt on naming an indiscernible sequence."},"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":"1007.4468","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-07-26T14:12:33Z","cross_cats_sorted":[],"title_canon_sha256":"b7000845ca1fedfb3766085fbccab1ddd71570032c22b1b77110869ca46b74a2","abstract_canon_sha256":"9980eb40cf4dcd2e490da945c0c9903a43a565248fe9e09148ba623f780e7a61"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:05.778512Z","signature_b64":"mhTh8LHA85XgxYr87NisOCEWAo3b0ZHP6+YMeAjy1FRr44sv3StoJUXQ0R8x1+UbuS1WQXNdTegZ53e3s8aOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08cbe07057d244784d719560f654a4116560792f2b21a12a5f7d98f81ffc3863","last_reissued_at":"2026-05-18T04:13:05.778090Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:05.778090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Externally definable sets and dependent pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Artem Chernikov, Pierre Simon","submitted_at":"2010-07-26T14:12:33Z","abstract_excerpt":"We prove that externally definable sets in first order NIP theories have honest definitions, giving a new proof of Shelah's expansion theorem. Also we discuss a weak notion of stable embeddedness true in this context. Those results are then used to prove a general theorem on dependent pairs, which in particular answers a question of Baldwin and Benedikt on naming an indiscernible sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4468","kind":"arxiv","version":2},"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":"1007.4468","created_at":"2026-05-18T04:13:05.778148+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.4468v2","created_at":"2026-05-18T04:13:05.778148+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4468","created_at":"2026-05-18T04:13:05.778148+00:00"},{"alias_kind":"pith_short_12","alias_value":"BDF6A4CX2JCH","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BDF6A4CX2JCHQTLR","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BDF6A4CX","created_at":"2026-05-18T12:26:05.355336+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/BDF6A4CX2JCHQTLRSVQPMVFECF","json":"https://pith.science/pith/BDF6A4CX2JCHQTLRSVQPMVFECF.json","graph_json":"https://pith.science/api/pith-number/BDF6A4CX2JCHQTLRSVQPMVFECF/graph.json","events_json":"https://pith.science/api/pith-number/BDF6A4CX2JCHQTLRSVQPMVFECF/events.json","paper":"https://pith.science/paper/BDF6A4CX"},"agent_actions":{"view_html":"https://pith.science/pith/BDF6A4CX2JCHQTLRSVQPMVFECF","download_json":"https://pith.science/pith/BDF6A4CX2JCHQTLRSVQPMVFECF.json","view_paper":"https://pith.science/paper/BDF6A4CX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.4468&json=true","fetch_graph":"https://pith.science/api/pith-number/BDF6A4CX2JCHQTLRSVQPMVFECF/graph.json","fetch_events":"https://pith.science/api/pith-number/BDF6A4CX2JCHQTLRSVQPMVFECF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BDF6A4CX2JCHQTLRSVQPMVFECF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BDF6A4CX2JCHQTLRSVQPMVFECF/action/storage_attestation","attest_author":"https://pith.science/pith/BDF6A4CX2JCHQTLRSVQPMVFECF/action/author_attestation","sign_citation":"https://pith.science/pith/BDF6A4CX2JCHQTLRSVQPMVFECF/action/citation_signature","submit_replication":"https://pith.science/pith/BDF6A4CX2JCHQTLRSVQPMVFECF/action/replication_record"}},"created_at":"2026-05-18T04:13:05.778148+00:00","updated_at":"2026-05-18T04:13:05.778148+00:00"}