{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BSWSBEQ3Z5SAQMH237W4INXODY","short_pith_number":"pith:BSWSBEQ3","schema_version":"1.0","canonical_sha256":"0cad20921bcf640830fadfedc436ee1e0a170d8b60a1c3b17cc24b11f4d8a9b8","source":{"kind":"arxiv","id":"1707.03486","version":1},"attestation_state":"computed","paper":{"title":"Bounded pregeometries and pairs of fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"(2) University of Illinois at Urbana-Champaign, Bogota-Colombia, Illinois), Leonardo Angel (1), Lou van den Dries (2) ((1) Universidad de los Andes","submitted_at":"2017-07-11T22:55:54Z","abstract_excerpt":"A definable set in a pair (K, k) of algebraically closed fields is co-analyzable relative to the subfield k of the pair if and only if it is almost internal to k. To prove this and some related results for tame pairs of real closed fields we introduce a certain kind of bounded pregeometry for such pairs."},"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":"1707.03486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-07-11T22:55:54Z","cross_cats_sorted":[],"title_canon_sha256":"0d6826c13595ddd76847c833b9200a488aec44b769d0780606d2a032d64cea36","abstract_canon_sha256":"3c31096afb64a2e45d17c9c1c86560358f917ae027e34e354482088b66a784fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:25.879035Z","signature_b64":"CkCqe8kcqn1tPFVJqByc5nORY/ZuvUH6dL/mQFRroquA3xPUYMMxJdLJRWaKR+M2fIDGKFs/0EzGubXMTIisDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cad20921bcf640830fadfedc436ee1e0a170d8b60a1c3b17cc24b11f4d8a9b8","last_reissued_at":"2026-05-18T00:40:25.878417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:25.878417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded pregeometries and pairs of fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"(2) University of Illinois at Urbana-Champaign, Bogota-Colombia, Illinois), Leonardo Angel (1), Lou van den Dries (2) ((1) Universidad de los Andes","submitted_at":"2017-07-11T22:55:54Z","abstract_excerpt":"A definable set in a pair (K, k) of algebraically closed fields is co-analyzable relative to the subfield k of the pair if and only if it is almost internal to k. To prove this and some related results for tame pairs of real closed fields we introduce a certain kind of bounded pregeometry for such pairs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03486","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":"1707.03486","created_at":"2026-05-18T00:40:25.878506+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.03486v1","created_at":"2026-05-18T00:40:25.878506+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.03486","created_at":"2026-05-18T00:40:25.878506+00:00"},{"alias_kind":"pith_short_12","alias_value":"BSWSBEQ3Z5SA","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BSWSBEQ3Z5SAQMH2","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BSWSBEQ3","created_at":"2026-05-18T12:31:08.081275+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/BSWSBEQ3Z5SAQMH237W4INXODY","json":"https://pith.science/pith/BSWSBEQ3Z5SAQMH237W4INXODY.json","graph_json":"https://pith.science/api/pith-number/BSWSBEQ3Z5SAQMH237W4INXODY/graph.json","events_json":"https://pith.science/api/pith-number/BSWSBEQ3Z5SAQMH237W4INXODY/events.json","paper":"https://pith.science/paper/BSWSBEQ3"},"agent_actions":{"view_html":"https://pith.science/pith/BSWSBEQ3Z5SAQMH237W4INXODY","download_json":"https://pith.science/pith/BSWSBEQ3Z5SAQMH237W4INXODY.json","view_paper":"https://pith.science/paper/BSWSBEQ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.03486&json=true","fetch_graph":"https://pith.science/api/pith-number/BSWSBEQ3Z5SAQMH237W4INXODY/graph.json","fetch_events":"https://pith.science/api/pith-number/BSWSBEQ3Z5SAQMH237W4INXODY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BSWSBEQ3Z5SAQMH237W4INXODY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BSWSBEQ3Z5SAQMH237W4INXODY/action/storage_attestation","attest_author":"https://pith.science/pith/BSWSBEQ3Z5SAQMH237W4INXODY/action/author_attestation","sign_citation":"https://pith.science/pith/BSWSBEQ3Z5SAQMH237W4INXODY/action/citation_signature","submit_replication":"https://pith.science/pith/BSWSBEQ3Z5SAQMH237W4INXODY/action/replication_record"}},"created_at":"2026-05-18T00:40:25.878506+00:00","updated_at":"2026-05-18T00:40:25.878506+00:00"}