{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MLTDISL6XO64T3KBGQ6HH5EJUL","short_pith_number":"pith:MLTDISL6","schema_version":"1.0","canonical_sha256":"62e634497ebbbdc9ed41343c73f489a2e19091765c2d4f67e4ad39ff0a5c5f60","source":{"kind":"arxiv","id":"1601.03345","version":1},"attestation_state":"computed","paper":{"title":"On definable Galois groups and the strong canonical base property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Anand Pillay, Daniel Palac\\'in","submitted_at":"2016-01-13T18:47:01Z","abstract_excerpt":"In \\cite{HPP}, Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that $T$ has the canonical base property in a strong form, \" internality to\" being replaced by \"algebraicity in\". In the current paper we give a reasonably robust definition of the \"strong canonical base property\" in a rather more general finite rank context than \\cite{HPP}, and prove its {\\em equivalence} with rigidity of the relevant definable Galois groups. The new direction is an elaboration on the old result that $1$-based groups are rigid."},"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":"1601.03345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-13T18:47:01Z","cross_cats_sorted":[],"title_canon_sha256":"913982d409b8fd45b7a4249c61423a794cc71f218ac413c26ebee875a4c8ec6c","abstract_canon_sha256":"e504ec2044eb8710c488c79726a9799cd740e21fd193c15a016df7dd44cd2be9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:54.732210Z","signature_b64":"irJ5n37QhfYGA+3K3Fsj45mqQ35RqdCQA/p1CYHrq3rvOOw+i+oh+UMHAyRHIR9qHmay9jqLz9G7rgx80CmxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62e634497ebbbdc9ed41343c73f489a2e19091765c2d4f67e4ad39ff0a5c5f60","last_reissued_at":"2026-05-18T01:22:54.731725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:54.731725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On definable Galois groups and the strong canonical base property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Anand Pillay, Daniel Palac\\'in","submitted_at":"2016-01-13T18:47:01Z","abstract_excerpt":"In \\cite{HPP}, Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that $T$ has the canonical base property in a strong form, \" internality to\" being replaced by \"algebraicity in\". In the current paper we give a reasonably robust definition of the \"strong canonical base property\" in a rather more general finite rank context than \\cite{HPP}, and prove its {\\em equivalence} with rigidity of the relevant definable Galois groups. The new direction is an elaboration on the old result that $1$-based groups are rigid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03345","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":"1601.03345","created_at":"2026-05-18T01:22:54.731792+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.03345v1","created_at":"2026-05-18T01:22:54.731792+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03345","created_at":"2026-05-18T01:22:54.731792+00:00"},{"alias_kind":"pith_short_12","alias_value":"MLTDISL6XO64","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MLTDISL6XO64T3KB","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MLTDISL6","created_at":"2026-05-18T12:30:32.724797+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/MLTDISL6XO64T3KBGQ6HH5EJUL","json":"https://pith.science/pith/MLTDISL6XO64T3KBGQ6HH5EJUL.json","graph_json":"https://pith.science/api/pith-number/MLTDISL6XO64T3KBGQ6HH5EJUL/graph.json","events_json":"https://pith.science/api/pith-number/MLTDISL6XO64T3KBGQ6HH5EJUL/events.json","paper":"https://pith.science/paper/MLTDISL6"},"agent_actions":{"view_html":"https://pith.science/pith/MLTDISL6XO64T3KBGQ6HH5EJUL","download_json":"https://pith.science/pith/MLTDISL6XO64T3KBGQ6HH5EJUL.json","view_paper":"https://pith.science/paper/MLTDISL6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.03345&json=true","fetch_graph":"https://pith.science/api/pith-number/MLTDISL6XO64T3KBGQ6HH5EJUL/graph.json","fetch_events":"https://pith.science/api/pith-number/MLTDISL6XO64T3KBGQ6HH5EJUL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MLTDISL6XO64T3KBGQ6HH5EJUL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MLTDISL6XO64T3KBGQ6HH5EJUL/action/storage_attestation","attest_author":"https://pith.science/pith/MLTDISL6XO64T3KBGQ6HH5EJUL/action/author_attestation","sign_citation":"https://pith.science/pith/MLTDISL6XO64T3KBGQ6HH5EJUL/action/citation_signature","submit_replication":"https://pith.science/pith/MLTDISL6XO64T3KBGQ6HH5EJUL/action/replication_record"}},"created_at":"2026-05-18T01:22:54.731792+00:00","updated_at":"2026-05-18T01:22:54.731792+00:00"}