{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WEXHCBRZNS5D5AP4EUCCUPSMBL","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":"25c09fecbba7e8f14fc358d078ee3e4166b599957e5d22ff6bc212c6c447e6d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-18T14:50:57Z","title_canon_sha256":"8173d3514d84c88365da46587af0b43f82ce2d9f754a15e4330ce53b69e56919"},"schema_version":"1.0","source":{"id":"1103.3638","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3638","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3638v1","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3638","created_at":"2026-05-18T04:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"WEXHCBRZNS5D","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WEXHCBRZNS5D5AP4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WEXHCBRZ","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:6958af29c99e15ae870101c3e57f92369a37a399a86faa7977d556558f412da0","target":"graph","created_at":"2026-05-18T04:26:32Z","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":"An intermediate stage in Hrushovski's construction of flat strongly minimal structures in a relational language L produces omega-stable structures of rank omega. We analyze the pregeometries given by forking on the regular type of rank omega in these structures. We show that varying L can affect the (local) isomorphism type of the pregeometry, but not its finite subpregeometries. A sequel will compare these to the pregeometries of the strongly minimal structures.","authors_text":"David M. Evans, Marco S. Ferreira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-18T14:50:57Z","title":"The geometry of Hrushovski constructions, I. The uncollapsed case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3638","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:dcf38683506d471d872da832e712183c4341c4c713efd005ed975ec38d2d01d1","target":"record","created_at":"2026-05-18T04:26:32Z","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":"25c09fecbba7e8f14fc358d078ee3e4166b599957e5d22ff6bc212c6c447e6d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-18T14:50:57Z","title_canon_sha256":"8173d3514d84c88365da46587af0b43f82ce2d9f754a15e4330ce53b69e56919"},"schema_version":"1.0","source":{"id":"1103.3638","kind":"arxiv","version":1}},"canonical_sha256":"b12e7106396cba3e81fc25042a3e4c0aca20ec2564e9bf50a6c9de7cf8e1d917","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b12e7106396cba3e81fc25042a3e4c0aca20ec2564e9bf50a6c9de7cf8e1d917","first_computed_at":"2026-05-18T04:26:32.232658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:32.232658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"frBujgTbMz6uNpKuvynJOkcwNu0NWf1UIEih7XGQQKe+e4iUespeaHRr9BWRiC0pkVq9Fv41MIbsal2Xuv/SBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:32.233126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3638","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcf38683506d471d872da832e712183c4341c4c713efd005ed975ec38d2d01d1","sha256:6958af29c99e15ae870101c3e57f92369a37a399a86faa7977d556558f412da0"],"state_sha256":"4b647057a4aaf9a091ab19f5f7c2fe88b7582aaf7ae9ca9f3287352185bbdf83"}