{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:43WFHJQQSNA3ORLRNV4HOQ7RIU","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":"ddfd06b2e17b13536a2183d0f25cabae074bc186eed2de2d62679401eee8b63e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-12-06T16:19:14Z","title_canon_sha256":"59391714bdbcb309cf1b3526f2fdd4ce7ad87fbcd57733d98d4341016c485172"},"schema_version":"1.0","source":{"id":"0912.1115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.1115","created_at":"2026-05-18T04:40:20Z"},{"alias_kind":"arxiv_version","alias_value":"0912.1115v2","created_at":"2026-05-18T04:40:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.1115","created_at":"2026-05-18T04:40:20Z"},{"alias_kind":"pith_short_12","alias_value":"43WFHJQQSNA3","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"43WFHJQQSNA3ORLR","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"43WFHJQQ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:5408fbea12ad6a99000074ddcc34c30a29ea3a5d2566ca3784c8779e3db95a31","target":"graph","created_at":"2026-05-18T04:40:20Z","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 study the notions generic stability, regularity, homogeneous pregeometries, quasiminimality, and their mutual relations, in an arbitrary first order theory T. We prove that \"infinite-dimensional homogeneous pregeometries\" coincide with generically stable strongly regular types (p(x),x=x). We prove that quasiminimal structures of cardinality at least aleph-2 are homogeneous pregeometries, We prove that the generic type of an arbitrary quasiminimal structure is locally strongly regular. Some of the results depend on a general dichotomy for regular-like types: generic stability, or existence o","authors_text":"Anand Pillay, Predrag Tanovic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-12-06T16:19:14Z","title":"Generic stability, regularity, and quasiminimality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1115","kind":"arxiv","version":2},"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":"sha256:99e906b3d499611edb4a98e578689a01fa64cab866a5b5878b7c9c37ec9d5c4c","target":"record","created_at":"2026-05-18T04:40:20Z","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":"ddfd06b2e17b13536a2183d0f25cabae074bc186eed2de2d62679401eee8b63e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-12-06T16:19:14Z","title_canon_sha256":"59391714bdbcb309cf1b3526f2fdd4ce7ad87fbcd57733d98d4341016c485172"},"schema_version":"1.0","source":{"id":"0912.1115","kind":"arxiv","version":2}},"canonical_sha256":"e6ec53a6109341b745716d787743f145031bf1d62482ca319bf239527fd1d09c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6ec53a6109341b745716d787743f145031bf1d62482ca319bf239527fd1d09c","first_computed_at":"2026-05-18T04:40:20.459190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:20.459190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1BLfZUymcsnGZCteBsWnhlnpuvbmGxaV7dsgJaU4d372TjXfs0rjYObUD4RAqplPdsW9/EJuXLhTebqWRAcdDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:20.459831Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.1115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99e906b3d499611edb4a98e578689a01fa64cab866a5b5878b7c9c37ec9d5c4c","sha256:5408fbea12ad6a99000074ddcc34c30a29ea3a5d2566ca3784c8779e3db95a31"],"state_sha256":"c79798f03b2cc5c9634395e7bd0b2779d5ab6face52a459b48d510e9a44920b0"}