{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SZIFOLPZ2TT77BHJVO7Q22XMRL","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":"f574c9f2c51ec31eabe324977435ebbf4b505ddec9655cc6d53373218c53f191","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-09-27T17:02:14Z","title_canon_sha256":"e0034484cb013a03131c7a68695f9c51a59ac3916fd3313f5995160c9aade7b6"},"schema_version":"1.0","source":{"id":"1709.09626","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09626","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09626v2","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09626","created_at":"2026-05-17T23:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"SZIFOLPZ2TT7","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SZIFOLPZ2TT77BHJ","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SZIFOLPZ","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:495216a1f323940f423c0950ad619c4ec4b27aa9b9a75067dd3e6a4044bd767f","target":"graph","created_at":"2026-05-17T23:43:38Z","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 theory $T_{m,n}$ of existentially closed incidence structures omitting the complete incidence structure $K_{m,n}$, which can also be viewed as existentially closed $K_{m,n}$-free bipartite graphs. In the case $m = n = 2$, this is the theory of existentially closed projective planes. We give an $\\forall\\exists$-axiomatization of $T_{m,n}$, show that $T_{m,n}$ does not have a countable saturated model when $m,n\\geq 2$, and show that the existence of a prime model for $T_{2,2}$ is equivalent to a longstanding open question about finite projective planes. Finally, we analyze model the","authors_text":"Alex Kruckman, Gabriel Conant","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-09-27T17:02:14Z","title":"Independence in generic incidence structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09626","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:de83d109033733d49d2d56933f6e80833f918d4e65e0944c4d63905485ca7aed","target":"record","created_at":"2026-05-17T23:43:38Z","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":"f574c9f2c51ec31eabe324977435ebbf4b505ddec9655cc6d53373218c53f191","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-09-27T17:02:14Z","title_canon_sha256":"e0034484cb013a03131c7a68695f9c51a59ac3916fd3313f5995160c9aade7b6"},"schema_version":"1.0","source":{"id":"1709.09626","kind":"arxiv","version":2}},"canonical_sha256":"9650572df9d4e7ff84e9abbf0d6aec8ac07b73f0f8f3c2bce89ae5e1963e2db5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9650572df9d4e7ff84e9abbf0d6aec8ac07b73f0f8f3c2bce89ae5e1963e2db5","first_computed_at":"2026-05-17T23:43:38.506993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:38.506993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1MY4xceJ34P1WYRfUe3oK6kM9iYv83WCrBWUoVpfeXXwzbV48ftWBp1wIP4I/97R/7Bujjgd0r6epG76Z16AAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:38.507590Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09626","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de83d109033733d49d2d56933f6e80833f918d4e65e0944c4d63905485ca7aed","sha256:495216a1f323940f423c0950ad619c4ec4b27aa9b9a75067dd3e6a4044bd767f"],"state_sha256":"343721aed04669d42f1cbf9e974f0580fae26f766e1a0df95590f55e1a52574e"}