{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BR5NRUKWGH3XQ2VB2MGPLN6OO2","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":"8355f60cc7c3d58feebba9ae466a4b825fa9fa8e87b0f3749b6daaa579b29d53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-05T18:50:41Z","title_canon_sha256":"7d3040fd6e616273eaf9e82f423dff2c9a7280e3b0030b44861348386f644dbf"},"schema_version":"1.0","source":{"id":"1803.01831","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01831","created_at":"2026-05-18T00:10:46Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01831v3","created_at":"2026-05-18T00:10:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01831","created_at":"2026-05-18T00:10:46Z"},{"alias_kind":"pith_short_12","alias_value":"BR5NRUKWGH3X","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BR5NRUKWGH3XQ2VB","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BR5NRUKW","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:d8aea3f129b5cfbf126be085dfc8111f9b7b49c84b6ea228d35f3136463dbd89","target":"graph","created_at":"2026-05-18T00:10:46Z","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 show that the quantifier elimination result for the Shelah-Spencer almost sure theories of sparse random graphs $G(n,n^{-\\alpha})$ given by Laskowski in $[7]$ extends to their various analogues. The analogues will be obtained as theories of generic structures of certain classes of finite structures with a notion of strong substructure induced by rank functions and we will call the generics Baldwin-Shi hypergraphs. In the process we give a method of constructing extensions whose `relative rank' is negative but arbitrarily small in context. We give a necessary and sufficient condition for the","authors_text":"Danul K. Gunatilleka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-05T18:50:41Z","title":"The theories of Baldwin-Shi hypergraphs and their atomic models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01831","kind":"arxiv","version":3},"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":"sha256:1661c769f9403eec9a452de7562a4775eaf4f483698b745f0e3625ed8ff04607","target":"record","created_at":"2026-05-18T00:10:46Z","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":"8355f60cc7c3d58feebba9ae466a4b825fa9fa8e87b0f3749b6daaa579b29d53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-03-05T18:50:41Z","title_canon_sha256":"7d3040fd6e616273eaf9e82f423dff2c9a7280e3b0030b44861348386f644dbf"},"schema_version":"1.0","source":{"id":"1803.01831","kind":"arxiv","version":3}},"canonical_sha256":"0c7ad8d15631f7786aa1d30cf5b7ce76958d418e0c7f74487439951a0ddc8e61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c7ad8d15631f7786aa1d30cf5b7ce76958d418e0c7f74487439951a0ddc8e61","first_computed_at":"2026-05-18T00:10:46.716955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:46.716955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/xfFOp2Ojql0g6Sjr1pUKiDh4GdBLP6gYCaAEAGm1VTAXpwfMdsUkA0r0D/rTN1N6ONt2jWfOSlRrmfR/xgvDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:46.717634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.01831","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1661c769f9403eec9a452de7562a4775eaf4f483698b745f0e3625ed8ff04607","sha256:d8aea3f129b5cfbf126be085dfc8111f9b7b49c84b6ea228d35f3136463dbd89"],"state_sha256":"42f09ff81e733d11dffaf686dafb347f5a62c23fc2e36ab30c92c260621fb575"}