{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BZIU2S7BMWBOBDOGPLTOWC7DRN","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":"bdedb8256c8f51d1b1795f5e3004439a2f6c248fcbe2ecadf0527019168b24ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-13T15:42:39Z","title_canon_sha256":"ed5ede08cdd3c87661c37b4c2817e7ee6f9cf19a515425cd530d272f988519aa"},"schema_version":"1.0","source":{"id":"1508.03252","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03252","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03252v4","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03252","created_at":"2026-05-18T00:46:32Z"},{"alias_kind":"pith_short_12","alias_value":"BZIU2S7BMWBO","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BZIU2S7BMWBOBDOG","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BZIU2S7B","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:3bb1ddd7e3ebb1c889fb0e98e79e78f49bb15ac7727030fa3727f7d449fd1d07","target":"graph","created_at":"2026-05-18T00:46:32Z","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":"This paper is part of a program initiated by Saharon Shelah to extend the model theory of first order logic to the non-elementary setting of abstract elementary classes (AECs). An abstract elementary class is a semantic generalization of the class of models of a complete first order theory with the elementary substructure relation. We examine the symmetry property of splitting (previously isolated by the first author) in AECs with amalgamation that satisfy a local definition of superstability.\n  The key results are a downward transfer of symmetry and a deduction of symmetry from failure of the","authors_text":"Monica M. VanDieren, Sebastien Vasey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-13T15:42:39Z","title":"Symmetry in abstract elementary classes with amalgamation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03252","kind":"arxiv","version":4},"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":"sha256:855e0e1b800bbdbf401a97d63c455f846381ea0ed342e52e39d0eab85c479851","target":"record","created_at":"2026-05-18T00:46:32Z","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":"bdedb8256c8f51d1b1795f5e3004439a2f6c248fcbe2ecadf0527019168b24ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-13T15:42:39Z","title_canon_sha256":"ed5ede08cdd3c87661c37b4c2817e7ee6f9cf19a515425cd530d272f988519aa"},"schema_version":"1.0","source":{"id":"1508.03252","kind":"arxiv","version":4}},"canonical_sha256":"0e514d4be16582e08dc67ae6eb0be38b4d5a41f3cab792f3ddbafc50b7c79436","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e514d4be16582e08dc67ae6eb0be38b4d5a41f3cab792f3ddbafc50b7c79436","first_computed_at":"2026-05-18T00:46:32.191288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:32.191288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ySJwJZFLS/zAQqPYLxaMy2mfn3oYKNYU9DFw0NUgT8htg6+G+lDr4SJeSvCglaD7yOdjEwE4qiQWCeCVaS4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:32.191983Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03252","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:855e0e1b800bbdbf401a97d63c455f846381ea0ed342e52e39d0eab85c479851","sha256:3bb1ddd7e3ebb1c889fb0e98e79e78f49bb15ac7727030fa3727f7d449fd1d07"],"state_sha256":"9798f955a160250a1abcf87181b180782778fbf938f2fc13774fca9eb6f57d5c"}