{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:62MH7PITYVMP4Y2PW3WZPF66EQ","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":"3da47680e55806188127dade15c7da842f83cf94d8c831e1f2764b106a2e078a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-20T13:25:00Z","title_canon_sha256":"769b0e668b936b7fc8dc3111682619a45ff82376d01241767abfd1b07d3d1390"},"schema_version":"1.0","source":{"id":"1305.4523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4523","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4523v1","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4523","created_at":"2026-05-18T03:25:23Z"},{"alias_kind":"pith_short_12","alias_value":"62MH7PITYVMP","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"62MH7PITYVMP4Y2P","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"62MH7PIT","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:48f893d75c2f03efb391923d4c0a7fbed1fd851c44d35603d9316d9d5b9efb53","target":"graph","created_at":"2026-05-18T03:25:23Z","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":"In this paper we introduce a model theoretic construction for the theories of uniform layered domains and semifields introduced in the paper of Izhakian, Knebusch and Rowen. We prove that, for a given layering semiring L, the theory of uniform L-layered divisibly closed semifields is complete. In the process of doing so, we prove that this theory has quantifier elimination and consequently is model complete. Model completeness of uniform L-layered divisibly closed has some important consequences regarding the uniform L-layered semifields theory. One example involves equating polynomials. Namel","authors_text":"Tal Perri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-20T13:25:00Z","title":"A model theoretic construction for layered semifields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4523","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":"sha256:245cf5a7730df4a397e0eb41e568f72851209f3a95deaa276c7793ace84a7ac2","target":"record","created_at":"2026-05-18T03:25:23Z","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":"3da47680e55806188127dade15c7da842f83cf94d8c831e1f2764b106a2e078a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-20T13:25:00Z","title_canon_sha256":"769b0e668b936b7fc8dc3111682619a45ff82376d01241767abfd1b07d3d1390"},"schema_version":"1.0","source":{"id":"1305.4523","kind":"arxiv","version":1}},"canonical_sha256":"f6987fbd13c558fe634fb6ed9797de2400b9c5bf56d5f05cd6dd1cdd1427615b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6987fbd13c558fe634fb6ed9797de2400b9c5bf56d5f05cd6dd1cdd1427615b","first_computed_at":"2026-05-18T03:25:23.478940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:23.478940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JF9/N5daBFXoXaWH8dHJahetTkR2+AyQBTqG3npzD83SNzLO8lHtZfub7lhD9L1uDGiicSkKPZWtQz1kZG/GDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:23.479671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:245cf5a7730df4a397e0eb41e568f72851209f3a95deaa276c7793ace84a7ac2","sha256:48f893d75c2f03efb391923d4c0a7fbed1fd851c44d35603d9316d9d5b9efb53"],"state_sha256":"0788bd32ddecd6cc8c472a08b19b9f5583ed69caa7995a1f41a54400c140f1ad"}