{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XMQIN3WSTTZE2JDWDCSFPQKSF2","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":"8fd6413668a6d566c63cd0de73c7b1accd3645880cd0327e81de3f94a07a78fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-30T01:38:52Z","title_canon_sha256":"9eec462cac827b3951161c1233be57c635cfb98f5f7d7b9a16e33c8fefbba31b"},"schema_version":"1.0","source":{"id":"1705.00261","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00261","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00261v1","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00261","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"pith_short_12","alias_value":"XMQIN3WSTTZE","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XMQIN3WSTTZE2JDW","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XMQIN3WS","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:2a62a8b28fc9eb89bd49e05c314f625b8c0e76489ca7029c43a84eb4674f94ce","target":"graph","created_at":"2026-05-18T00:45:20Z","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 model theory of the $2$-sorted structure $(\\mathbb{F}, \\mathbb{C};\\chi)$, where $\\mathbb{F}$ is an algebraic closure of a finite field of characteristic $p$, $\\mathbb{C}$ is the field of complex numbers and $\\chi: \\mathbb{F} \\to \\mathbb{C}$ is an injective, multiplication preserving map. We obtain an axiomatization $\\mathrm{ACFC}_p$ of $\\mathrm{Th}(\\mathbb{F},\\mathbb{C};\\chi)$ in a suitable language $L$, classify the models of $\\mathrm{ACFC}_p$ up to isomorphism, prove a modified model companion result, give various descriptions of definable sets inside a model of $\\mathrm{ACFC}_p","authors_text":"Minh Chieu Tran, Tigran Hakobyan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-30T01:38:52Z","title":"Algebraically Closed Fields with a Generic Multiplicative Character"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00261","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:bc541db49a9b3af83002ade0e6e9e3ca1951709d5973e8c273b242c0b1358dda","target":"record","created_at":"2026-05-18T00:45:20Z","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":"8fd6413668a6d566c63cd0de73c7b1accd3645880cd0327e81de3f94a07a78fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-04-30T01:38:52Z","title_canon_sha256":"9eec462cac827b3951161c1233be57c635cfb98f5f7d7b9a16e33c8fefbba31b"},"schema_version":"1.0","source":{"id":"1705.00261","kind":"arxiv","version":1}},"canonical_sha256":"bb2086eed29cf24d247618a457c1522ebe54f22868c31565ce3aae2e25b51aff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb2086eed29cf24d247618a457c1522ebe54f22868c31565ce3aae2e25b51aff","first_computed_at":"2026-05-18T00:45:20.984968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:20.984968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T9U7fQKqZXZC7weqAXnEGA3w0tRYvs6NIrct2iK2ZBCO89uZCmbZt7wYFOE8bLbu6GIsHINw9OT+BsxLCywEAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:20.985771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00261","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc541db49a9b3af83002ade0e6e9e3ca1951709d5973e8c273b242c0b1358dda","sha256:2a62a8b28fc9eb89bd49e05c314f625b8c0e76489ca7029c43a84eb4674f94ce"],"state_sha256":"d9ddcbb9089f082a983618fe5f9be365228d928508c08bcd93f8a648ef8f9f47"}