{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7HQW4OML5DDHB6OKPASRZDBAJN","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":"d2e4c82b3e317653fa219a326c7c43974993d13f3df49a91988df305960be615","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-15T19:59:28Z","title_canon_sha256":"6697ef68f8ab8b3474549b68188ce82331f8a5c5422468dc2a9830eb2ff8b510"},"schema_version":"1.0","source":{"id":"1408.3624","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3624","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3624v3","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3624","created_at":"2026-05-18T01:04:46Z"},{"alias_kind":"pith_short_12","alias_value":"7HQW4OML5DDH","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7HQW4OML5DDHB6OK","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7HQW4OML","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:4ededf057352d43bef35645c1c9427be583fb3fd7a91d4f3e91660b20c7f2181","target":"graph","created_at":"2026-05-18T01:04:46Z","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 give a presentation theorem for continuous first-order logic and Metric Abstract Elementary classes in terms of $L_{\\omega_1, \\omega}$ and Abstract Elementary Classes, respectively. This presentation is accomplished by analyzing dense subsets that are closed under functions. We extend this correspondence to types and saturation.","authors_text":"Will Boney","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-15T19:59:28Z","title":"A presentation theorem for continuous logic and Metric Abstract Elementary Classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3624","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":"sha256:087f1a92df2655d39090f8ca260af1a3bc9b207b90fb1c949984c38f12e08a3c","target":"record","created_at":"2026-05-18T01:04:46Z","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":"d2e4c82b3e317653fa219a326c7c43974993d13f3df49a91988df305960be615","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-15T19:59:28Z","title_canon_sha256":"6697ef68f8ab8b3474549b68188ce82331f8a5c5422468dc2a9830eb2ff8b510"},"schema_version":"1.0","source":{"id":"1408.3624","kind":"arxiv","version":3}},"canonical_sha256":"f9e16e398be8c670f9ca78251c8c204b6f27e4dcc705f7e1dfd58caef100a45b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9e16e398be8c670f9ca78251c8c204b6f27e4dcc705f7e1dfd58caef100a45b","first_computed_at":"2026-05-18T01:04:46.658601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:46.658601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CcV6wVPD69AiyDU/7/CRrMVZYJUpu8sdb+EmcE53lsRLlvJSVatGvqXQjwLFBBxunUl7mi3y3nZ2d74t3UUKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:46.659167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3624","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:087f1a92df2655d39090f8ca260af1a3bc9b207b90fb1c949984c38f12e08a3c","sha256:4ededf057352d43bef35645c1c9427be583fb3fd7a91d4f3e91660b20c7f2181"],"state_sha256":"648d68620112551b10adc424e54dfe74b438a1cf0ccc933a519e504f686a9b1d"}