{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:E63MSLHUQD7TCGZZ24GL3X4L2M","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":"1c3eb08d6ce61b1193d1616884fa9f004bf368835557d46d434a0612ce34194b","cross_cats_sorted":["math.AG","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-02-11T18:59:24Z","title_canon_sha256":"e6b6ada1da11e4de79009e8811c0708b2e60425456db2ba83d53cbc45ceff642"},"schema_version":"1.0","source":{"id":"1402.2600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2600","created_at":"2026-05-18T02:59:19Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2600v1","created_at":"2026-05-18T02:59:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2600","created_at":"2026-05-18T02:59:19Z"},{"alias_kind":"pith_short_12","alias_value":"E63MSLHUQD7T","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"E63MSLHUQD7TCGZZ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"E63MSLHU","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:8739f88b0ce681464369d6a7584044d2e65f3aa9dd515881266c0449d005052d","target":"graph","created_at":"2026-05-18T02:59:19Z","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":"Although contemporary model theory has been called \"algebraic geometry minus fields\", the formal methods of the two fields are radically different. This dissertation aims to shrink that gap by presenting a theory of logical schemes, geometric entities which relate to first-order logical theories in much the same way that algebraic schemes relate to commutative rings.\n  The construction relies on a Grothendieck-style representation theorem which associates every coherent or classical first-order theory with an affine scheme: a topological groupoid (the spectrum of the theory) together with a sh","authors_text":"Spencer Breiner","cross_cats":["math.AG","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-02-11T18:59:24Z","title":"Scheme representation for first-order logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2600","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":"sha256:8d8dab0a846c170ad89a133563f7ce837db20b23df460da6b11ab3ac1410c1db","target":"record","created_at":"2026-05-18T02:59:19Z","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":"1c3eb08d6ce61b1193d1616884fa9f004bf368835557d46d434a0612ce34194b","cross_cats_sorted":["math.AG","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-02-11T18:59:24Z","title_canon_sha256":"e6b6ada1da11e4de79009e8811c0708b2e60425456db2ba83d53cbc45ceff642"},"schema_version":"1.0","source":{"id":"1402.2600","kind":"arxiv","version":1}},"canonical_sha256":"27b6c92cf480ff311b39d70cbddf8bd30c9e7b799d9b034ba2e72b3c515fac5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27b6c92cf480ff311b39d70cbddf8bd30c9e7b799d9b034ba2e72b3c515fac5c","first_computed_at":"2026-05-18T02:59:19.153427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:19.153427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EidpScoAXKqLIg8AiOHJ3GA+ED7elc+wwQNvbv40roIIVyy+rrc5rzgyVCMK6OogshhZHtKHeSgzagQDn8p3Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:19.154183Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d8dab0a846c170ad89a133563f7ce837db20b23df460da6b11ab3ac1410c1db","sha256:8739f88b0ce681464369d6a7584044d2e65f3aa9dd515881266c0449d005052d"],"state_sha256":"03ebd5e349a5d63e6a3848a465282efacd52054073626ac20d383ff7bed6fe10"}