{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2RP26V7PVPUXAQ3PVWF24C5KNO","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":"2b65bf5669cabda871906dfed80fa457bbd0e430d1e2293d177993c5b0a7a94a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-06-30T17:20:03Z","title_canon_sha256":"b1fb0b7d7fda624e62c9f705d7e45400fe3e4eb765e106180d3ac14179c57102"},"schema_version":"1.0","source":{"id":"1207.0118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0118","created_at":"2026-05-18T03:52:00Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0118v1","created_at":"2026-05-18T03:52:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0118","created_at":"2026-05-18T03:52:00Z"},{"alias_kind":"pith_short_12","alias_value":"2RP26V7PVPUX","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2RP26V7PVPUXAQ3P","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2RP26V7P","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:7c319c7abd53e2a321a64cb847f61b39cd69ce0210a95ae7ee91b0aef020d449","target":"graph","created_at":"2026-05-18T03:52:00Z","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":"Let $A$ be an infinite set. Let $\\Omega(A)$ be the algebra over $A$ where every constant is a fundamental constant and every finitary function is a fundamental operation. We shall give a method of representing any algebra $\\mathcal{L}$ in the variety generated by $\\Omega(A)$ as limit reduced powers and even direct limits of limit reduced powers of $\\mathcal{L}$. If the algebra $\\mathcal{L}$ is elementarily equivalent to $\\Omega(A)$, then this construction represents $\\Omega(A)$ as a limit ultrapower and also as direct limits of limit ultrapowers of $\\Omega(A)$. This method therefore gives a me","authors_text":"Joseph Van Name","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-06-30T17:20:03Z","title":"Constructing Ultrapowers from Elementary Extensions of Full Clones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0118","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":"sha256:81a36f0aa9b9524a200a82c178432814622d57ce63a0e47db1b2798435a16d1c","target":"record","created_at":"2026-05-18T03:52:00Z","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":"2b65bf5669cabda871906dfed80fa457bbd0e430d1e2293d177993c5b0a7a94a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-06-30T17:20:03Z","title_canon_sha256":"b1fb0b7d7fda624e62c9f705d7e45400fe3e4eb765e106180d3ac14179c57102"},"schema_version":"1.0","source":{"id":"1207.0118","kind":"arxiv","version":1}},"canonical_sha256":"d45faf57efabe970436fad8bae0baa6ba4f43f7aa88071db2e31b5afab8387aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d45faf57efabe970436fad8bae0baa6ba4f43f7aa88071db2e31b5afab8387aa","first_computed_at":"2026-05-18T03:52:00.305021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:00.305021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SqdY0bvkbv/eaYWaMkNMgjaahuW0HbOhZQSN8fOG//iatw/oL/m8GWGec1QuEvX7TzTBqGdTWpRtopN8vGFLAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:00.305600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81a36f0aa9b9524a200a82c178432814622d57ce63a0e47db1b2798435a16d1c","sha256:7c319c7abd53e2a321a64cb847f61b39cd69ce0210a95ae7ee91b0aef020d449"],"state_sha256":"4bc702e4de5028dd66e99ef098168ea4978caa2db751aacb0bf7004c3be1a3e4"}