{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KPSZO7TWGNMKCWZ4SQLXIPZDL4","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":"54c272dd3ec6223c814c8bb40f07740a4c92205f858cfc2c50e8482dfd0c8327","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-03-12T19:54:41Z","title_canon_sha256":"fb5bd6942c10c521e72215e56efdca41be0c118ac87e52a7bb3d67a5ddba9d6f"},"schema_version":"1.0","source":{"id":"1403.3079","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3079","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3079v3","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3079","created_at":"2026-05-18T02:25:26Z"},{"alias_kind":"pith_short_12","alias_value":"KPSZO7TWGNMK","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KPSZO7TWGNMKCWZ4","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KPSZO7TW","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:1d9482946c6aea0412d69f24022d2d9e73e0184d7cedb3300e4615d1f54d87ac","target":"graph","created_at":"2026-05-18T02:25:26Z","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 definable sets $D$ of SU-rank 1 in $M^{eq}$, where $M$ is a countable homogeneous and simple structure in a language with finite relational vocabulary. Each such $D$ can be seen as a `canonically embedded structure', which inherits all relations on $D$ which are definable in $M^{eq}$, and has no other definable relations. Our results imply that if no relation symbol of the language of $M$ has arity higher than 2, then there is a close relationship between triviality of dependence and $D$ being a reduct of a binary random structure. Somewhat more preciely: (a) if for every $n \\geq 2$, ","authors_text":"Ove Ahlman, Vera Koponen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-03-12T19:54:41Z","title":"On sets with rank one in simple homogeneous structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3079","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":"sha256:4da4ab27b1d4e3862c82053bfb91549617dfb04606e1e6e285b647e517de36d0","target":"record","created_at":"2026-05-18T02:25:26Z","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":"54c272dd3ec6223c814c8bb40f07740a4c92205f858cfc2c50e8482dfd0c8327","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-03-12T19:54:41Z","title_canon_sha256":"fb5bd6942c10c521e72215e56efdca41be0c118ac87e52a7bb3d67a5ddba9d6f"},"schema_version":"1.0","source":{"id":"1403.3079","kind":"arxiv","version":3}},"canonical_sha256":"53e5977e763358a15b3c9417743f235f2f8be052148dc4711c505d78211fdca3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53e5977e763358a15b3c9417743f235f2f8be052148dc4711c505d78211fdca3","first_computed_at":"2026-05-18T02:25:26.570351Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:26.570351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EeKMUDAGq0UU9aSVPg78KLLAKgygBUpryGLqrQ9Fc7bzHf31S1yxfT8gSmj3mIRNgTv/K4luH3q+IjlQgEGzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:26.570891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3079","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4da4ab27b1d4e3862c82053bfb91549617dfb04606e1e6e285b647e517de36d0","sha256:1d9482946c6aea0412d69f24022d2d9e73e0184d7cedb3300e4615d1f54d87ac"],"state_sha256":"46df87ad7bc132663559665935848b6b483aeefa1207d52cc1a328dbe683a3f1"}