{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GBGNJ2RTNV746QJFYLNAXK6RU7","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":"2c4310c22d80183a91cdb13a49d8d35038e4d9b073dfca845c11ed3b90bb8ab7","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-20T17:48:45Z","title_canon_sha256":"34a899fae092abf2a29bee675d0bc0d4882164234d6d0d27846ccfd5e3d715ba"},"schema_version":"1.0","source":{"id":"1211.4814","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4814","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4814v4","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4814","created_at":"2026-05-18T01:19:14Z"},{"alias_kind":"pith_short_12","alias_value":"GBGNJ2RTNV74","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GBGNJ2RTNV746QJF","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GBGNJ2RT","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:51b62a54c861eb22f621a9b59ab8b9228bd0938a4a12dd79667de6ffc383f632","target":"graph","created_at":"2026-05-18T01:19:14Z","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 question of when the space of embeddings of a separable Banach space $E$ into the separable Gurarij space $\\mathbf G$ admits a generic orbit under the action of the linear isometry group of $\\mathbf G$.  The question is recast in model-theoretic terms, namely type isolation and the existence of prime models.  We characterise isolated types over $E$ using tools from convex analysis.  We show that if the set of isolated types over $E$ is dense, then a dense $G\\_\\delta$ orbit exists, and otherwise all orbits are meagre.  We then study some (families of) examples with respect to this ","authors_text":"C. Ward Henson, Ita\\\"i Ben Yaacov (ICJ)","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-20T17:48:45Z","title":"Generic orbits and type isolation in the Gurarij space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4814","kind":"arxiv","version":4},"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:fd2b4cbe62e72c9868f31a4d2fe265e50b1ff1c7abc140f661055dfa3bdbb340","target":"record","created_at":"2026-05-18T01:19:14Z","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":"2c4310c22d80183a91cdb13a49d8d35038e4d9b073dfca845c11ed3b90bb8ab7","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-20T17:48:45Z","title_canon_sha256":"34a899fae092abf2a29bee675d0bc0d4882164234d6d0d27846ccfd5e3d715ba"},"schema_version":"1.0","source":{"id":"1211.4814","kind":"arxiv","version":4}},"canonical_sha256":"304cd4ea336d7fcf4125c2da0babd1a7f2f752fa22dc4038111ea1a81ef2f816","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"304cd4ea336d7fcf4125c2da0babd1a7f2f752fa22dc4038111ea1a81ef2f816","first_computed_at":"2026-05-18T01:19:14.577759Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:14.577759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9x+vaiNwN0USz1iBC/TSNGlUSnRqW5H3nQfSUMv5fQGtUiVi7AYuuhr0uyEWdw/iY00lMCER9/EB4BJTJu8rCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:14.578268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4814","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd2b4cbe62e72c9868f31a4d2fe265e50b1ff1c7abc140f661055dfa3bdbb340","sha256:51b62a54c861eb22f621a9b59ab8b9228bd0938a4a12dd79667de6ffc383f632"],"state_sha256":"1c6aec592f5d210d2d0cb6db5626e7c24756cc9491e4c28479ff7b4589fedcd9"}