{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GBGNJ2RTNV746QJFYLNAXK6RU7","short_pith_number":"pith:GBGNJ2RT","schema_version":"1.0","canonical_sha256":"304cd4ea336d7fcf4125c2da0babd1a7f2f752fa22dc4038111ea1a81ef2f816","source":{"kind":"arxiv","id":"1211.4814","version":4},"attestation_state":"computed","paper":{"title":"Generic orbits and type isolation in the Gurarij space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.FA","authors_text":"C. Ward Henson, Ita\\\"i Ben Yaacov (ICJ)","submitted_at":"2012-11-20T17:48:45Z","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1211.4814","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-20T17:48:45Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"34a899fae092abf2a29bee675d0bc0d4882164234d6d0d27846ccfd5e3d715ba","abstract_canon_sha256":"2c4310c22d80183a91cdb13a49d8d35038e4d9b073dfca845c11ed3b90bb8ab7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:14.578268Z","signature_b64":"9x+vaiNwN0USz1iBC/TSNGlUSnRqW5H3nQfSUMv5fQGtUiVi7AYuuhr0uyEWdw/iY00lMCER9/EB4BJTJu8rCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"304cd4ea336d7fcf4125c2da0babd1a7f2f752fa22dc4038111ea1a81ef2f816","last_reissued_at":"2026-05-18T01:19:14.577759Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:14.577759Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generic orbits and type isolation in the Gurarij space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.FA","authors_text":"C. Ward Henson, Ita\\\"i Ben Yaacov (ICJ)","submitted_at":"2012-11-20T17:48:45Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4814","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.4814","created_at":"2026-05-18T01:19:14.577839+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.4814v4","created_at":"2026-05-18T01:19:14.577839+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4814","created_at":"2026-05-18T01:19:14.577839+00:00"},{"alias_kind":"pith_short_12","alias_value":"GBGNJ2RTNV74","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GBGNJ2RTNV746QJF","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GBGNJ2RT","created_at":"2026-05-18T12:27:06.952714+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GBGNJ2RTNV746QJFYLNAXK6RU7","json":"https://pith.science/pith/GBGNJ2RTNV746QJFYLNAXK6RU7.json","graph_json":"https://pith.science/api/pith-number/GBGNJ2RTNV746QJFYLNAXK6RU7/graph.json","events_json":"https://pith.science/api/pith-number/GBGNJ2RTNV746QJFYLNAXK6RU7/events.json","paper":"https://pith.science/paper/GBGNJ2RT"},"agent_actions":{"view_html":"https://pith.science/pith/GBGNJ2RTNV746QJFYLNAXK6RU7","download_json":"https://pith.science/pith/GBGNJ2RTNV746QJFYLNAXK6RU7.json","view_paper":"https://pith.science/paper/GBGNJ2RT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.4814&json=true","fetch_graph":"https://pith.science/api/pith-number/GBGNJ2RTNV746QJFYLNAXK6RU7/graph.json","fetch_events":"https://pith.science/api/pith-number/GBGNJ2RTNV746QJFYLNAXK6RU7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GBGNJ2RTNV746QJFYLNAXK6RU7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GBGNJ2RTNV746QJFYLNAXK6RU7/action/storage_attestation","attest_author":"https://pith.science/pith/GBGNJ2RTNV746QJFYLNAXK6RU7/action/author_attestation","sign_citation":"https://pith.science/pith/GBGNJ2RTNV746QJFYLNAXK6RU7/action/citation_signature","submit_replication":"https://pith.science/pith/GBGNJ2RTNV746QJFYLNAXK6RU7/action/replication_record"}},"created_at":"2026-05-18T01:19:14.577839+00:00","updated_at":"2026-05-18T01:19:14.577839+00:00"}