{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VHWWS4VB6GH2ACKPLW76DB7773","short_pith_number":"pith:VHWWS4VB","schema_version":"1.0","canonical_sha256":"a9ed6972a1f18fa0094f5dbfe187fffef99bb6b5264893eaebc7dc0edc68215d","source":{"kind":"arxiv","id":"1405.1532","version":2},"attestation_state":"computed","paper":{"title":"Consequences of the existence of ample generics and automorphism groups of homogeneous metric structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Maciej Malicki","submitted_at":"2014-05-07T08:27:47Z","abstract_excerpt":"We define a simple criterion for a homogeneous, complete metric structure $X$ that implies that the automorphism group $\\mbox{Aut}(X)$ satisfies all the main consequences of the existence of ample generics: it has the small index property, the automatic continuity property, and uncountable cofinality for non-open subgroups. Then we verify it for the Urysohn space $\\mbox{U}$, the Lebesgue probability measure algebra $\\mbox{MALG}$, and the Hilbert space $\\ell_2$, thus proving that $\\mbox{Iso}(\\mbox{U})$, $\\mbox{Aut}(\\mbox{MALG})$, $U(\\ell_2)$, and $O(\\ell_2)$ share these properties. We also form"},"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":"1405.1532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-05-07T08:27:47Z","cross_cats_sorted":[],"title_canon_sha256":"3326dac6f7ac7fdacfae00729014c9bd9ebb4179872c590f9ead705ffdb91f83","abstract_canon_sha256":"126f4b4744c4c88a5433bc68bf03f80f8315089d48af455e54955eeef1867b5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:03.090204Z","signature_b64":"Bj1JMWNVgV/y4tsXtEyXU4xGqllOeFp5TPaCnAWCzgpxs/uMRz6ANIMOLzUw+rjAhNVwFfwBmahsXh9rurOsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9ed6972a1f18fa0094f5dbfe187fffef99bb6b5264893eaebc7dc0edc68215d","last_reissued_at":"2026-05-18T01:26:03.089692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:03.089692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Consequences of the existence of ample generics and automorphism groups of homogeneous metric structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Maciej Malicki","submitted_at":"2014-05-07T08:27:47Z","abstract_excerpt":"We define a simple criterion for a homogeneous, complete metric structure $X$ that implies that the automorphism group $\\mbox{Aut}(X)$ satisfies all the main consequences of the existence of ample generics: it has the small index property, the automatic continuity property, and uncountable cofinality for non-open subgroups. Then we verify it for the Urysohn space $\\mbox{U}$, the Lebesgue probability measure algebra $\\mbox{MALG}$, and the Hilbert space $\\ell_2$, thus proving that $\\mbox{Iso}(\\mbox{U})$, $\\mbox{Aut}(\\mbox{MALG})$, $U(\\ell_2)$, and $O(\\ell_2)$ share these properties. We also form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1532","kind":"arxiv","version":2},"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":"1405.1532","created_at":"2026-05-18T01:26:03.089783+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.1532v2","created_at":"2026-05-18T01:26:03.089783+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1532","created_at":"2026-05-18T01:26:03.089783+00:00"},{"alias_kind":"pith_short_12","alias_value":"VHWWS4VB6GH2","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"VHWWS4VB6GH2ACKP","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"VHWWS4VB","created_at":"2026-05-18T12:28:54.890064+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/VHWWS4VB6GH2ACKPLW76DB7773","json":"https://pith.science/pith/VHWWS4VB6GH2ACKPLW76DB7773.json","graph_json":"https://pith.science/api/pith-number/VHWWS4VB6GH2ACKPLW76DB7773/graph.json","events_json":"https://pith.science/api/pith-number/VHWWS4VB6GH2ACKPLW76DB7773/events.json","paper":"https://pith.science/paper/VHWWS4VB"},"agent_actions":{"view_html":"https://pith.science/pith/VHWWS4VB6GH2ACKPLW76DB7773","download_json":"https://pith.science/pith/VHWWS4VB6GH2ACKPLW76DB7773.json","view_paper":"https://pith.science/paper/VHWWS4VB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.1532&json=true","fetch_graph":"https://pith.science/api/pith-number/VHWWS4VB6GH2ACKPLW76DB7773/graph.json","fetch_events":"https://pith.science/api/pith-number/VHWWS4VB6GH2ACKPLW76DB7773/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VHWWS4VB6GH2ACKPLW76DB7773/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VHWWS4VB6GH2ACKPLW76DB7773/action/storage_attestation","attest_author":"https://pith.science/pith/VHWWS4VB6GH2ACKPLW76DB7773/action/author_attestation","sign_citation":"https://pith.science/pith/VHWWS4VB6GH2ACKPLW76DB7773/action/citation_signature","submit_replication":"https://pith.science/pith/VHWWS4VB6GH2ACKPLW76DB7773/action/replication_record"}},"created_at":"2026-05-18T01:26:03.089783+00:00","updated_at":"2026-05-18T01:26:03.089783+00:00"}