{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:CDUJU4DXL5CXI4B4374FRKIBPD","short_pith_number":"pith:CDUJU4DX","schema_version":"1.0","canonical_sha256":"10e89a70775f4574703cdff858a90178e5cf15896d5479133a8fcc2cb6019a78","source":{"kind":"arxiv","id":"2605.20568","version":1},"attestation_state":"computed","paper":{"title":"On dense free subgroups of Lie groups -- revisited","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Emmanuel Breuillard, Tsachik Gelander","submitted_at":"2026-05-20T00:00:45Z","abstract_excerpt":"We show that every dense subgroup of a connected Lie group G contains a dense subgroup generated by 2d elements, where d=dim(G). We also give a detailed proof for the quantitive characterization of a contracting projective transformation in terms of the ratio between the two leading terms in its Cartan decomposition."},"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":"2605.20568","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-20T00:00:45Z","cross_cats_sorted":[],"title_canon_sha256":"85fad33e417a7882501d51b979432ec93cd076d33316fc846a495ed5160778fa","abstract_canon_sha256":"0d6ffa30a8deb0c91175d1d1becf0a88bf3832461b5683ee2310922e16100040"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:42.721647Z","signature_b64":"5CAh3uIflDiIGXvcAKSbGF718iZ6HzVURs96V7EXM8XZ4WMEUbLrjCybn0HHPxUn2qLkCmuBlSTkNtRSY3xEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10e89a70775f4574703cdff858a90178e5cf15896d5479133a8fcc2cb6019a78","last_reissued_at":"2026-05-21T01:04:42.721014Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:42.721014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On dense free subgroups of Lie groups -- revisited","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Emmanuel Breuillard, Tsachik Gelander","submitted_at":"2026-05-20T00:00:45Z","abstract_excerpt":"We show that every dense subgroup of a connected Lie group G contains a dense subgroup generated by 2d elements, where d=dim(G). We also give a detailed proof for the quantitive characterization of a contracting projective transformation in terms of the ratio between the two leading terms in its Cartan decomposition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20568","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.20568/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.20568","created_at":"2026-05-21T01:04:42.721114+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20568v1","created_at":"2026-05-21T01:04:42.721114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20568","created_at":"2026-05-21T01:04:42.721114+00:00"},{"alias_kind":"pith_short_12","alias_value":"CDUJU4DXL5CX","created_at":"2026-05-21T01:04:42.721114+00:00"},{"alias_kind":"pith_short_16","alias_value":"CDUJU4DXL5CXI4B4","created_at":"2026-05-21T01:04:42.721114+00:00"},{"alias_kind":"pith_short_8","alias_value":"CDUJU4DX","created_at":"2026-05-21T01:04:42.721114+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/CDUJU4DXL5CXI4B4374FRKIBPD","json":"https://pith.science/pith/CDUJU4DXL5CXI4B4374FRKIBPD.json","graph_json":"https://pith.science/api/pith-number/CDUJU4DXL5CXI4B4374FRKIBPD/graph.json","events_json":"https://pith.science/api/pith-number/CDUJU4DXL5CXI4B4374FRKIBPD/events.json","paper":"https://pith.science/paper/CDUJU4DX"},"agent_actions":{"view_html":"https://pith.science/pith/CDUJU4DXL5CXI4B4374FRKIBPD","download_json":"https://pith.science/pith/CDUJU4DXL5CXI4B4374FRKIBPD.json","view_paper":"https://pith.science/paper/CDUJU4DX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20568&json=true","fetch_graph":"https://pith.science/api/pith-number/CDUJU4DXL5CXI4B4374FRKIBPD/graph.json","fetch_events":"https://pith.science/api/pith-number/CDUJU4DXL5CXI4B4374FRKIBPD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CDUJU4DXL5CXI4B4374FRKIBPD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CDUJU4DXL5CXI4B4374FRKIBPD/action/storage_attestation","attest_author":"https://pith.science/pith/CDUJU4DXL5CXI4B4374FRKIBPD/action/author_attestation","sign_citation":"https://pith.science/pith/CDUJU4DXL5CXI4B4374FRKIBPD/action/citation_signature","submit_replication":"https://pith.science/pith/CDUJU4DXL5CXI4B4374FRKIBPD/action/replication_record"}},"created_at":"2026-05-21T01:04:42.721114+00:00","updated_at":"2026-05-21T01:04:42.721114+00:00"}