{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OIOXG45VCGQQDKRTBEJW5CFJBH","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":"5630f706fdcb4e7768ae6f41775280f184b556d48c48d6c6c553125485d4678b","cross_cats_sorted":["math.DS","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-04-12T21:09:59Z","title_canon_sha256":"0ddc8d7c940fd7127d7ec4d3dc575d5ad27cdeabbd6b4e39e45dfa829cec7244"},"schema_version":"1.0","source":{"id":"1004.2060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2060","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2060v1","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2060","created_at":"2026-05-18T02:41:50Z"},{"alias_kind":"pith_short_12","alias_value":"OIOXG45VCGQQ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OIOXG45VCGQQDKRT","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OIOXG45V","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:df1f136796f268c44546ba631ff5dc30f59e9e7e0444bb531d4e488dfe258e35","target":"graph","created_at":"2026-05-18T02:41:50Z","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 prove that a free group F_2 admits a faithful discrete representation into Diff_{+}(I). We also prove that F_2 admits a faithful discrete representation into Homeo_{+}(I). Some properties of these representations have been studied. In the last section we raise several questions.","authors_text":"Azer Akhmedov","cross_cats":["math.DS","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-04-12T21:09:59Z","title":"On free discrete subgroups of Diff(I)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2060","kind":"arxiv","version":1},"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":"sha256:3c4a06d086d02d4a7db67898d202b8131a4a9f208c477ed47f1e81cf7b04ddda","target":"record","created_at":"2026-05-18T02:41:50Z","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":"5630f706fdcb4e7768ae6f41775280f184b556d48c48d6c6c553125485d4678b","cross_cats_sorted":["math.DS","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2010-04-12T21:09:59Z","title_canon_sha256":"0ddc8d7c940fd7127d7ec4d3dc575d5ad27cdeabbd6b4e39e45dfa829cec7244"},"schema_version":"1.0","source":{"id":"1004.2060","kind":"arxiv","version":1}},"canonical_sha256":"721d7373b511a101aa3309136e88a909f5c84ed59da7327a0b819612e0bea10f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"721d7373b511a101aa3309136e88a909f5c84ed59da7327a0b819612e0bea10f","first_computed_at":"2026-05-18T02:41:50.894448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:50.894448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5IB8Uzbs/yP/1dls7p1Bm4x54FU4B0SzREhRS1SPK0Tdxpp7mLy0G4yATARopQtFeAKGuZJh4gTZ3wmDuBxeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:50.895010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.2060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c4a06d086d02d4a7db67898d202b8131a4a9f208c477ed47f1e81cf7b04ddda","sha256:df1f136796f268c44546ba631ff5dc30f59e9e7e0444bb531d4e488dfe258e35"],"state_sha256":"f7f81063c062ec64fe124933f0134e8ed9cf9e789e9e699ab966c0676da33f13"}