{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:4VOO7FOAMTDMHMDL4345L4CREV","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":"3acacbc5f64408b380b857992a4fe2ca35270a663c19b51c1af67bebdb10f588","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-17T04:05:10Z","title_canon_sha256":"cbd20be9fadfb77c811926fe70b35516b2d19d40706cfdc2a726951c7358ab72"},"schema_version":"1.0","source":{"id":"0904.2626","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2626","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2626v2","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2626","created_at":"2026-05-18T03:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"4VOO7FOAMTDM","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4VOO7FOAMTDMHMDL","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4VOO7FOA","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:00c0492bfad867ca622ad607ba6d072907adc605233fb33235def56681d74b0b","target":"graph","created_at":"2026-05-18T03:14:27Z","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 show that the free group of rank 2 is a limit of 2-markings of Thompson's group F in the space of all 2-marked groups. More specifically, we find a sequence of generating pairs for F so that as one goes out the sequence, the length of the shortest relation satisfied by the generating pair goes to infinity.","authors_text":"Matthew G. Brin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-17T04:05:10Z","title":"The Free Group of Rank 2 is a Limit of Thompson's Group F"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2626","kind":"arxiv","version":2},"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":"sha256:449efd9e9136724931d2d7b00399d73f2966ba80f31cb9d7011b98300618b571","target":"record","created_at":"2026-05-18T03:14:27Z","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":"3acacbc5f64408b380b857992a4fe2ca35270a663c19b51c1af67bebdb10f588","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-04-17T04:05:10Z","title_canon_sha256":"cbd20be9fadfb77c811926fe70b35516b2d19d40706cfdc2a726951c7358ab72"},"schema_version":"1.0","source":{"id":"0904.2626","kind":"arxiv","version":2}},"canonical_sha256":"e55cef95c064c6c3b06be6f9d5f0512560382db8511714fe5ddd74fd92e7b62e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e55cef95c064c6c3b06be6f9d5f0512560382db8511714fe5ddd74fd92e7b62e","first_computed_at":"2026-05-18T03:14:27.128518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:27.128518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"42Tbxn9Au6YW7vek0Hns9rhwFHSv0PjEHFxJu8kfxNWKwvfnBZR1GDXejbJtvL7MKzo8zEI6LWWm6aYqbrXuAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:27.129149Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2626","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:449efd9e9136724931d2d7b00399d73f2966ba80f31cb9d7011b98300618b571","sha256:00c0492bfad867ca622ad607ba6d072907adc605233fb33235def56681d74b0b"],"state_sha256":"032410c844d923979dc73f25bea80dbc14077745e29b5f3ba9c381e19841edda"}