{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KCGXKL3E4VQ6FKCPQTXPVLFSHY","short_pith_number":"pith:KCGXKL3E","canonical_record":{"source":{"id":"1312.1855","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-06T13:33:00Z","cross_cats_sorted":[],"title_canon_sha256":"9eaa91c8c9a64ced111059dd0003538c82686dde16ab2cef4475aeafc68a76e9","abstract_canon_sha256":"418571b831cea55cba51e2c201130f10355bf05e0b52ba80463410ae83085c84"},"schema_version":"1.0"},"canonical_sha256":"508d752f64e561e2a84f84eefaacb23e2c8c167310883542f3efa12aaaebae12","source":{"kind":"arxiv","id":"1312.1855","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1855","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1855v1","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1855","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"KCGXKL3E4VQ6","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KCGXKL3E4VQ6FKCP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KCGXKL3E","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KCGXKL3E4VQ6FKCPQTXPVLFSHY","target":"record","payload":{"canonical_record":{"source":{"id":"1312.1855","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-06T13:33:00Z","cross_cats_sorted":[],"title_canon_sha256":"9eaa91c8c9a64ced111059dd0003538c82686dde16ab2cef4475aeafc68a76e9","abstract_canon_sha256":"418571b831cea55cba51e2c201130f10355bf05e0b52ba80463410ae83085c84"},"schema_version":"1.0"},"canonical_sha256":"508d752f64e561e2a84f84eefaacb23e2c8c167310883542f3efa12aaaebae12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:29.290266Z","signature_b64":"mQqv/Eua42v0+jkuA85RR/HuPoOuc+4U43XUALMwxn1aZBg6Xnw4V9orc147XVilbUt/j8aedRBsrjCq+sJmCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"508d752f64e561e2a84f84eefaacb23e2c8c167310883542f3efa12aaaebae12","last_reissued_at":"2026-05-18T00:44:29.289608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:29.289608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.1855","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IGTXPt+Te/3pBwEVymBELtDdAPwbw3hp+6+KsT5W2+1dInGQ68zbPCfRmZ8bXezDy3maSpe8tOM8q7zOdFQaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:32:36.706425Z"},"content_sha256":"d315763ce591243c745fc7aeee77a3b91ee5bac18fc36113cc03534a8207f5c7","schema_version":"1.0","event_id":"sha256:d315763ce591243c745fc7aeee77a3b91ee5bac18fc36113cc03534a8207f5c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KCGXKL3E4VQ6FKCPQTXPVLFSHY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Embeddings into Thompson's group $V$ and $co\\mathcal{CF}$ groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Collin Bleak, Francesco Matucci, Max Neunh\\\"offer","submitted_at":"2013-12-06T13:33:00Z","abstract_excerpt":"Lehnert and Schweitzer show in [20] that R. Thompson's group $V$ is a co-context-free ($co\\mathcal{CF}$) group, thus implying that all of its finitely generated subgroups are also $co\\mathcal{CF}$ groups. Also, Lehnert shows in his thesis that $V$ embeds inside the $co\\mathcal{CF}$ group $\\mathrm{QAut}(\\mathcal{T}_{2,c})$, which is a group of particular bijections on the vertices of an infinite binary $2$-edge-colored tree, and he conjectures that $\\mathrm{QAut}(\\mathcal{T}_{2,c})$ is a universal $co\\mathcal{CF}$ group. We show that $\\mathrm{QAut}(\\mathcal{T}_{2,c})$ embeds into $V$, and thus "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1855","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lOgLh03aUZBf56JwRNw0NqZkVcGSyd5fr0yaWpmaq42revVSAGPh/JzKcTnX4fjTkmDTVVTtWoe2cZ43X5LtAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:32:36.706811Z"},"content_sha256":"970fe168d4abec95e0d1787ace9504f2cf6e9efd2b08be3264649befb0de25e7","schema_version":"1.0","event_id":"sha256:970fe168d4abec95e0d1787ace9504f2cf6e9efd2b08be3264649befb0de25e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KCGXKL3E4VQ6FKCPQTXPVLFSHY/bundle.json","state_url":"https://pith.science/pith/KCGXKL3E4VQ6FKCPQTXPVLFSHY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KCGXKL3E4VQ6FKCPQTXPVLFSHY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T19:32:36Z","links":{"resolver":"https://pith.science/pith/KCGXKL3E4VQ6FKCPQTXPVLFSHY","bundle":"https://pith.science/pith/KCGXKL3E4VQ6FKCPQTXPVLFSHY/bundle.json","state":"https://pith.science/pith/KCGXKL3E4VQ6FKCPQTXPVLFSHY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KCGXKL3E4VQ6FKCPQTXPVLFSHY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KCGXKL3E4VQ6FKCPQTXPVLFSHY","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":"418571b831cea55cba51e2c201130f10355bf05e0b52ba80463410ae83085c84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-06T13:33:00Z","title_canon_sha256":"9eaa91c8c9a64ced111059dd0003538c82686dde16ab2cef4475aeafc68a76e9"},"schema_version":"1.0","source":{"id":"1312.1855","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1855","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1855v1","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1855","created_at":"2026-05-18T00:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"KCGXKL3E4VQ6","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KCGXKL3E4VQ6FKCP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KCGXKL3E","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:970fe168d4abec95e0d1787ace9504f2cf6e9efd2b08be3264649befb0de25e7","target":"graph","created_at":"2026-05-18T00:44:29Z","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":"Lehnert and Schweitzer show in [20] that R. Thompson's group $V$ is a co-context-free ($co\\mathcal{CF}$) group, thus implying that all of its finitely generated subgroups are also $co\\mathcal{CF}$ groups. Also, Lehnert shows in his thesis that $V$ embeds inside the $co\\mathcal{CF}$ group $\\mathrm{QAut}(\\mathcal{T}_{2,c})$, which is a group of particular bijections on the vertices of an infinite binary $2$-edge-colored tree, and he conjectures that $\\mathrm{QAut}(\\mathcal{T}_{2,c})$ is a universal $co\\mathcal{CF}$ group. We show that $\\mathrm{QAut}(\\mathcal{T}_{2,c})$ embeds into $V$, and thus ","authors_text":"Collin Bleak, Francesco Matucci, Max Neunh\\\"offer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-06T13:33:00Z","title":"Embeddings into Thompson's group $V$ and $co\\mathcal{CF}$ groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1855","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:d315763ce591243c745fc7aeee77a3b91ee5bac18fc36113cc03534a8207f5c7","target":"record","created_at":"2026-05-18T00:44:29Z","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":"418571b831cea55cba51e2c201130f10355bf05e0b52ba80463410ae83085c84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-06T13:33:00Z","title_canon_sha256":"9eaa91c8c9a64ced111059dd0003538c82686dde16ab2cef4475aeafc68a76e9"},"schema_version":"1.0","source":{"id":"1312.1855","kind":"arxiv","version":1}},"canonical_sha256":"508d752f64e561e2a84f84eefaacb23e2c8c167310883542f3efa12aaaebae12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"508d752f64e561e2a84f84eefaacb23e2c8c167310883542f3efa12aaaebae12","first_computed_at":"2026-05-18T00:44:29.289608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:29.289608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mQqv/Eua42v0+jkuA85RR/HuPoOuc+4U43XUALMwxn1aZBg6Xnw4V9orc147XVilbUt/j8aedRBsrjCq+sJmCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:29.290266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1855","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d315763ce591243c745fc7aeee77a3b91ee5bac18fc36113cc03534a8207f5c7","sha256:970fe168d4abec95e0d1787ace9504f2cf6e9efd2b08be3264649befb0de25e7"],"state_sha256":"7ed7a384c598b5eb46883509c4f6c2a715bd53e94d53477fff884bafe82a2f1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DHQWWnyfeDqgrZjkL0qcWntwuJXH2FNM7kQg+IxJcULBrS8IyfyKVSOHdIS7HSzHtS4NpEwBr9ctGSCliOQFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:32:36.708804Z","bundle_sha256":"c15a72d6a7fa763268e04e9e7a088183e3ed69a4c84e855ec792d93112ddc9f8"}}