{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:6SJMWG754NE2KQYEWPOWW6KO2L","short_pith_number":"pith:6SJMWG75","canonical_record":{"source":{"id":"0902.4709","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-02-26T21:40:07Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"db3058d029985063b104acf87d8ebd2fe7bc6c01381452d046890d95ebec4587","abstract_canon_sha256":"1083f718a2e50e536f9a781881dfbfd64d8c87c3d349c93fdaf481753ffad128"},"schema_version":"1.0"},"canonical_sha256":"f492cb1bfde349a54304b3dd6b794ed2dee1c8bf14d08cae0b61ed9a1c2b744f","source":{"kind":"arxiv","id":"0902.4709","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.4709","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"0902.4709v1","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.4709","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"6SJMWG754NE2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6SJMWG754NE2KQYE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6SJMWG75","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:6SJMWG754NE2KQYEWPOWW6KO2L","target":"record","payload":{"canonical_record":{"source":{"id":"0902.4709","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-02-26T21:40:07Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"db3058d029985063b104acf87d8ebd2fe7bc6c01381452d046890d95ebec4587","abstract_canon_sha256":"1083f718a2e50e536f9a781881dfbfd64d8c87c3d349c93fdaf481753ffad128"},"schema_version":"1.0"},"canonical_sha256":"f492cb1bfde349a54304b3dd6b794ed2dee1c8bf14d08cae0b61ed9a1c2b744f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:18.911361Z","signature_b64":"tbqr/MViuHP6b5SseWBvlC6c5M1ZfO2MrKjDQkKFTbvenEpyiKQogiax/U0CkAWSVZ52CSiULWJxa/EfAeR5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f492cb1bfde349a54304b3dd6b794ed2dee1c8bf14d08cae0b61ed9a1c2b744f","last_reissued_at":"2026-05-18T02:38:18.910710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:18.910710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.4709","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":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"usUlflEPMOA3qUHuA8uEpmUuiDnllvZSOtyuNEOB/1egqH0Nu9a+JgPX8TxzuzwNmjGc+SPQXkrbNYk+T8lxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:18:17.730425Z"},"content_sha256":"5aeeae233f106b96f7dfc3676cf881e7e02c8623c3d724805fb40294a50ef4f4","schema_version":"1.0","event_id":"sha256:5aeeae233f106b96f7dfc3676cf881e7e02c8623c3d724805fb40294a50ef4f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:6SJMWG754NE2KQYEWPOWW6KO2L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A finitely generated, locally indicable group with no faithful action by C^1 diffeomorphisms of the interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Andr\\'es Navas","submitted_at":"2009-02-26T21:40:07Z","abstract_excerpt":"According to Thurston's stability theorem, every group of C^1 diffeomorphisms of the closed interval is locally indicable (.e., every finitely generated subgroup factors through Z). We show that, even for finitely generated groups, the converse of this statement is not true. More precisely, we show that the semi-direct product between F_2 an Z^2, although locally indicable, does not embed into Diff_+^1 (]0,1[). (Here F_2 is any free subgroup of SL(2,Z), and its action on Z^2 is the projective one.) Moreover, we show that for every non-solvable subgroup G of SL(2,Z), the semi-direct product bet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4709","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":"2026-05-18T02:38:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l1NTco5uM591+UCWbpvTR3Fvgm/BwpTqrz0hox7vnrGjwQWQTUeeuMpFHyciXna3c/sezRTE9LsVwI/axNq4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:18:17.731334Z"},"content_sha256":"48926675d1053d92f7fe2eb849d2caf99bd21fc589469d7cb0dc0382cdfe47ec","schema_version":"1.0","event_id":"sha256:48926675d1053d92f7fe2eb849d2caf99bd21fc589469d7cb0dc0382cdfe47ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6SJMWG754NE2KQYEWPOWW6KO2L/bundle.json","state_url":"https://pith.science/pith/6SJMWG754NE2KQYEWPOWW6KO2L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6SJMWG754NE2KQYEWPOWW6KO2L/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":"2026-06-01T00:18:17Z","links":{"resolver":"https://pith.science/pith/6SJMWG754NE2KQYEWPOWW6KO2L","bundle":"https://pith.science/pith/6SJMWG754NE2KQYEWPOWW6KO2L/bundle.json","state":"https://pith.science/pith/6SJMWG754NE2KQYEWPOWW6KO2L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6SJMWG754NE2KQYEWPOWW6KO2L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6SJMWG754NE2KQYEWPOWW6KO2L","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":"1083f718a2e50e536f9a781881dfbfd64d8c87c3d349c93fdaf481753ffad128","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-02-26T21:40:07Z","title_canon_sha256":"db3058d029985063b104acf87d8ebd2fe7bc6c01381452d046890d95ebec4587"},"schema_version":"1.0","source":{"id":"0902.4709","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.4709","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"0902.4709v1","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.4709","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"6SJMWG754NE2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6SJMWG754NE2KQYE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6SJMWG75","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:48926675d1053d92f7fe2eb849d2caf99bd21fc589469d7cb0dc0382cdfe47ec","target":"graph","created_at":"2026-05-18T02:38:18Z","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":"According to Thurston's stability theorem, every group of C^1 diffeomorphisms of the closed interval is locally indicable (.e., every finitely generated subgroup factors through Z). We show that, even for finitely generated groups, the converse of this statement is not true. More precisely, we show that the semi-direct product between F_2 an Z^2, although locally indicable, does not embed into Diff_+^1 (]0,1[). (Here F_2 is any free subgroup of SL(2,Z), and its action on Z^2 is the projective one.) Moreover, we show that for every non-solvable subgroup G of SL(2,Z), the semi-direct product bet","authors_text":"Andr\\'es Navas","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-02-26T21:40:07Z","title":"A finitely generated, locally indicable group with no faithful action by C^1 diffeomorphisms of the interval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4709","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":"sha256:5aeeae233f106b96f7dfc3676cf881e7e02c8623c3d724805fb40294a50ef4f4","target":"record","created_at":"2026-05-18T02:38:18Z","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":"1083f718a2e50e536f9a781881dfbfd64d8c87c3d349c93fdaf481753ffad128","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-02-26T21:40:07Z","title_canon_sha256":"db3058d029985063b104acf87d8ebd2fe7bc6c01381452d046890d95ebec4587"},"schema_version":"1.0","source":{"id":"0902.4709","kind":"arxiv","version":1}},"canonical_sha256":"f492cb1bfde349a54304b3dd6b794ed2dee1c8bf14d08cae0b61ed9a1c2b744f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f492cb1bfde349a54304b3dd6b794ed2dee1c8bf14d08cae0b61ed9a1c2b744f","first_computed_at":"2026-05-18T02:38:18.910710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:18.910710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tbqr/MViuHP6b5SseWBvlC6c5M1ZfO2MrKjDQkKFTbvenEpyiKQogiax/U0CkAWSVZ52CSiULWJxa/EfAeR5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:18.911361Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.4709","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5aeeae233f106b96f7dfc3676cf881e7e02c8623c3d724805fb40294a50ef4f4","sha256:48926675d1053d92f7fe2eb849d2caf99bd21fc589469d7cb0dc0382cdfe47ec"],"state_sha256":"12dcaa8cd1c68abf46a29497624287422317dbd691479b83ce0fb9bca0595cda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eq5fjrtnwgdQGLnTrVQfg7/NJKaU2ECR+cITbarAcvVAI2u5veQZDubkgmy3MApTF053qKJFB8zcwo+XxxB/Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:18:17.735612Z","bundle_sha256":"44f8d9d4b4b75975e94c6a62e5ea29b89f3fabdf38f26478c3d71babd0262dcc"}}