{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:B6SJF44IO4WOXWYNTNKNDTWBP6","short_pith_number":"pith:B6SJF44I","canonical_record":{"source":{"id":"0802.2707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-02-19T20:42:11Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"1f1ba5adf3d7f08956d286efa0da47069fb340a37aaa3c723ee53a9779e22062","abstract_canon_sha256":"c607575e568f4f8edfea8fdae7ba7ed26a8e679db453c4c425220f48dad51734"},"schema_version":"1.0"},"canonical_sha256":"0fa492f388772cebdb0d9b54d1cec17fa28061e7f6ed6d1b9ee938e35b0e83e3","source":{"kind":"arxiv","id":"0802.2707","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.2707","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0802.2707v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.2707","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"B6SJF44IO4WO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"B6SJF44IO4WOXWYN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"B6SJF44I","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:B6SJF44IO4WOXWYNTNKNDTWBP6","target":"record","payload":{"canonical_record":{"source":{"id":"0802.2707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-02-19T20:42:11Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"1f1ba5adf3d7f08956d286efa0da47069fb340a37aaa3c723ee53a9779e22062","abstract_canon_sha256":"c607575e568f4f8edfea8fdae7ba7ed26a8e679db453c4c425220f48dad51734"},"schema_version":"1.0"},"canonical_sha256":"0fa492f388772cebdb0d9b54d1cec17fa28061e7f6ed6d1b9ee938e35b0e83e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:51.765963Z","signature_b64":"hX+97MjMbptOmq/Ys/GVAcEi30kCM16xtsaRszMRiCyA2T8ZkJlfbsue5io5RxUPO0EL1tRbOYdHWij+bRevAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fa492f388772cebdb0d9b54d1cec17fa28061e7f6ed6d1b9ee938e35b0e83e3","last_reissued_at":"2026-05-18T02:41:51.765397Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:51.765397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0802.2707","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":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SwMGeY0tRZg4ZD4ormpr6U7NkVhvaVMuXtocJzvTIlD2wF5LxPala0G2wtO4v2jQGYNj8hkUDOnydrPCn7dgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:35:03.106888Z"},"content_sha256":"fb8a832d5c0c23960d78edb7f4aaf156a149612b29b91ae195f6d1304ab51443","schema_version":"1.0","event_id":"sha256:fb8a832d5c0c23960d78edb7f4aaf156a149612b29b91ae195f6d1304ab51443"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:B6SJF44IO4WOXWYNTNKNDTWBP6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonsmoothable, locally indicable group actions on the interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.DS","authors_text":"Danny Calegari","submitted_at":"2008-02-19T20:42:11Z","abstract_excerpt":"By the Thurston stability theorem, a group of C^1 orientation-preserving diffeomorphisms of the closed unit interval is locally indicable. We show that the local order structure of orbits gives a stronger criterion for nonsmoothability that can be used to produce new examples of locally indicable groups of homeomorphisms of the interval that are not conjugate to groups of C^1 diffeomorphisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.2707","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":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkKwpqWUXI3O8F62dmYI9a1RkW32DPSjdAq7IKECcvMVjzhiM+cZMckUNzX/5XkekhCBXulgor0BwfSuMO7BBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:35:03.107549Z"},"content_sha256":"33d2a841f4387f9f579aaad033c356c52baded670363a859d49836866e0219e6","schema_version":"1.0","event_id":"sha256:33d2a841f4387f9f579aaad033c356c52baded670363a859d49836866e0219e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6SJF44IO4WOXWYNTNKNDTWBP6/bundle.json","state_url":"https://pith.science/pith/B6SJF44IO4WOXWYNTNKNDTWBP6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6SJF44IO4WOXWYNTNKNDTWBP6/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":"2026-05-27T05:35:03Z","links":{"resolver":"https://pith.science/pith/B6SJF44IO4WOXWYNTNKNDTWBP6","bundle":"https://pith.science/pith/B6SJF44IO4WOXWYNTNKNDTWBP6/bundle.json","state":"https://pith.science/pith/B6SJF44IO4WOXWYNTNKNDTWBP6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6SJF44IO4WOXWYNTNKNDTWBP6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:B6SJF44IO4WOXWYNTNKNDTWBP6","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":"c607575e568f4f8edfea8fdae7ba7ed26a8e679db453c4c425220f48dad51734","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-02-19T20:42:11Z","title_canon_sha256":"1f1ba5adf3d7f08956d286efa0da47069fb340a37aaa3c723ee53a9779e22062"},"schema_version":"1.0","source":{"id":"0802.2707","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.2707","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0802.2707v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.2707","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"B6SJF44IO4WO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"B6SJF44IO4WOXWYN","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"B6SJF44I","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:33d2a841f4387f9f579aaad033c356c52baded670363a859d49836866e0219e6","target":"graph","created_at":"2026-05-18T02:41:51Z","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":"By the Thurston stability theorem, a group of C^1 orientation-preserving diffeomorphisms of the closed unit interval is locally indicable. We show that the local order structure of orbits gives a stronger criterion for nonsmoothability that can be used to produce new examples of locally indicable groups of homeomorphisms of the interval that are not conjugate to groups of C^1 diffeomorphisms.","authors_text":"Danny Calegari","cross_cats":["math.GR","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-02-19T20:42:11Z","title":"Nonsmoothable, locally indicable group actions on the interval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.2707","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:fb8a832d5c0c23960d78edb7f4aaf156a149612b29b91ae195f6d1304ab51443","target":"record","created_at":"2026-05-18T02:41:51Z","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":"c607575e568f4f8edfea8fdae7ba7ed26a8e679db453c4c425220f48dad51734","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-02-19T20:42:11Z","title_canon_sha256":"1f1ba5adf3d7f08956d286efa0da47069fb340a37aaa3c723ee53a9779e22062"},"schema_version":"1.0","source":{"id":"0802.2707","kind":"arxiv","version":1}},"canonical_sha256":"0fa492f388772cebdb0d9b54d1cec17fa28061e7f6ed6d1b9ee938e35b0e83e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fa492f388772cebdb0d9b54d1cec17fa28061e7f6ed6d1b9ee938e35b0e83e3","first_computed_at":"2026-05-18T02:41:51.765397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:51.765397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hX+97MjMbptOmq/Ys/GVAcEi30kCM16xtsaRszMRiCyA2T8ZkJlfbsue5io5RxUPO0EL1tRbOYdHWij+bRevAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:51.765963Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.2707","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb8a832d5c0c23960d78edb7f4aaf156a149612b29b91ae195f6d1304ab51443","sha256:33d2a841f4387f9f579aaad033c356c52baded670363a859d49836866e0219e6"],"state_sha256":"ba0c6111952eacf20379a0325b3d840aca95faa746e11a70f2dbf643e0a56e52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o4YzfdXi/hRdsTiZCK1APaqLcWPFZYZp11l2vquRwuvDHLh8y1LWWyXhS2eS401CzopeL7+aRPwBZXG81mPhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:35:03.110732Z","bundle_sha256":"744cf3faef5c8c4ca52647c1f2cf12215031b65e611faeadfd6ba9c3e25e7367"}}