{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VP4FOLE3BNRPQZIO7FPFQD5CG7","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":"8331b1b59da6fb35cb9504b9baf038625559c495f5842f799c99791b123ca4f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-09T07:59:32Z","title_canon_sha256":"46b4daeadc030c9fc8983b4dad67177756a5687c9cd4a0b8f1e0e4a8735180de"},"schema_version":"1.0","source":{"id":"1710.02980","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.02980","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1710.02980v5","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.02980","created_at":"2026-05-18T00:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"VP4FOLE3BNRP","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VP4FOLE3BNRPQZIO","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VP4FOLE3","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:1a3386a87a2ee799f494b20a350845f96f77318ef6bfd6dde01ef7f29af98450","target":"graph","created_at":"2026-05-18T00:19:03Z","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":"For every group $G$, we show that either $G$ has a topologically transitive action on the line $\\mathbb R$ by orientation-preserving homeomorphisms, or every orientation-preserving action of $G$ on $\\mathbb R$ has a wandering interval. According to this result, all groups are divided into two types: transitive type and wandering type, and the types of several groups are determined. We also show that every finitely generated orderable group of wandering type is indicable. As a corollary, we show that if a higher rank lattice $\\Gamma$ is orderable, then $\\Gamma$ is of transitive type.","authors_text":"Enhui Shi, Lizhen Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-09T07:59:32Z","title":"Topological transitivity and wandering intervals for group actions on the line $\\mathbb R$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.02980","kind":"arxiv","version":5},"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":"sha256:2a0b4afb7fcad7aa0d7c78986a522ae323ece6ce1a88dd6aa828673b99196f49","target":"record","created_at":"2026-05-18T00:19:03Z","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":"8331b1b59da6fb35cb9504b9baf038625559c495f5842f799c99791b123ca4f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-09T07:59:32Z","title_canon_sha256":"46b4daeadc030c9fc8983b4dad67177756a5687c9cd4a0b8f1e0e4a8735180de"},"schema_version":"1.0","source":{"id":"1710.02980","kind":"arxiv","version":5}},"canonical_sha256":"abf8572c9b0b62f8650ef95e580fa237cc99808e911d24b0797d842e24dfb4af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abf8572c9b0b62f8650ef95e580fa237cc99808e911d24b0797d842e24dfb4af","first_computed_at":"2026-05-18T00:19:03.356594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:03.356594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZEuRwkR+FPv9DiUaDW0oj+13qBE9H7EeJlKl7mxk1UINAnPKQkfcLPpyUlwf+OGBsGzBCC/Ve5KskQk1eTJtBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:03.357370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.02980","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a0b4afb7fcad7aa0d7c78986a522ae323ece6ce1a88dd6aa828673b99196f49","sha256:1a3386a87a2ee799f494b20a350845f96f77318ef6bfd6dde01ef7f29af98450"],"state_sha256":"5f9f337b083f5184551b13e8f6b995ff375d3a878a0ef3c3485bb011ae9c9526"}