{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6ILEUN5J5B7FVZ6XDYGVE74O4O","short_pith_number":"pith:6ILEUN5J","canonical_record":{"source":{"id":"1403.4870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-19T16:18:29Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"8bb584dd776c89ccdd85c823ce9810ee2a60af20d30f43340a86c0e22db76506","abstract_canon_sha256":"86841fc258afce43932b96f9693246973c1c23f49c1037bf34c3216940e54620"},"schema_version":"1.0"},"canonical_sha256":"f2164a37a9e87e5ae7d71e0d527f8ee38caaedcc74b868b6797bf2895e74ebc6","source":{"kind":"arxiv","id":"1403.4870","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4870","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4870v1","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4870","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"6ILEUN5J5B7F","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6ILEUN5J5B7FVZ6X","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6ILEUN5J","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6ILEUN5J5B7FVZ6XDYGVE74O4O","target":"record","payload":{"canonical_record":{"source":{"id":"1403.4870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-19T16:18:29Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"8bb584dd776c89ccdd85c823ce9810ee2a60af20d30f43340a86c0e22db76506","abstract_canon_sha256":"86841fc258afce43932b96f9693246973c1c23f49c1037bf34c3216940e54620"},"schema_version":"1.0"},"canonical_sha256":"f2164a37a9e87e5ae7d71e0d527f8ee38caaedcc74b868b6797bf2895e74ebc6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:04.279291Z","signature_b64":"cdAPqWcPa4AmIblkmrdhemtVbC8bmNmSXLc9bt0QqwG7LgyPTdAhKgg9OpN/k/jAD/AecI6YSFfg5MtQGBfZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2164a37a9e87e5ae7d71e0d527f8ee38caaedcc74b868b6797bf2895e74ebc6","last_reissued_at":"2026-05-18T02:56:04.278885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:04.278885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.4870","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":"2026-05-18T02:56:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fLKvsPtFcAaylZMx5A6/sNyWdgQ64SlJqx6RL6GXVk4vhlxAXlWjxt11DbBZLYH5LBv+TtKHtZn0uHdwJ8RiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:31:32.967466Z"},"content_sha256":"428268dfe345667ce101e030b4257dc587875b85c433e5c87c5ab917b6e11516","schema_version":"1.0","event_id":"sha256:428268dfe345667ce101e030b4257dc587875b85c433e5c87c5ab917b6e11516"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6ILEUN5J5B7FVZ6XDYGVE74O4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low Dimensional Topology and Ordering Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AT","authors_text":"Dale Rolfsen","submitted_at":"2014-03-19T16:18:29Z","abstract_excerpt":"This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and mappings between them. A final section explores currently ongoing research regarding spaces of homeomorphisms and their orderability properties. This is not meant to be a comprehensive survey, but rather just a taste of the rich relationship between topology and the theory of ordered groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4870","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":"2026-05-18T02:56:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s3iAHh+UGv8puER+XA846lfRPO2AB/7PvJE9XBam4i4is8qsMdUpQYkRsYVo4duAJd8NCAruC11B1pjT+YoYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:31:32.967838Z"},"content_sha256":"e0292e7fdd3957d798c50dae30c184f0de00fe497213d0f6d2f835b17fcb2ea2","schema_version":"1.0","event_id":"sha256:e0292e7fdd3957d798c50dae30c184f0de00fe497213d0f6d2f835b17fcb2ea2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ILEUN5J5B7FVZ6XDYGVE74O4O/bundle.json","state_url":"https://pith.science/pith/6ILEUN5J5B7FVZ6XDYGVE74O4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ILEUN5J5B7FVZ6XDYGVE74O4O/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":"2026-05-27T15:31:32Z","links":{"resolver":"https://pith.science/pith/6ILEUN5J5B7FVZ6XDYGVE74O4O","bundle":"https://pith.science/pith/6ILEUN5J5B7FVZ6XDYGVE74O4O/bundle.json","state":"https://pith.science/pith/6ILEUN5J5B7FVZ6XDYGVE74O4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ILEUN5J5B7FVZ6XDYGVE74O4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6ILEUN5J5B7FVZ6XDYGVE74O4O","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":"86841fc258afce43932b96f9693246973c1c23f49c1037bf34c3216940e54620","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-19T16:18:29Z","title_canon_sha256":"8bb584dd776c89ccdd85c823ce9810ee2a60af20d30f43340a86c0e22db76506"},"schema_version":"1.0","source":{"id":"1403.4870","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4870","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4870v1","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4870","created_at":"2026-05-18T02:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"6ILEUN5J5B7F","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6ILEUN5J5B7FVZ6X","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6ILEUN5J","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:e0292e7fdd3957d798c50dae30c184f0de00fe497213d0f6d2f835b17fcb2ea2","target":"graph","created_at":"2026-05-18T02:56:04Z","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":"This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and mappings between them. A final section explores currently ongoing research regarding spaces of homeomorphisms and their orderability properties. This is not meant to be a comprehensive survey, but rather just a taste of the rich relationship between topology and the theory of ordered groups.","authors_text":"Dale Rolfsen","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-19T16:18:29Z","title":"Low Dimensional Topology and Ordering Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4870","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":"sha256:428268dfe345667ce101e030b4257dc587875b85c433e5c87c5ab917b6e11516","target":"record","created_at":"2026-05-18T02:56:04Z","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":"86841fc258afce43932b96f9693246973c1c23f49c1037bf34c3216940e54620","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-03-19T16:18:29Z","title_canon_sha256":"8bb584dd776c89ccdd85c823ce9810ee2a60af20d30f43340a86c0e22db76506"},"schema_version":"1.0","source":{"id":"1403.4870","kind":"arxiv","version":1}},"canonical_sha256":"f2164a37a9e87e5ae7d71e0d527f8ee38caaedcc74b868b6797bf2895e74ebc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2164a37a9e87e5ae7d71e0d527f8ee38caaedcc74b868b6797bf2895e74ebc6","first_computed_at":"2026-05-18T02:56:04.278885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:04.278885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cdAPqWcPa4AmIblkmrdhemtVbC8bmNmSXLc9bt0QqwG7LgyPTdAhKgg9OpN/k/jAD/AecI6YSFfg5MtQGBfZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:04.279291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4870","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:428268dfe345667ce101e030b4257dc587875b85c433e5c87c5ab917b6e11516","sha256:e0292e7fdd3957d798c50dae30c184f0de00fe497213d0f6d2f835b17fcb2ea2"],"state_sha256":"6e0b9168977aa22b913ffcfa42f2b37ab6dc6ec933f1892e2c748430a85aaa71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D3AQgmcSaeYjGOqvxz+cGn1wSRQ8KT40ZRExfNRzijCEY2IIE9tsdjCGdrUKlH2aVwZ9RgXYL/xR4up4cCMvDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:31:32.973033Z","bundle_sha256":"d384609b59217eb576ad3afbe755aa7c53c3f86fe2a8c070c7149e6b1b516473"}}