{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JNFM5RPTXYX5MKE3JU7B2NFJ7Q","short_pith_number":"pith:JNFM5RPT","canonical_record":{"source":{"id":"1712.00066","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-30T20:31:11Z","cross_cats_sorted":["math.DS","math.RT"],"title_canon_sha256":"66625576c3c7da5393b5556f5b9e5c412e7fb04719b699bcfe360d757f34101c","abstract_canon_sha256":"472c8a6c8e29f8dd50567381defe61523cb642dc1745e4015db3d1d4ed4b1e19"},"schema_version":"1.0"},"canonical_sha256":"4b4acec5f3be2fd6289b4d3e1d34a9fc2afeaa6d799654a975b14f2ceffd17ea","source":{"kind":"arxiv","id":"1712.00066","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00066","created_at":"2026-05-17T23:58:05Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00066v2","created_at":"2026-05-17T23:58:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00066","created_at":"2026-05-17T23:58:05Z"},{"alias_kind":"pith_short_12","alias_value":"JNFM5RPTXYX5","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JNFM5RPTXYX5MKE3","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JNFM5RPT","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JNFM5RPTXYX5MKE3JU7B2NFJ7Q","target":"record","payload":{"canonical_record":{"source":{"id":"1712.00066","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-30T20:31:11Z","cross_cats_sorted":["math.DS","math.RT"],"title_canon_sha256":"66625576c3c7da5393b5556f5b9e5c412e7fb04719b699bcfe360d757f34101c","abstract_canon_sha256":"472c8a6c8e29f8dd50567381defe61523cb642dc1745e4015db3d1d4ed4b1e19"},"schema_version":"1.0"},"canonical_sha256":"4b4acec5f3be2fd6289b4d3e1d34a9fc2afeaa6d799654a975b14f2ceffd17ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:05.296994Z","signature_b64":"93u4677BosA0S4SzIy17Oh4VZXWY8HP1DvBkKuSHonRtFTmRGKhK2zg3I1FwkVUfeNat9tk20822epfYk0+rCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b4acec5f3be2fd6289b4d3e1d34a9fc2afeaa6d799654a975b14f2ceffd17ea","last_reissued_at":"2026-05-17T23:58:05.296546Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:05.296546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.00066","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wUqBttUKGPqjH8IcKq8izW+fK29L5k6DD4CUk4Xzg8IGUcNrIhqeWLmHFjEbA7uMNLb4XyboUAWn07LfxFDHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T00:57:29.877589Z"},"content_sha256":"f49a77edfe0e7e2524ac86eb261e3283dfe71c3631a7b60c2e7ec2e5ee13e586","schema_version":"1.0","event_id":"sha256:f49a77edfe0e7e2524ac86eb261e3283dfe71c3631a7b60c2e7ec2e5ee13e586"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JNFM5RPTXYX5MKE3JU7B2NFJ7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spaces of orders of some one-relator groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.RT"],"primary_cat":"math.GR","authors_text":"Joaquin Brum, Juan Alonso","submitted_at":"2017-11-30T20:31:11Z","abstract_excerpt":"We show that certain orderable groups admit no isolated left orders. The groups we consider are cyclic amalgamations of a free group with a general orderable group, the HNN extensions of free groups over cyclic subgroups, and a particular class of one-relator groups. In order to prove the results about orders, we develop perturbation techniques for actions of these groups on the line."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00066","kind":"arxiv","version":2},"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":"2026-05-17T23:58:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DYdHOWYMuz7pA1K2wPc4bd0DMpY+x7P6CGFJNVIclMPTe9LhTA9CVX3Eqcakf3+/oX20l6iW7t6O6wvGD6LECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T00:57:29.877937Z"},"content_sha256":"87b39ce58d0b4550a2008e5da408360de7d5a1258808973c5a388f7196c2d950","schema_version":"1.0","event_id":"sha256:87b39ce58d0b4550a2008e5da408360de7d5a1258808973c5a388f7196c2d950"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JNFM5RPTXYX5MKE3JU7B2NFJ7Q/bundle.json","state_url":"https://pith.science/pith/JNFM5RPTXYX5MKE3JU7B2NFJ7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JNFM5RPTXYX5MKE3JU7B2NFJ7Q/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":"2026-06-21T00:57:29Z","links":{"resolver":"https://pith.science/pith/JNFM5RPTXYX5MKE3JU7B2NFJ7Q","bundle":"https://pith.science/pith/JNFM5RPTXYX5MKE3JU7B2NFJ7Q/bundle.json","state":"https://pith.science/pith/JNFM5RPTXYX5MKE3JU7B2NFJ7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JNFM5RPTXYX5MKE3JU7B2NFJ7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JNFM5RPTXYX5MKE3JU7B2NFJ7Q","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":"472c8a6c8e29f8dd50567381defe61523cb642dc1745e4015db3d1d4ed4b1e19","cross_cats_sorted":["math.DS","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-30T20:31:11Z","title_canon_sha256":"66625576c3c7da5393b5556f5b9e5c412e7fb04719b699bcfe360d757f34101c"},"schema_version":"1.0","source":{"id":"1712.00066","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.00066","created_at":"2026-05-17T23:58:05Z"},{"alias_kind":"arxiv_version","alias_value":"1712.00066v2","created_at":"2026-05-17T23:58:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00066","created_at":"2026-05-17T23:58:05Z"},{"alias_kind":"pith_short_12","alias_value":"JNFM5RPTXYX5","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JNFM5RPTXYX5MKE3","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JNFM5RPT","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:87b39ce58d0b4550a2008e5da408360de7d5a1258808973c5a388f7196c2d950","target":"graph","created_at":"2026-05-17T23:58:05Z","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":"We show that certain orderable groups admit no isolated left orders. The groups we consider are cyclic amalgamations of a free group with a general orderable group, the HNN extensions of free groups over cyclic subgroups, and a particular class of one-relator groups. In order to prove the results about orders, we develop perturbation techniques for actions of these groups on the line.","authors_text":"Joaquin Brum, Juan Alonso","cross_cats":["math.DS","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-30T20:31:11Z","title":"Spaces of orders of some one-relator groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00066","kind":"arxiv","version":2},"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:f49a77edfe0e7e2524ac86eb261e3283dfe71c3631a7b60c2e7ec2e5ee13e586","target":"record","created_at":"2026-05-17T23:58:05Z","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":"472c8a6c8e29f8dd50567381defe61523cb642dc1745e4015db3d1d4ed4b1e19","cross_cats_sorted":["math.DS","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-11-30T20:31:11Z","title_canon_sha256":"66625576c3c7da5393b5556f5b9e5c412e7fb04719b699bcfe360d757f34101c"},"schema_version":"1.0","source":{"id":"1712.00066","kind":"arxiv","version":2}},"canonical_sha256":"4b4acec5f3be2fd6289b4d3e1d34a9fc2afeaa6d799654a975b14f2ceffd17ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b4acec5f3be2fd6289b4d3e1d34a9fc2afeaa6d799654a975b14f2ceffd17ea","first_computed_at":"2026-05-17T23:58:05.296546Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:05.296546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"93u4677BosA0S4SzIy17Oh4VZXWY8HP1DvBkKuSHonRtFTmRGKhK2zg3I1FwkVUfeNat9tk20822epfYk0+rCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:05.296994Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.00066","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f49a77edfe0e7e2524ac86eb261e3283dfe71c3631a7b60c2e7ec2e5ee13e586","sha256:87b39ce58d0b4550a2008e5da408360de7d5a1258808973c5a388f7196c2d950"],"state_sha256":"9a8c3d68661cc0a89a65bb9119bfc1e3d05699772e2de7b0160a16dd422cb644"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWIsycO8kW0FaVr8kVDjvPiLkuSTMYVYyBJ6umwhgpePoxttqQQHGITzm34UtNWvUXlfo6Bf+UBy99sXCVlsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T00:57:29.879979Z","bundle_sha256":"9f7ab78c24a99de2f5e59ecb75f71525d5beb446a68311506a8f45ceb8c0be5c"}}