{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KM2K4MXCY2SS6CRMCDSLM6DTFZ","short_pith_number":"pith:KM2K4MXC","canonical_record":{"source":{"id":"1107.0545","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-07-04T07:10:13Z","cross_cats_sorted":[],"title_canon_sha256":"cbfcf45c12dc2b1ac6e2c1014af29bf0e6522c0d5d0d424156096c1f2f99bc75","abstract_canon_sha256":"13c6b9ee1199adab28b7a507f7a7bbb6979c35edb5fd21fa5121ede786aa3f84"},"schema_version":"1.0"},"canonical_sha256":"5334ae32e2c6a52f0a2c10e4b678732e583a922e8fa63eb1e6261f115d448e0a","source":{"kind":"arxiv","id":"1107.0545","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0545","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0545v3","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0545","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"KM2K4MXCY2SS","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KM2K4MXCY2SS6CRM","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KM2K4MXC","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KM2K4MXCY2SS6CRMCDSLM6DTFZ","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0545","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-07-04T07:10:13Z","cross_cats_sorted":[],"title_canon_sha256":"cbfcf45c12dc2b1ac6e2c1014af29bf0e6522c0d5d0d424156096c1f2f99bc75","abstract_canon_sha256":"13c6b9ee1199adab28b7a507f7a7bbb6979c35edb5fd21fa5121ede786aa3f84"},"schema_version":"1.0"},"canonical_sha256":"5334ae32e2c6a52f0a2c10e4b678732e583a922e8fa63eb1e6261f115d448e0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:12.137070Z","signature_b64":"LvHWS/+feThKYxVoUKb8rMhqkVk8+Uau3152LZAlEB2IOLPllnSfMzCPgA83mfuUeCbCtExODyXzQAgH6uGZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5334ae32e2c6a52f0a2c10e4b678732e583a922e8fa63eb1e6261f115d448e0a","last_reissued_at":"2026-05-18T03:33:12.136200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:12.136200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0545","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:33:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T8GaKy1+PJEvsCfZIzT7j21GxKmMJFShlDOu1m823cyyJ/ixlIAkLKWW2IABYGDiD3Em0j0WapNEvhmdxn1sBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:55:37.083592Z"},"content_sha256":"60fc2a3458ec9e2966d2689bf09e5eac474c6a20aaf366491e19fe8039d4885c","schema_version":"1.0","event_id":"sha256:60fc2a3458ec9e2966d2689bf09e5eac474c6a20aaf366491e19fe8039d4885c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KM2K4MXCY2SS6CRMCDSLM6DTFZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of isolated left orderings via partially central cyclic amalgamation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Tetsuya Ito","submitted_at":"2011-07-04T07:10:13Z","abstract_excerpt":"We give a new method to construct isolated left orderings of groups whose positive cones are finitely generated. Our construction uses an amalgamated free product of two groups having an isolated ordering. We construct a lot of new examples of isolated orderings, and give an example of isolated left orderings having various properties which previously known isolated orderings do not have."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0545","kind":"arxiv","version":3},"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":"2026-05-18T03:33:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6fXd9HijBeh/ViRMr+ap69hopzK94Bib4HN5hC6TGykU2m72cm4Dd9b2jmxp/4+FR1IGFYZEdeYsb7yv7bDcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:55:37.083940Z"},"content_sha256":"2e5eb0969e7ce62dc0d5eb8e1a94fc6667c85dc9c1e76ad64bb0b487c01c941f","schema_version":"1.0","event_id":"sha256:2e5eb0969e7ce62dc0d5eb8e1a94fc6667c85dc9c1e76ad64bb0b487c01c941f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KM2K4MXCY2SS6CRMCDSLM6DTFZ/bundle.json","state_url":"https://pith.science/pith/KM2K4MXCY2SS6CRMCDSLM6DTFZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KM2K4MXCY2SS6CRMCDSLM6DTFZ/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":"2026-06-23T02:55:37Z","links":{"resolver":"https://pith.science/pith/KM2K4MXCY2SS6CRMCDSLM6DTFZ","bundle":"https://pith.science/pith/KM2K4MXCY2SS6CRMCDSLM6DTFZ/bundle.json","state":"https://pith.science/pith/KM2K4MXCY2SS6CRMCDSLM6DTFZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KM2K4MXCY2SS6CRMCDSLM6DTFZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KM2K4MXCY2SS6CRMCDSLM6DTFZ","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":"13c6b9ee1199adab28b7a507f7a7bbb6979c35edb5fd21fa5121ede786aa3f84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-07-04T07:10:13Z","title_canon_sha256":"cbfcf45c12dc2b1ac6e2c1014af29bf0e6522c0d5d0d424156096c1f2f99bc75"},"schema_version":"1.0","source":{"id":"1107.0545","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0545","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0545v3","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0545","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"KM2K4MXCY2SS","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KM2K4MXCY2SS6CRM","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KM2K4MXC","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:2e5eb0969e7ce62dc0d5eb8e1a94fc6667c85dc9c1e76ad64bb0b487c01c941f","target":"graph","created_at":"2026-05-18T03:33:12Z","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 give a new method to construct isolated left orderings of groups whose positive cones are finitely generated. Our construction uses an amalgamated free product of two groups having an isolated ordering. We construct a lot of new examples of isolated orderings, and give an example of isolated left orderings having various properties which previously known isolated orderings do not have.","authors_text":"Tetsuya Ito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-07-04T07:10:13Z","title":"Construction of isolated left orderings via partially central cyclic amalgamation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0545","kind":"arxiv","version":3},"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":"sha256:60fc2a3458ec9e2966d2689bf09e5eac474c6a20aaf366491e19fe8039d4885c","target":"record","created_at":"2026-05-18T03:33:12Z","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":"13c6b9ee1199adab28b7a507f7a7bbb6979c35edb5fd21fa5121ede786aa3f84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-07-04T07:10:13Z","title_canon_sha256":"cbfcf45c12dc2b1ac6e2c1014af29bf0e6522c0d5d0d424156096c1f2f99bc75"},"schema_version":"1.0","source":{"id":"1107.0545","kind":"arxiv","version":3}},"canonical_sha256":"5334ae32e2c6a52f0a2c10e4b678732e583a922e8fa63eb1e6261f115d448e0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5334ae32e2c6a52f0a2c10e4b678732e583a922e8fa63eb1e6261f115d448e0a","first_computed_at":"2026-05-18T03:33:12.136200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:12.136200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LvHWS/+feThKYxVoUKb8rMhqkVk8+Uau3152LZAlEB2IOLPllnSfMzCPgA83mfuUeCbCtExODyXzQAgH6uGZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:12.137070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0545","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60fc2a3458ec9e2966d2689bf09e5eac474c6a20aaf366491e19fe8039d4885c","sha256:2e5eb0969e7ce62dc0d5eb8e1a94fc6667c85dc9c1e76ad64bb0b487c01c941f"],"state_sha256":"f8dd12f1379c6904b437bf48f578b6d77a8135a0b81f0fb507a495954419e5d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wMInWKBCBI1qPbUxDFrqznDwBt+eVZqPoQkRM+XGBLLc4eVWP8SktGfQS/O7ad/OlDH+y8K7SJXDLO7Vtzl/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:55:37.086217Z","bundle_sha256":"14ef3804ff54b64fdaffb352336562cf53c1012a2cc16395208727e81f0b56fb"}}