{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:ZEOIYARY6UMXXUWMOADSXBPGHI","short_pith_number":"pith:ZEOIYARY","schema_version":"1.0","canonical_sha256":"c91c8c0238f5197bd2cc70072b85e63a3ba98010f7c35e6c364208307f355ad8","source":{"kind":"arxiv","id":"1204.0454","version":2},"attestation_state":"computed","paper":{"title":"The space of bi-invariant orders on a nilpotent group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Dave Witte Morris","submitted_at":"2012-04-02T16:24:54Z","abstract_excerpt":"We prove a few basic facts about the space of bi-invariant (or left-invariant) total order relations on a torsion-free, nonabelian, nilpotent group G. For instance, we show that the space of bi-invariant orders has no isolated points (so it is a Cantor set if G is countable), and give examples to show that the outer automorphism group of G does not always act faithfully on this space. Also, it is not difficult to see that the abstract commensurator group of G has a natural action on the space of left-invariant orders, and we show that this action is faithful. These results are related to recen"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1204.0454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-04-02T16:24:54Z","cross_cats_sorted":[],"title_canon_sha256":"0747b745427f99e8072dc5cfa37cf28959c5cbe354166a3512ff787ae8857e36","abstract_canon_sha256":"e4ae23bbfe09db1624a73e13c857fb389fded93c0cddbcdd0468267ac48da03b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:52.689142Z","signature_b64":"HNy4CohXe4doMf1QYg/Llo4Nw8u4KQg9rlJQZCV28IuHe60saDtAsImyLLyaGVyyXJoYxT+jBrHDbCvG9jE2DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c91c8c0238f5197bd2cc70072b85e63a3ba98010f7c35e6c364208307f355ad8","last_reissued_at":"2026-05-18T03:57:52.688739Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:52.688739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The space of bi-invariant orders on a nilpotent group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Dave Witte Morris","submitted_at":"2012-04-02T16:24:54Z","abstract_excerpt":"We prove a few basic facts about the space of bi-invariant (or left-invariant) total order relations on a torsion-free, nonabelian, nilpotent group G. For instance, we show that the space of bi-invariant orders has no isolated points (so it is a Cantor set if G is countable), and give examples to show that the outer automorphism group of G does not always act faithfully on this space. Also, it is not difficult to see that the abstract commensurator group of G has a natural action on the space of left-invariant orders, and we show that this action is faithful. These results are related to recen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0454","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1204.0454","created_at":"2026-05-18T03:57:52.688799+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.0454v2","created_at":"2026-05-18T03:57:52.688799+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0454","created_at":"2026-05-18T03:57:52.688799+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZEOIYARY6UMX","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZEOIYARY6UMXXUWM","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZEOIYARY","created_at":"2026-05-18T12:27:30.460161+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZEOIYARY6UMXXUWMOADSXBPGHI","json":"https://pith.science/pith/ZEOIYARY6UMXXUWMOADSXBPGHI.json","graph_json":"https://pith.science/api/pith-number/ZEOIYARY6UMXXUWMOADSXBPGHI/graph.json","events_json":"https://pith.science/api/pith-number/ZEOIYARY6UMXXUWMOADSXBPGHI/events.json","paper":"https://pith.science/paper/ZEOIYARY"},"agent_actions":{"view_html":"https://pith.science/pith/ZEOIYARY6UMXXUWMOADSXBPGHI","download_json":"https://pith.science/pith/ZEOIYARY6UMXXUWMOADSXBPGHI.json","view_paper":"https://pith.science/paper/ZEOIYARY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.0454&json=true","fetch_graph":"https://pith.science/api/pith-number/ZEOIYARY6UMXXUWMOADSXBPGHI/graph.json","fetch_events":"https://pith.science/api/pith-number/ZEOIYARY6UMXXUWMOADSXBPGHI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZEOIYARY6UMXXUWMOADSXBPGHI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZEOIYARY6UMXXUWMOADSXBPGHI/action/storage_attestation","attest_author":"https://pith.science/pith/ZEOIYARY6UMXXUWMOADSXBPGHI/action/author_attestation","sign_citation":"https://pith.science/pith/ZEOIYARY6UMXXUWMOADSXBPGHI/action/citation_signature","submit_replication":"https://pith.science/pith/ZEOIYARY6UMXXUWMOADSXBPGHI/action/replication_record"}},"created_at":"2026-05-18T03:57:52.688799+00:00","updated_at":"2026-05-18T03:57:52.688799+00:00"}