{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:RK6OUOGDPVYVTSTTUD3U2HV7HD","short_pith_number":"pith:RK6OUOGD","schema_version":"1.0","canonical_sha256":"8abcea38c37d7159ca73a0f74d1ebf38c3cb17f5b691cff5945574a3bda086ff","source":{"kind":"arxiv","id":"1212.6305","version":1},"attestation_state":"computed","paper":{"title":"Left-orderable fundamental group and Dehn surgery on twist knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Masakazu Teragaito, Ryoto Hakamata","submitted_at":"2012-12-27T05:29:07Z","abstract_excerpt":"For any hyperbolic twist knot in the 3-sphere, we show that the resulting manifold by $r$-surgery on the knot has left-orderable fundamental group if the slope $r$ satisfies the inequality $0\\le r \\le 4$."},"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":"1212.6305","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-12-27T05:29:07Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"8cb6d6e22007c04e7a7fddfffa18c70bb60f3efe2bf261ce201fafd584294be1","abstract_canon_sha256":"8bddaa86c5f982f09429b142769e351f7546aaa71038e655c4e29b723b5d778c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:40.246121Z","signature_b64":"uYjWqm3GCi3RZbg58hGfuiKhFcAU5aNb+k6mZRf/NxbbB8T5V0IF8SHEv79qaFXrHrOEUkRCvHnSa7iQhsbXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8abcea38c37d7159ca73a0f74d1ebf38c3cb17f5b691cff5945574a3bda086ff","last_reissued_at":"2026-05-18T03:37:40.245331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:40.245331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Left-orderable fundamental group and Dehn surgery on twist knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Masakazu Teragaito, Ryoto Hakamata","submitted_at":"2012-12-27T05:29:07Z","abstract_excerpt":"For any hyperbolic twist knot in the 3-sphere, we show that the resulting manifold by $r$-surgery on the knot has left-orderable fundamental group if the slope $r$ satisfies the inequality $0\\le r \\le 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6305","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.6305","created_at":"2026-05-18T03:37:40.245422+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.6305v1","created_at":"2026-05-18T03:37:40.245422+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6305","created_at":"2026-05-18T03:37:40.245422+00:00"},{"alias_kind":"pith_short_12","alias_value":"RK6OUOGDPVYV","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"RK6OUOGDPVYVTSTT","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"RK6OUOGD","created_at":"2026-05-18T12:27:20.899486+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/RK6OUOGDPVYVTSTTUD3U2HV7HD","json":"https://pith.science/pith/RK6OUOGDPVYVTSTTUD3U2HV7HD.json","graph_json":"https://pith.science/api/pith-number/RK6OUOGDPVYVTSTTUD3U2HV7HD/graph.json","events_json":"https://pith.science/api/pith-number/RK6OUOGDPVYVTSTTUD3U2HV7HD/events.json","paper":"https://pith.science/paper/RK6OUOGD"},"agent_actions":{"view_html":"https://pith.science/pith/RK6OUOGDPVYVTSTTUD3U2HV7HD","download_json":"https://pith.science/pith/RK6OUOGDPVYVTSTTUD3U2HV7HD.json","view_paper":"https://pith.science/paper/RK6OUOGD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.6305&json=true","fetch_graph":"https://pith.science/api/pith-number/RK6OUOGDPVYVTSTTUD3U2HV7HD/graph.json","fetch_events":"https://pith.science/api/pith-number/RK6OUOGDPVYVTSTTUD3U2HV7HD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RK6OUOGDPVYVTSTTUD3U2HV7HD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RK6OUOGDPVYVTSTTUD3U2HV7HD/action/storage_attestation","attest_author":"https://pith.science/pith/RK6OUOGDPVYVTSTTUD3U2HV7HD/action/author_attestation","sign_citation":"https://pith.science/pith/RK6OUOGDPVYVTSTTUD3U2HV7HD/action/citation_signature","submit_replication":"https://pith.science/pith/RK6OUOGDPVYVTSTTUD3U2HV7HD/action/replication_record"}},"created_at":"2026-05-18T03:37:40.245422+00:00","updated_at":"2026-05-18T03:37:40.245422+00:00"}