{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3A53SVTIGYLC4UWLYHADCU3AJZ","short_pith_number":"pith:3A53SVTI","schema_version":"1.0","canonical_sha256":"d83bb9566836162e52cbc1c03153604e405416a1dc7ce6a2308a250ad7f01444","source":{"kind":"arxiv","id":"1301.0665","version":2},"attestation_state":"computed","paper":{"title":"On left-orderable fundamental groups and Dehn surgeries on twist knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Anh T. Tran","submitted_at":"2013-01-04T03:38:21Z","abstract_excerpt":"We show that the resulting manifold by $r$-surgery on the hyperbolic twist knot $K_m, \\, m \\ge 2$, has left-orderable fundamental group if the slope $r$ satisfies the condition $r \\in (-4,2m)$ if $m$ is even, and $r \\in [0,4] \\cup (\\frac{4m}{\\omega}+4, 2m+4)$ if $m$ is odd, where $\\omega>1$ is the unique real solution of the equation $x e^{x}=4m$."},"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":"1301.0665","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-04T03:38:21Z","cross_cats_sorted":[],"title_canon_sha256":"d7cc56e3878e730470b33f7872407ea4959aa2cc2efda66767f2bf889c79088b","abstract_canon_sha256":"cd3aadc0687c2fa05961a5bfc3e7e9e13d8e202cbbba2c947a1ac4ebde0607d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:06.309190Z","signature_b64":"CDmguSJxtoARxw/nKIycLY6pIGuOoTxCDWKpnuVJpL+ay3JkGLCHlqTExFZ7REUcE+gK9kb1AqCiutIWF0rXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d83bb9566836162e52cbc1c03153604e405416a1dc7ce6a2308a250ad7f01444","last_reissued_at":"2026-05-18T03:31:06.308615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:06.308615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On left-orderable fundamental groups and Dehn surgeries on twist knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Anh T. Tran","submitted_at":"2013-01-04T03:38:21Z","abstract_excerpt":"We show that the resulting manifold by $r$-surgery on the hyperbolic twist knot $K_m, \\, m \\ge 2$, has left-orderable fundamental group if the slope $r$ satisfies the condition $r \\in (-4,2m)$ if $m$ is even, and $r \\in [0,4] \\cup (\\frac{4m}{\\omega}+4, 2m+4)$ if $m$ is odd, where $\\omega>1$ is the unique real solution of the equation $x e^{x}=4m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0665","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":"1301.0665","created_at":"2026-05-18T03:31:06.308706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.0665v2","created_at":"2026-05-18T03:31:06.308706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0665","created_at":"2026-05-18T03:31:06.308706+00:00"},{"alias_kind":"pith_short_12","alias_value":"3A53SVTIGYLC","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3A53SVTIGYLC4UWL","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3A53SVTI","created_at":"2026-05-18T12:27:32.513160+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/3A53SVTIGYLC4UWLYHADCU3AJZ","json":"https://pith.science/pith/3A53SVTIGYLC4UWLYHADCU3AJZ.json","graph_json":"https://pith.science/api/pith-number/3A53SVTIGYLC4UWLYHADCU3AJZ/graph.json","events_json":"https://pith.science/api/pith-number/3A53SVTIGYLC4UWLYHADCU3AJZ/events.json","paper":"https://pith.science/paper/3A53SVTI"},"agent_actions":{"view_html":"https://pith.science/pith/3A53SVTIGYLC4UWLYHADCU3AJZ","download_json":"https://pith.science/pith/3A53SVTIGYLC4UWLYHADCU3AJZ.json","view_paper":"https://pith.science/paper/3A53SVTI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.0665&json=true","fetch_graph":"https://pith.science/api/pith-number/3A53SVTIGYLC4UWLYHADCU3AJZ/graph.json","fetch_events":"https://pith.science/api/pith-number/3A53SVTIGYLC4UWLYHADCU3AJZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3A53SVTIGYLC4UWLYHADCU3AJZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3A53SVTIGYLC4UWLYHADCU3AJZ/action/storage_attestation","attest_author":"https://pith.science/pith/3A53SVTIGYLC4UWLYHADCU3AJZ/action/author_attestation","sign_citation":"https://pith.science/pith/3A53SVTIGYLC4UWLYHADCU3AJZ/action/citation_signature","submit_replication":"https://pith.science/pith/3A53SVTIGYLC4UWLYHADCU3AJZ/action/replication_record"}},"created_at":"2026-05-18T03:31:06.308706+00:00","updated_at":"2026-05-18T03:31:06.308706+00:00"}