{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WKPFMY6QATNHNRXEIEG7GB6UCF","short_pith_number":"pith:WKPFMY6Q","schema_version":"1.0","canonical_sha256":"b29e5663d004da76c6e4410df307d41165709ba85dfdacae7fa81c0bb4f35261","source":{"kind":"arxiv","id":"1609.03673","version":2},"attestation_state":"computed","paper":{"title":"Alexander polynomial obstruction of bi-orderability for rationally homologically fibered knot groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Tetsuya Ito","submitted_at":"2016-09-13T04:15:37Z","abstract_excerpt":"We show that if the fundamental group of the complement of a rationally homologically fibered knot in a rational homology 3-sphere is bi-orderable, then its Alexander polynomial has at least one positive real root. Our argument can be applied for a finitely generated group which is an HNN extension with certain properties."},"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":"1609.03673","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-13T04:15:37Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"769c466cd9ae10300d2e11566c62c5ed7d24421ae0b0f6b5aff3e8f8a109ccd9","abstract_canon_sha256":"4d4391d263d6fcac2479de3d6b5e65b3264dee45c0e3fb5b8a1a1d40255d34fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:51.667031Z","signature_b64":"erAL0KEWR2LG1+RHsWM//us1+k/GVkoUdq55wCBnLTWAZRHVmkXSNEUtB36qywVJpWqVONm4nExsChRRowhoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b29e5663d004da76c6e4410df307d41165709ba85dfdacae7fa81c0bb4f35261","last_reissued_at":"2026-05-18T00:46:51.666409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:51.666409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Alexander polynomial obstruction of bi-orderability for rationally homologically fibered knot groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GT","authors_text":"Tetsuya Ito","submitted_at":"2016-09-13T04:15:37Z","abstract_excerpt":"We show that if the fundamental group of the complement of a rationally homologically fibered knot in a rational homology 3-sphere is bi-orderable, then its Alexander polynomial has at least one positive real root. Our argument can be applied for a finitely generated group which is an HNN extension with certain properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03673","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":"1609.03673","created_at":"2026-05-18T00:46:51.666507+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.03673v2","created_at":"2026-05-18T00:46:51.666507+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03673","created_at":"2026-05-18T00:46:51.666507+00:00"},{"alias_kind":"pith_short_12","alias_value":"WKPFMY6QATNH","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"WKPFMY6QATNHNRXE","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"WKPFMY6Q","created_at":"2026-05-18T12:30:48.956258+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/WKPFMY6QATNHNRXEIEG7GB6UCF","json":"https://pith.science/pith/WKPFMY6QATNHNRXEIEG7GB6UCF.json","graph_json":"https://pith.science/api/pith-number/WKPFMY6QATNHNRXEIEG7GB6UCF/graph.json","events_json":"https://pith.science/api/pith-number/WKPFMY6QATNHNRXEIEG7GB6UCF/events.json","paper":"https://pith.science/paper/WKPFMY6Q"},"agent_actions":{"view_html":"https://pith.science/pith/WKPFMY6QATNHNRXEIEG7GB6UCF","download_json":"https://pith.science/pith/WKPFMY6QATNHNRXEIEG7GB6UCF.json","view_paper":"https://pith.science/paper/WKPFMY6Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.03673&json=true","fetch_graph":"https://pith.science/api/pith-number/WKPFMY6QATNHNRXEIEG7GB6UCF/graph.json","fetch_events":"https://pith.science/api/pith-number/WKPFMY6QATNHNRXEIEG7GB6UCF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WKPFMY6QATNHNRXEIEG7GB6UCF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WKPFMY6QATNHNRXEIEG7GB6UCF/action/storage_attestation","attest_author":"https://pith.science/pith/WKPFMY6QATNHNRXEIEG7GB6UCF/action/author_attestation","sign_citation":"https://pith.science/pith/WKPFMY6QATNHNRXEIEG7GB6UCF/action/citation_signature","submit_replication":"https://pith.science/pith/WKPFMY6QATNHNRXEIEG7GB6UCF/action/replication_record"}},"created_at":"2026-05-18T00:46:51.666507+00:00","updated_at":"2026-05-18T00:46:51.666507+00:00"}