{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QVAEVSMWFH6HR4DN3RF6C3PJO4","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":"8628b0edc2def8cb1f9faa6fd048fa6d8358aca43cc39e807a4932828a850a5f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-09T07:32:43Z","title_canon_sha256":"54d7997054426e106d07012581bba97e32794dfba7312354122c9f864c5fbb96"},"schema_version":"1.0","source":{"id":"1702.02731","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02731","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02731v2","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02731","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"pith_short_12","alias_value":"QVAEVSMWFH6H","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QVAEVSMWFH6HR4DN","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QVAEVSMW","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:a327b7515d092ae6be561eb27edf644f188fa68a30598455e7571eaa17c3a214","target":"graph","created_at":"2026-05-17T23:48:12Z","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 prove that every lens space contains a genus one homologically fibered knot, which is contrast to the fact that some lens spaces contain no genus one fibered knot. In the proof, the Chebotarev density theorem and binary quadratic forms in number theory play a key role. We also discuss the Alexander polynomial of homologically fibered knots.","authors_text":"Yuta Nozaki","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-09T07:32:43Z","title":"Every lens space contains a genus one homologically fibered knot"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02731","kind":"arxiv","version":2},"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":"sha256:3939a9fc2cfe678dfafbb165d8180345e2e9b134179fccbc6b8985a802043280","target":"record","created_at":"2026-05-17T23:48:12Z","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":"8628b0edc2def8cb1f9faa6fd048fa6d8358aca43cc39e807a4932828a850a5f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-02-09T07:32:43Z","title_canon_sha256":"54d7997054426e106d07012581bba97e32794dfba7312354122c9f864c5fbb96"},"schema_version":"1.0","source":{"id":"1702.02731","kind":"arxiv","version":2}},"canonical_sha256":"85404ac99629fc78f06ddc4be16de9773e9e19c29dab91184bf45220a32b37ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85404ac99629fc78f06ddc4be16de9773e9e19c29dab91184bf45220a32b37ca","first_computed_at":"2026-05-17T23:48:12.107066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:12.107066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"19pKkc0gKiQskbtlEQSpVCejAjryroq49Ql0zPuDNLVoi6Fm53PhPI0YX069diRk8BMsIXFpjxk04vzq3PoACw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:12.107730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02731","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3939a9fc2cfe678dfafbb165d8180345e2e9b134179fccbc6b8985a802043280","sha256:a327b7515d092ae6be561eb27edf644f188fa68a30598455e7571eaa17c3a214"],"state_sha256":"94ba7a513cd58c3ebe3d3b9aaf17d5733dd848907a7b5290d55a67d8df7b9d32"}