{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KWKIPX4AF5672WITZYM5QMATOI","short_pith_number":"pith:KWKIPX4A","schema_version":"1.0","canonical_sha256":"559487df802f7dfd5913ce19d8301372216ec2301336b36065621403950dc68c","source":{"kind":"arxiv","id":"2401.05853","version":4},"attestation_state":"computed","paper":{"title":"On the cyclotomic field $\\mathbb{Q}(e^{2\\pi {\\bf i}/p})$ and Zhi-Wei Sun's conjecture on $\\det M_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hai-Liang Wu, Li-Yuan Wang","submitted_at":"2024-01-11T11:55:17Z","abstract_excerpt":"In 2019, Zhi-Wei Sun posed an interesting conjecture on certain determinants with Legendre symbol entries. In this paper, by using the arithmetic properties of $p$-th cyclotomic field and the finite field $\\mathbb{F}_p$, we confirm this conjecture."},"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":"2401.05853","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2024-01-11T11:55:17Z","cross_cats_sorted":[],"title_canon_sha256":"a35320b6e5892b34efe57ea834d2d6c7d98db54f18bcc1469e5cc560555de52a","abstract_canon_sha256":"983a8a9102a12acaf09bc1f6181d54d1b17350eade7c0ddc28c58080fcba3761"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:21:57.054242Z","signature_b64":"DByG9GJjMKImGYR47L99voMrk8nxCHj0XR8HLcpCb2ymEY2KugUNAD/6b8fze16VSAmyt1e1+2Z4dZJI16fbDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"559487df802f7dfd5913ce19d8301372216ec2301336b36065621403950dc68c","last_reissued_at":"2026-07-05T10:21:57.053752Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:21:57.053752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the cyclotomic field $\\mathbb{Q}(e^{2\\pi {\\bf i}/p})$ and Zhi-Wei Sun's conjecture on $\\det M_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hai-Liang Wu, Li-Yuan Wang","submitted_at":"2024-01-11T11:55:17Z","abstract_excerpt":"In 2019, Zhi-Wei Sun posed an interesting conjecture on certain determinants with Legendre symbol entries. In this paper, by using the arithmetic properties of $p$-th cyclotomic field and the finite field $\\mathbb{F}_p$, we confirm this conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.05853","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.05853/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2401.05853","created_at":"2026-07-05T10:21:57.053807+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.05853v4","created_at":"2026-07-05T10:21:57.053807+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.05853","created_at":"2026-07-05T10:21:57.053807+00:00"},{"alias_kind":"pith_short_12","alias_value":"KWKIPX4AF567","created_at":"2026-07-05T10:21:57.053807+00:00"},{"alias_kind":"pith_short_16","alias_value":"KWKIPX4AF5672WIT","created_at":"2026-07-05T10:21:57.053807+00:00"},{"alias_kind":"pith_short_8","alias_value":"KWKIPX4A","created_at":"2026-07-05T10:21:57.053807+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.01695","citing_title":"A Pfaffian Proof and Generalization of a Conjecture of Sun Zhiwei","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KWKIPX4AF5672WITZYM5QMATOI","json":"https://pith.science/pith/KWKIPX4AF5672WITZYM5QMATOI.json","graph_json":"https://pith.science/api/pith-number/KWKIPX4AF5672WITZYM5QMATOI/graph.json","events_json":"https://pith.science/api/pith-number/KWKIPX4AF5672WITZYM5QMATOI/events.json","paper":"https://pith.science/paper/KWKIPX4A"},"agent_actions":{"view_html":"https://pith.science/pith/KWKIPX4AF5672WITZYM5QMATOI","download_json":"https://pith.science/pith/KWKIPX4AF5672WITZYM5QMATOI.json","view_paper":"https://pith.science/paper/KWKIPX4A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.05853&json=true","fetch_graph":"https://pith.science/api/pith-number/KWKIPX4AF5672WITZYM5QMATOI/graph.json","fetch_events":"https://pith.science/api/pith-number/KWKIPX4AF5672WITZYM5QMATOI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KWKIPX4AF5672WITZYM5QMATOI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KWKIPX4AF5672WITZYM5QMATOI/action/storage_attestation","attest_author":"https://pith.science/pith/KWKIPX4AF5672WITZYM5QMATOI/action/author_attestation","sign_citation":"https://pith.science/pith/KWKIPX4AF5672WITZYM5QMATOI/action/citation_signature","submit_replication":"https://pith.science/pith/KWKIPX4AF5672WITZYM5QMATOI/action/replication_record"}},"created_at":"2026-07-05T10:21:57.053807+00:00","updated_at":"2026-07-05T10:21:57.053807+00:00"}