{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:R7K37WYFK3B4NS77NPXBCT2ET5","short_pith_number":"pith:R7K37WYF","schema_version":"1.0","canonical_sha256":"8fd5bfdb0556c3c6cbff6bee114f449f6b5a507bf0274ab2fbd90b282d4b4c72","source":{"kind":"arxiv","id":"2508.10484","version":2},"attestation_state":"computed","paper":{"title":"Counting w-coprime S-integers and S-integral ideals in positive characteristic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jia-Yan Yao, Si-Han Liu, Zhe-Cheng Liu","submitted_at":"2025-08-14T09:37:43Z","abstract_excerpt":"Let Fq be the finite field with q elements, and K an algebraic function field over with Fq as its field of constants. Let S be a finite nonempty set of prime divisors over K, and OS be the ring of integers of K attached to S. Let w greater than 1 be an integer. In this work we shall count w coprime S integers and S integral ideals, and our proofs are a combination of analytic methods and the Riemann Roch theorem and the Weil theorem for function fields in positive characteristic."},"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":"2508.10484","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-14T09:37:43Z","cross_cats_sorted":[],"title_canon_sha256":"7bc583b619b389ae85ee81daaed36cf0fe0c67f3653f6bb28f1cf3478a4db2d0","abstract_canon_sha256":"b70422fc4087922f8ce3d0957ad7246d0a011c841d7d6da1fcd608553eae908c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:14:21.622952Z","signature_b64":"olhwfHQmuCS4kgVRksD0ctgyI6ekS7WlXExsIzM+6445B4gXSNNnBpf3WpY/M9JI6Lx94whbiRueua8ouyLCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fd5bfdb0556c3c6cbff6bee114f449f6b5a507bf0274ab2fbd90b282d4b4c72","last_reissued_at":"2026-06-24T01:14:21.622404Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:14:21.622404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting w-coprime S-integers and S-integral ideals in positive characteristic","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jia-Yan Yao, Si-Han Liu, Zhe-Cheng Liu","submitted_at":"2025-08-14T09:37:43Z","abstract_excerpt":"Let Fq be the finite field with q elements, and K an algebraic function field over with Fq as its field of constants. Let S be a finite nonempty set of prime divisors over K, and OS be the ring of integers of K attached to S. Let w greater than 1 be an integer. In this work we shall count w coprime S integers and S integral ideals, and our proofs are a combination of analytic methods and the Riemann Roch theorem and the Weil theorem for function fields in positive characteristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.10484","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.10484/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":"2508.10484","created_at":"2026-06-24T01:14:21.622463+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.10484v2","created_at":"2026-06-24T01:14:21.622463+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.10484","created_at":"2026-06-24T01:14:21.622463+00:00"},{"alias_kind":"pith_short_12","alias_value":"R7K37WYFK3B4","created_at":"2026-06-24T01:14:21.622463+00:00"},{"alias_kind":"pith_short_16","alias_value":"R7K37WYFK3B4NS77","created_at":"2026-06-24T01:14:21.622463+00:00"},{"alias_kind":"pith_short_8","alias_value":"R7K37WYF","created_at":"2026-06-24T01:14:21.622463+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/R7K37WYFK3B4NS77NPXBCT2ET5","json":"https://pith.science/pith/R7K37WYFK3B4NS77NPXBCT2ET5.json","graph_json":"https://pith.science/api/pith-number/R7K37WYFK3B4NS77NPXBCT2ET5/graph.json","events_json":"https://pith.science/api/pith-number/R7K37WYFK3B4NS77NPXBCT2ET5/events.json","paper":"https://pith.science/paper/R7K37WYF"},"agent_actions":{"view_html":"https://pith.science/pith/R7K37WYFK3B4NS77NPXBCT2ET5","download_json":"https://pith.science/pith/R7K37WYFK3B4NS77NPXBCT2ET5.json","view_paper":"https://pith.science/paper/R7K37WYF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.10484&json=true","fetch_graph":"https://pith.science/api/pith-number/R7K37WYFK3B4NS77NPXBCT2ET5/graph.json","fetch_events":"https://pith.science/api/pith-number/R7K37WYFK3B4NS77NPXBCT2ET5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R7K37WYFK3B4NS77NPXBCT2ET5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R7K37WYFK3B4NS77NPXBCT2ET5/action/storage_attestation","attest_author":"https://pith.science/pith/R7K37WYFK3B4NS77NPXBCT2ET5/action/author_attestation","sign_citation":"https://pith.science/pith/R7K37WYFK3B4NS77NPXBCT2ET5/action/citation_signature","submit_replication":"https://pith.science/pith/R7K37WYFK3B4NS77NPXBCT2ET5/action/replication_record"}},"created_at":"2026-06-24T01:14:21.622463+00:00","updated_at":"2026-06-24T01:14:21.622463+00:00"}