{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:BWKFHY4WKCQYYPB4YMH75PEF2E","short_pith_number":"pith:BWKFHY4W","schema_version":"1.0","canonical_sha256":"0d9453e39650a18c3c3cc30ffebc85d1051c999a1b761ac7e611f936f4406e7b","source":{"kind":"arxiv","id":"2505.23274","version":1},"attestation_state":"computed","paper":{"title":"Pure Gaps at Many Places and Multi-point AG Codes from Arbitrary Kummer Extensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chang-An Zhao, Huachao Zhang","submitted_at":"2025-05-29T09:23:07Z","abstract_excerpt":"For a Kummer extension defined by the affine equation $y^{m}=\\prod_{i=1}^{r} (x-\\a_i)^{\\lambda_i}$ over\n  an algebraic extension $K$ of a finite field $\\fq$, where $\\la_i\\in \\Z\\backslash\\{0\\}$ for $1\\leq i\\leq r$, $\\gcd(m,q) = 1$, and $\\a_1,\\cdots,\\a_r\\in K$ are pairwise distinct elements,\n  we propose a simple and efficient method to find all pure gaps at many totally ramified places.\n  We introduce a bottom set of pure gaps and indicate that the set of pure gaps is completely determined by the bottom set.\n  Furthermore, we demonstrate that a pure gap can be deduced from a known pure gap by e"},"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":"2505.23274","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2025-05-29T09:23:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a268fbf43e140191009c0fec634a9b34ee9077263faf3886bf2cb7b5475705d4","abstract_canon_sha256":"57fe6f0444981b22afe3e6a4d56da751d4f3b40dd591448a2df075fc21f064af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:58.717661Z","signature_b64":"e2379to8aJqT+0twFhYgOHAW/2SepJ9dGNZaLtp4SRGlqrzPwLKxdhD32rZusVWMMXGHAzLi71J6ptqjf6CUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d9453e39650a18c3c3cc30ffebc85d1051c999a1b761ac7e611f936f4406e7b","last_reissued_at":"2026-07-05T11:11:58.717158Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:58.717158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pure Gaps at Many Places and Multi-point AG Codes from Arbitrary Kummer Extensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chang-An Zhao, Huachao Zhang","submitted_at":"2025-05-29T09:23:07Z","abstract_excerpt":"For a Kummer extension defined by the affine equation $y^{m}=\\prod_{i=1}^{r} (x-\\a_i)^{\\lambda_i}$ over\n  an algebraic extension $K$ of a finite field $\\fq$, where $\\la_i\\in \\Z\\backslash\\{0\\}$ for $1\\leq i\\leq r$, $\\gcd(m,q) = 1$, and $\\a_1,\\cdots,\\a_r\\in K$ are pairwise distinct elements,\n  we propose a simple and efficient method to find all pure gaps at many totally ramified places.\n  We introduce a bottom set of pure gaps and indicate that the set of pure gaps is completely determined by the bottom set.\n  Furthermore, we demonstrate that a pure gap can be deduced from a known pure gap by e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23274","kind":"arxiv","version":1},"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/2505.23274/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":"2505.23274","created_at":"2026-07-05T11:11:58.717212+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.23274v1","created_at":"2026-07-05T11:11:58.717212+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23274","created_at":"2026-07-05T11:11:58.717212+00:00"},{"alias_kind":"pith_short_12","alias_value":"BWKFHY4WKCQY","created_at":"2026-07-05T11:11:58.717212+00:00"},{"alias_kind":"pith_short_16","alias_value":"BWKFHY4WKCQYYPB4","created_at":"2026-07-05T11:11:58.717212+00:00"},{"alias_kind":"pith_short_8","alias_value":"BWKFHY4W","created_at":"2026-07-05T11:11:58.717212+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/BWKFHY4WKCQYYPB4YMH75PEF2E","json":"https://pith.science/pith/BWKFHY4WKCQYYPB4YMH75PEF2E.json","graph_json":"https://pith.science/api/pith-number/BWKFHY4WKCQYYPB4YMH75PEF2E/graph.json","events_json":"https://pith.science/api/pith-number/BWKFHY4WKCQYYPB4YMH75PEF2E/events.json","paper":"https://pith.science/paper/BWKFHY4W"},"agent_actions":{"view_html":"https://pith.science/pith/BWKFHY4WKCQYYPB4YMH75PEF2E","download_json":"https://pith.science/pith/BWKFHY4WKCQYYPB4YMH75PEF2E.json","view_paper":"https://pith.science/paper/BWKFHY4W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.23274&json=true","fetch_graph":"https://pith.science/api/pith-number/BWKFHY4WKCQYYPB4YMH75PEF2E/graph.json","fetch_events":"https://pith.science/api/pith-number/BWKFHY4WKCQYYPB4YMH75PEF2E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BWKFHY4WKCQYYPB4YMH75PEF2E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BWKFHY4WKCQYYPB4YMH75PEF2E/action/storage_attestation","attest_author":"https://pith.science/pith/BWKFHY4WKCQYYPB4YMH75PEF2E/action/author_attestation","sign_citation":"https://pith.science/pith/BWKFHY4WKCQYYPB4YMH75PEF2E/action/citation_signature","submit_replication":"https://pith.science/pith/BWKFHY4WKCQYYPB4YMH75PEF2E/action/replication_record"}},"created_at":"2026-07-05T11:11:58.717212+00:00","updated_at":"2026-07-05T11:11:58.717212+00:00"}