{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:HIM2VHAP35L4T34N4CDT2DXRQC","short_pith_number":"pith:HIM2VHAP","schema_version":"1.0","canonical_sha256":"3a19aa9c0fdf57c9ef8de0873d0ef180a3b4e4727e5561f82f5da565a6438f94","source":{"kind":"arxiv","id":"2607.01165","version":1},"attestation_state":"computed","paper":{"title":"An absolute bound for generalized Diophantine tuples over polynomial rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chi Hoi Yip, Kin Ming Tsang","submitted_at":"2026-07-01T16:50:11Z","abstract_excerpt":"Let $\\mathbb F$ be an algebraically closed field of characteristic $0$. Let $k\\geq 2$ be an integer, and let $n\\in \\mathbb F[x]\\setminus\\{0\\}$. We study generalized Diophantine tuples $A\\subset \\mathbb F[x]$ with property $D_k(n)$, meaning that $ab+n$ is a $k$-th power in $\\mathbb F[x]$ for all distinct elements $a,b\\in A$. For $k\\ge18$, we prove that every such tuple satisfies $|A|\\le6$, except for the necessary exceptional family in which $n=s^2$ is a $k$-th power and $A\\subset s\\mathbb{F}$. This bound is absolute: it is independent of both $n$ and $\\operatorname{deg} n$. Our proof develops "},"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":"2607.01165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-01T16:50:11Z","cross_cats_sorted":[],"title_canon_sha256":"8f852df29b67c4a31a55f56981051b3ac74f50c4c103c1e52be40d16ea98273d","abstract_canon_sha256":"c1f6100387a5380a8070d3ccd31d6d5fce7ffabe51443840505d1fb35bf19e33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:18:30.960366Z","signature_b64":"YrbD9ynkegKRtXQ5wcME38S5IA21ixBwcYICt54AbyWL+UZL31GKi9dZzWo17R+nOCdHBoQc5R0gGSKys4k4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a19aa9c0fdf57c9ef8de0873d0ef180a3b4e4727e5561f82f5da565a6438f94","last_reissued_at":"2026-07-02T01:18:30.960008Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:18:30.960008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An absolute bound for generalized Diophantine tuples over polynomial rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chi Hoi Yip, Kin Ming Tsang","submitted_at":"2026-07-01T16:50:11Z","abstract_excerpt":"Let $\\mathbb F$ be an algebraically closed field of characteristic $0$. Let $k\\geq 2$ be an integer, and let $n\\in \\mathbb F[x]\\setminus\\{0\\}$. We study generalized Diophantine tuples $A\\subset \\mathbb F[x]$ with property $D_k(n)$, meaning that $ab+n$ is a $k$-th power in $\\mathbb F[x]$ for all distinct elements $a,b\\in A$. For $k\\ge18$, we prove that every such tuple satisfies $|A|\\le6$, except for the necessary exceptional family in which $n=s^2$ is a $k$-th power and $A\\subset s\\mathbb{F}$. This bound is absolute: it is independent of both $n$ and $\\operatorname{deg} n$. Our proof develops "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01165","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/2607.01165/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":"2607.01165","created_at":"2026-07-02T01:18:30.960071+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.01165v1","created_at":"2026-07-02T01:18:30.960071+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01165","created_at":"2026-07-02T01:18:30.960071+00:00"},{"alias_kind":"pith_short_12","alias_value":"HIM2VHAP35L4","created_at":"2026-07-02T01:18:30.960071+00:00"},{"alias_kind":"pith_short_16","alias_value":"HIM2VHAP35L4T34N","created_at":"2026-07-02T01:18:30.960071+00:00"},{"alias_kind":"pith_short_8","alias_value":"HIM2VHAP","created_at":"2026-07-02T01:18:30.960071+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/HIM2VHAP35L4T34N4CDT2DXRQC","json":"https://pith.science/pith/HIM2VHAP35L4T34N4CDT2DXRQC.json","graph_json":"https://pith.science/api/pith-number/HIM2VHAP35L4T34N4CDT2DXRQC/graph.json","events_json":"https://pith.science/api/pith-number/HIM2VHAP35L4T34N4CDT2DXRQC/events.json","paper":"https://pith.science/paper/HIM2VHAP"},"agent_actions":{"view_html":"https://pith.science/pith/HIM2VHAP35L4T34N4CDT2DXRQC","download_json":"https://pith.science/pith/HIM2VHAP35L4T34N4CDT2DXRQC.json","view_paper":"https://pith.science/paper/HIM2VHAP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.01165&json=true","fetch_graph":"https://pith.science/api/pith-number/HIM2VHAP35L4T34N4CDT2DXRQC/graph.json","fetch_events":"https://pith.science/api/pith-number/HIM2VHAP35L4T34N4CDT2DXRQC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HIM2VHAP35L4T34N4CDT2DXRQC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HIM2VHAP35L4T34N4CDT2DXRQC/action/storage_attestation","attest_author":"https://pith.science/pith/HIM2VHAP35L4T34N4CDT2DXRQC/action/author_attestation","sign_citation":"https://pith.science/pith/HIM2VHAP35L4T34N4CDT2DXRQC/action/citation_signature","submit_replication":"https://pith.science/pith/HIM2VHAP35L4T34N4CDT2DXRQC/action/replication_record"}},"created_at":"2026-07-02T01:18:30.960071+00:00","updated_at":"2026-07-02T01:18:30.960071+00:00"}