{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:QKDZHZV2F67L35DPDAYYGOWAES","short_pith_number":"pith:QKDZHZV2","schema_version":"1.0","canonical_sha256":"828793e6ba2fbebdf46f1831833ac02495d0ff943dccefb3e848e2eefcc9dcf8","source":{"kind":"arxiv","id":"2510.17612","version":3},"attestation_state":"computed","paper":{"title":"On a Conjecture of Erd\\H{o}s over Function Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Likun Xie","submitted_at":"2025-10-20T14:59:01Z","abstract_excerpt":"Using Katz's equidistribution framework, we show that for any squarefree polynomial $f \\in \\mathbb{F}_q[t]$ of degree $n \\ge 2$, every residue class modulo $f$ can be represented as a product of two monic irreducible polynomials of degree at most $n$, provided $q$ is sufficiently large in terms of $n$. This gives the function-field analogue of a conjecture of Erd\\H{o}s in the large-$q$ regime.\n  Sawin previously proved this representation with stronger square-root cancellation via a higher-dimensional sheaf-theoretic construction. This note presents a one-dimensional argument that yields a nat"},"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":"2510.17612","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-10-20T14:59:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e3629e72539e50d881c1bf21bdeb1e65be7777dfa1fa9c2035b47decfde247d4","abstract_canon_sha256":"ea3a4fd91eb567620241a7de05c83d2de9fb3aefd219c478ed6e4d5c4a2d77a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T02:19:41.518060Z","signature_b64":"YqesZ5ruLA3xgMxv6OT9jNba9Oxeq39HN9QIXPlpNTFY94RBkwiH8nS6D6wPJjk4AtiYwo2f5tV5UxU1t0AoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"828793e6ba2fbebdf46f1831833ac02495d0ff943dccefb3e848e2eefcc9dcf8","last_reissued_at":"2026-07-07T02:19:41.516984Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T02:19:41.516984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a Conjecture of Erd\\H{o}s over Function Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Likun Xie","submitted_at":"2025-10-20T14:59:01Z","abstract_excerpt":"Using Katz's equidistribution framework, we show that for any squarefree polynomial $f \\in \\mathbb{F}_q[t]$ of degree $n \\ge 2$, every residue class modulo $f$ can be represented as a product of two monic irreducible polynomials of degree at most $n$, provided $q$ is sufficiently large in terms of $n$. This gives the function-field analogue of a conjecture of Erd\\H{o}s in the large-$q$ regime.\n  Sawin previously proved this representation with stronger square-root cancellation via a higher-dimensional sheaf-theoretic construction. This note presents a one-dimensional argument that yields a nat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.17612","kind":"arxiv","version":3},"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/2510.17612/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":"2510.17612","created_at":"2026-07-07T02:19:41.517117+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.17612v3","created_at":"2026-07-07T02:19:41.517117+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.17612","created_at":"2026-07-07T02:19:41.517117+00:00"},{"alias_kind":"pith_short_12","alias_value":"QKDZHZV2F67L","created_at":"2026-07-07T02:19:41.517117+00:00"},{"alias_kind":"pith_short_16","alias_value":"QKDZHZV2F67L35DP","created_at":"2026-07-07T02:19:41.517117+00:00"},{"alias_kind":"pith_short_8","alias_value":"QKDZHZV2","created_at":"2026-07-07T02:19:41.517117+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.30567","citing_title":"Products of prime ideals in ray class groups","ref_index":27,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QKDZHZV2F67L35DPDAYYGOWAES","json":"https://pith.science/pith/QKDZHZV2F67L35DPDAYYGOWAES.json","graph_json":"https://pith.science/api/pith-number/QKDZHZV2F67L35DPDAYYGOWAES/graph.json","events_json":"https://pith.science/api/pith-number/QKDZHZV2F67L35DPDAYYGOWAES/events.json","paper":"https://pith.science/paper/QKDZHZV2"},"agent_actions":{"view_html":"https://pith.science/pith/QKDZHZV2F67L35DPDAYYGOWAES","download_json":"https://pith.science/pith/QKDZHZV2F67L35DPDAYYGOWAES.json","view_paper":"https://pith.science/paper/QKDZHZV2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.17612&json=true","fetch_graph":"https://pith.science/api/pith-number/QKDZHZV2F67L35DPDAYYGOWAES/graph.json","fetch_events":"https://pith.science/api/pith-number/QKDZHZV2F67L35DPDAYYGOWAES/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QKDZHZV2F67L35DPDAYYGOWAES/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QKDZHZV2F67L35DPDAYYGOWAES/action/storage_attestation","attest_author":"https://pith.science/pith/QKDZHZV2F67L35DPDAYYGOWAES/action/author_attestation","sign_citation":"https://pith.science/pith/QKDZHZV2F67L35DPDAYYGOWAES/action/citation_signature","submit_replication":"https://pith.science/pith/QKDZHZV2F67L35DPDAYYGOWAES/action/replication_record"}},"created_at":"2026-07-07T02:19:41.517117+00:00","updated_at":"2026-07-07T02:19:41.517117+00:00"}