{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3RDPQUI65HYXFOO7XSIG2PATJC","short_pith_number":"pith:3RDPQUI6","schema_version":"1.0","canonical_sha256":"dc46f8511ee9f172b9dfbc906d3c134897f8d7e21343585a28e8000616e72499","source":{"kind":"arxiv","id":"1211.5493","version":2},"attestation_state":"computed","paper":{"title":"A sum-product theorem in function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Thomas Bloom, Timothy G. F. Jones","submitted_at":"2012-11-23T13:07:29Z","abstract_excerpt":"Let $A$ be a finite subset of $\\ffield$, the field of Laurent series in $1/t$ over a finite field $\\mathbb{F}_q$. We show that for any $\\epsilon>0$ there exists a constant $C$ dependent only on $\\epsilon$ and $q$ such that $\\max\\{|A+A|,|AA|\\}\\geq C |A|^{6/5-\\epsilon}$. In particular such a result is obtained for the rational function field $\\mathbb{F}_q(t)$. Identical results are also obtained for finite subsets of the $p$-adic field $\\mathbb{Q}_p$ for any prime $p$."},"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":"1211.5493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-23T13:07:29Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a1e2535d0e4746c9968d1ca2df3dde381c41421caed77aef4749fac3e02e90af","abstract_canon_sha256":"fbce486c0addec99e908cd4b34a9c868ca9e1625a804abd4d1c720171d3c40c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:05.101607Z","signature_b64":"HPwlCyNxCLyveJLVKP3GXOt3NO/OeOOFw/ztgxDy1vGX4HT9jpciyd2vDY738B257mcQOgwAZBMM+GoghiGsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc46f8511ee9f172b9dfbc906d3c134897f8d7e21343585a28e8000616e72499","last_reissued_at":"2026-05-18T03:32:05.100961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:05.100961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sum-product theorem in function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Thomas Bloom, Timothy G. F. Jones","submitted_at":"2012-11-23T13:07:29Z","abstract_excerpt":"Let $A$ be a finite subset of $\\ffield$, the field of Laurent series in $1/t$ over a finite field $\\mathbb{F}_q$. We show that for any $\\epsilon>0$ there exists a constant $C$ dependent only on $\\epsilon$ and $q$ such that $\\max\\{|A+A|,|AA|\\}\\geq C |A|^{6/5-\\epsilon}$. In particular such a result is obtained for the rational function field $\\mathbb{F}_q(t)$. Identical results are also obtained for finite subsets of the $p$-adic field $\\mathbb{Q}_p$ for any prime $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5493","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":""},"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":"1211.5493","created_at":"2026-05-18T03:32:05.101087+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.5493v2","created_at":"2026-05-18T03:32:05.101087+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5493","created_at":"2026-05-18T03:32:05.101087+00:00"},{"alias_kind":"pith_short_12","alias_value":"3RDPQUI65HYX","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3RDPQUI65HYXFOO7","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3RDPQUI6","created_at":"2026-05-18T12:26:53.410803+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/3RDPQUI65HYXFOO7XSIG2PATJC","json":"https://pith.science/pith/3RDPQUI65HYXFOO7XSIG2PATJC.json","graph_json":"https://pith.science/api/pith-number/3RDPQUI65HYXFOO7XSIG2PATJC/graph.json","events_json":"https://pith.science/api/pith-number/3RDPQUI65HYXFOO7XSIG2PATJC/events.json","paper":"https://pith.science/paper/3RDPQUI6"},"agent_actions":{"view_html":"https://pith.science/pith/3RDPQUI65HYXFOO7XSIG2PATJC","download_json":"https://pith.science/pith/3RDPQUI65HYXFOO7XSIG2PATJC.json","view_paper":"https://pith.science/paper/3RDPQUI6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.5493&json=true","fetch_graph":"https://pith.science/api/pith-number/3RDPQUI65HYXFOO7XSIG2PATJC/graph.json","fetch_events":"https://pith.science/api/pith-number/3RDPQUI65HYXFOO7XSIG2PATJC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3RDPQUI65HYXFOO7XSIG2PATJC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3RDPQUI65HYXFOO7XSIG2PATJC/action/storage_attestation","attest_author":"https://pith.science/pith/3RDPQUI65HYXFOO7XSIG2PATJC/action/author_attestation","sign_citation":"https://pith.science/pith/3RDPQUI65HYXFOO7XSIG2PATJC/action/citation_signature","submit_replication":"https://pith.science/pith/3RDPQUI65HYXFOO7XSIG2PATJC/action/replication_record"}},"created_at":"2026-05-18T03:32:05.101087+00:00","updated_at":"2026-05-18T03:32:05.101087+00:00"}