{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:G6RRUBDLNC5NLOTHV2YFKOSDHY","short_pith_number":"pith:G6RRUBDL","schema_version":"1.0","canonical_sha256":"37a31a046b68bad5ba67aeb0553a433e2019a6cfde186ed11686023d1e2a623e","source":{"kind":"arxiv","id":"1807.11065","version":1},"attestation_state":"computed","paper":{"title":"On growth of the set $A(A+1)$ in arbitrary finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ali Mohammadi","submitted_at":"2018-07-29T14:53:51Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be a finite field of order $q$, where $q$ is a power of a prime. For a set $A \\subset \\mathbb{F}_q$, under certain structural restrictions, we prove a new explicit lower bound on the size of the product set $A(A + 1)$. Our result improves on the previous best known bound due to Zhelezov and holds under more relaxed restrictions."},"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":"1807.11065","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-07-29T14:53:51Z","cross_cats_sorted":[],"title_canon_sha256":"0370f8c1c6079cf544d3d9b73b79b73a6e5120316899b4e687c344656323f2ae","abstract_canon_sha256":"4a7bb778727ac8cee4e404c9f824f78a356d7864c6e0e964b82750fb412e20ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:33.047490Z","signature_b64":"RlIny6B3xCvDA37v3KIOW5tPmQBt3Pwy3bQZQ3XJ0Go8cUQ6s/nkevZKCTUB4+HQ1V/g9agQyXc0lFpJGcnmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37a31a046b68bad5ba67aeb0553a433e2019a6cfde186ed11686023d1e2a623e","last_reissued_at":"2026-05-18T00:09:33.046951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:33.046951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On growth of the set $A(A+1)$ in arbitrary finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ali Mohammadi","submitted_at":"2018-07-29T14:53:51Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be a finite field of order $q$, where $q$ is a power of a prime. For a set $A \\subset \\mathbb{F}_q$, under certain structural restrictions, we prove a new explicit lower bound on the size of the product set $A(A + 1)$. Our result improves on the previous best known bound due to Zhelezov and holds under more relaxed restrictions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11065","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":""},"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":"1807.11065","created_at":"2026-05-18T00:09:33.047024+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.11065v1","created_at":"2026-05-18T00:09:33.047024+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11065","created_at":"2026-05-18T00:09:33.047024+00:00"},{"alias_kind":"pith_short_12","alias_value":"G6RRUBDLNC5N","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"G6RRUBDLNC5NLOTH","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"G6RRUBDL","created_at":"2026-05-18T12:32:25.280505+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/G6RRUBDLNC5NLOTHV2YFKOSDHY","json":"https://pith.science/pith/G6RRUBDLNC5NLOTHV2YFKOSDHY.json","graph_json":"https://pith.science/api/pith-number/G6RRUBDLNC5NLOTHV2YFKOSDHY/graph.json","events_json":"https://pith.science/api/pith-number/G6RRUBDLNC5NLOTHV2YFKOSDHY/events.json","paper":"https://pith.science/paper/G6RRUBDL"},"agent_actions":{"view_html":"https://pith.science/pith/G6RRUBDLNC5NLOTHV2YFKOSDHY","download_json":"https://pith.science/pith/G6RRUBDLNC5NLOTHV2YFKOSDHY.json","view_paper":"https://pith.science/paper/G6RRUBDL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.11065&json=true","fetch_graph":"https://pith.science/api/pith-number/G6RRUBDLNC5NLOTHV2YFKOSDHY/graph.json","fetch_events":"https://pith.science/api/pith-number/G6RRUBDLNC5NLOTHV2YFKOSDHY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G6RRUBDLNC5NLOTHV2YFKOSDHY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G6RRUBDLNC5NLOTHV2YFKOSDHY/action/storage_attestation","attest_author":"https://pith.science/pith/G6RRUBDLNC5NLOTHV2YFKOSDHY/action/author_attestation","sign_citation":"https://pith.science/pith/G6RRUBDLNC5NLOTHV2YFKOSDHY/action/citation_signature","submit_replication":"https://pith.science/pith/G6RRUBDLNC5NLOTHV2YFKOSDHY/action/replication_record"}},"created_at":"2026-05-18T00:09:33.047024+00:00","updated_at":"2026-05-18T00:09:33.047024+00:00"}