{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7CAW3C7FF2FVXO42TLKAXNZHYZ","short_pith_number":"pith:7CAW3C7F","schema_version":"1.0","canonical_sha256":"f8816d8be52e8b5bbb9a9ad40bb727c645d13913a89cf9554db8d2b43614e39b","source":{"kind":"arxiv","id":"1703.03309","version":2},"attestation_state":"computed","paper":{"title":"Conditional expanding bounds for two-variable functions over arbitrary fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Hossein Nassajian Mojarrad, Thang Pham","submitted_at":"2017-03-09T15:52:06Z","abstract_excerpt":"In this short note, we use Rudnev's point-plane incidence bound to improve some results on conditional expanding bounds for two-variable functions over arbitrary fields due to Hegyv\\'ari and Hennecart."},"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":"1703.03309","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-09T15:52:06Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"6ce3a60332795d916c0938270334c79d48315ae88851f404059ea8201c269494","abstract_canon_sha256":"a25453516fe6ee95194b5d02d585f37dda52f1b7b49099bb39736c6564beb8c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:56.349177Z","signature_b64":"KhPl+KtSIl3mbZYUJ643clt5Mq9itZPLHKfaGuzEDtYswxUEnT51ZOyzEka2g4eGeQbIF/NXqPhk8G9CFxQrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8816d8be52e8b5bbb9a9ad40bb727c645d13913a89cf9554db8d2b43614e39b","last_reissued_at":"2026-05-18T00:47:56.348769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:56.348769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conditional expanding bounds for two-variable functions over arbitrary fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Hossein Nassajian Mojarrad, Thang Pham","submitted_at":"2017-03-09T15:52:06Z","abstract_excerpt":"In this short note, we use Rudnev's point-plane incidence bound to improve some results on conditional expanding bounds for two-variable functions over arbitrary fields due to Hegyv\\'ari and Hennecart."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03309","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":"1703.03309","created_at":"2026-05-18T00:47:56.348826+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.03309v2","created_at":"2026-05-18T00:47:56.348826+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.03309","created_at":"2026-05-18T00:47:56.348826+00:00"},{"alias_kind":"pith_short_12","alias_value":"7CAW3C7FF2FV","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"7CAW3C7FF2FVXO42","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"7CAW3C7F","created_at":"2026-05-18T12:31:03.183658+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/7CAW3C7FF2FVXO42TLKAXNZHYZ","json":"https://pith.science/pith/7CAW3C7FF2FVXO42TLKAXNZHYZ.json","graph_json":"https://pith.science/api/pith-number/7CAW3C7FF2FVXO42TLKAXNZHYZ/graph.json","events_json":"https://pith.science/api/pith-number/7CAW3C7FF2FVXO42TLKAXNZHYZ/events.json","paper":"https://pith.science/paper/7CAW3C7F"},"agent_actions":{"view_html":"https://pith.science/pith/7CAW3C7FF2FVXO42TLKAXNZHYZ","download_json":"https://pith.science/pith/7CAW3C7FF2FVXO42TLKAXNZHYZ.json","view_paper":"https://pith.science/paper/7CAW3C7F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.03309&json=true","fetch_graph":"https://pith.science/api/pith-number/7CAW3C7FF2FVXO42TLKAXNZHYZ/graph.json","fetch_events":"https://pith.science/api/pith-number/7CAW3C7FF2FVXO42TLKAXNZHYZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7CAW3C7FF2FVXO42TLKAXNZHYZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7CAW3C7FF2FVXO42TLKAXNZHYZ/action/storage_attestation","attest_author":"https://pith.science/pith/7CAW3C7FF2FVXO42TLKAXNZHYZ/action/author_attestation","sign_citation":"https://pith.science/pith/7CAW3C7FF2FVXO42TLKAXNZHYZ/action/citation_signature","submit_replication":"https://pith.science/pith/7CAW3C7FF2FVXO42TLKAXNZHYZ/action/replication_record"}},"created_at":"2026-05-18T00:47:56.348826+00:00","updated_at":"2026-05-18T00:47:56.348826+00:00"}